The Standard Model prediction for the anomalous magnetic moment of the muon, presented in the 2025 White Paper of the Muon g-2 Theory Initiative, is based on consolidated lattice averages for the two leading hadronic contributions, hadronic vacuum polarization and hadronic light-by-light. In this talk, I review the results from lattice QCD+QED calculations that were used in these averages and...
For twenty years, a persistent discrepancy between experimental
measurements and theoretical calculations of the muon anomalous magnetic
moment have provided tantalising hints of new physics. In recent years,
improvements to the experimental precision have appeared to make the
tension stronger and stronger. However, at the same time, our lattice calculation overturned the theoretical...
In recent years, lattice QCD calculations of hadron spectroscopy have concentrated on resonances and shallow bound states detected via poles in two- and three-hadron scattering amplitudes. Hadron interactions have therefore become a key focus. The primary tools for this are finite-volume spectroscopy and finite-volume quantization conditions. I will review the current state of the art and...
Grounding nuclear physics in the Standard Model has been a longstanding goal for many in the lattice QCD community. The combined issues of signal-to-noise and difficulties associated with quantifying multi-hadronic interactions have required enormous efforts and improvements in computational techniques and analysis over the course of decades. Now, we have reached a time when computational and...
We introduce a novel quantum computational framework for simulating lattice gauge theories by leveraging the advantages of both discrete (qubit) and continuous variables (qumode) quantum computing. The simulations of these hybrid systems can be realized with various quantum hardware platforms like trapped-ion and photonic systems.
By explicitly solving Gauss’s Law at each vertex of the...
We compute the next-to-leading order (NLO) hadronic vacuum polarisation (HVP) contribution to the muon anomalous magnetic moment, $a_\mu^{\mathrm{hvp}}[\mathrm{NLO}]$ in lattice QCD. The kernel functions required for the three NLO diagrams are considered in the time-momentum representation (TMR), following the methodology of Balzani, Laporta, and Passera. For higher-order (HO) corrections...
The properties of QCD with massless quarks, particularly the chiral phase transition, have important implications for our understanding of QCD at the physical point. Once the number of massless fermions exceeds a critical value, $N_f^*$, QCD enters the conformal window and becomes chirally symmetric already in the vacuum. Determining $N_f^*$ has long been a challenge in lattice QCD, as...
We present the most precise determination to date of the ground-state masses of the triply charmed baryons with both parities, obtained by continuum extrapolation from two complementary lattice setups and thus fully addressing the systematic uncertainties. The calculations are performed on six $N_f=2+1+1$ HISQ ensembles generated by the MILC collaboration. In the valence sector we use HISQ...
We focus on the fact that the Hamiltonian of the $1+1$D staggered fermion system can be smoothly deformed into that of Wilson fermions. We reinterpret the structure of the axial charge operator proposed by A. Chatterjee, S. D. Pace, and S.-H. Shao using Wilson fermions.
We show that the eigenstates of the axial charge operator can be interpreted as fermion states with a well-defined...
The numerical sign problem remains one of the central challenges in first-principles simulations. The Worldvolume Hybrid Monte Carlo (WV-HMC) has recently emerged as a reliable and computationally efficient algorithm, and, crucially, avoids the ergodicity issues inherent in Lefschetz-thimble approaches. In this talk, after outlining the key ideas behind WV-HMC, I will present its extension to...
We study the profile of the flux tube in non-Abelian gauge theories in the confined phase, by means of precise lattice numerical simulations. We observe a non-Gaussian profile with prominent exponentially decaying tails. From the characteristic decay length length, we extract the intrinsic width of the flux tube. We compute this scale at different values of the temperature in the confined...
The symmetric mass generation (SMG) approach to the construction of lattice
chiral gauge theories attempts to use interactions to render mirror fermions
massive without symmetry breaking, to obtain the desired chiral massless
spectrum. If the zeros that often replace the mirror poles of fermion
two-point functions in an SMG phase are “kinematical” singularities, general...
A quantitative analysis of the universal aspects of QCD phase transition is required to achieve good control of the continuum as well as, infinite volume and chiral limits. In this talk, we will present a careful analysis of the latter two limits, taken at fixed values of lattice cut-off in the framework of (2+1)-flavor QCD. Although this does not yet allow to determine the universality class...
We apply the Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] to the two-dimensional doped Hubbard model, a system structurally similar to finite-density QCD. This model is known to suffer from a severe sign problem at low temperatures and away from half filling (doped), which renders traditional Determinantal Quantum Monte Carlo (DQMC) approaches ineffective. We demonstrate...
We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, $a_\mu$, on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size $144^3 \times 288$ sites. Within the low-mode averaging...
The masses of the lowest charmonium states are determined on a set of over 50 coordinated lattice simulations (CLS) gauge ensembles with $N_f=2+1$ sea quark flavours of non-perturbatively improved Wilson fermions. The inverse lattice spacing is varied from about 2 GeV up to more than 5 GeV, whereas various combinations of pion and kaon masses cover the quark mass plane, with the pion mass...
We propose a way to formulate a realistic chiral gauge theory like the standard model on a lattice (or a general simplicial complex in curved spacetime), so that it has the correct continuum limit, with the correct symmetries and (co)homological properties, and no unwanted doublers or anomalies. Building on recent progress by Catterall and collaborators, our approach uses restricted...
We study the mass spectra of heavy hadrons containing one or more bottom quarks, along with their hyperfine splittings and mass differences, using MILC's Nf = 2+1+1 HISQ gauge ensembles at three lattice spacings. To simulate the valence quark flavors, we employ a combination of lattice actions adapted to their masses: the NRQCD action is used for bottom quarks, the anisotropic Clover action is...
Phase boundary in the lower left corner of Columbia plot has been studied extensively. We have been tackling this problem using Möbius domain wall fermions of JLQCD type. With an extended analysis as well as the increased statistic around the physical $ud$ quark mass for the three degenerate quarks, we will make conclusion for the $N_t=12$ lattice. With that and glancing the results so far...
I present the current status of the RBC/UKQCD HVP program and will give an outlook on the remaining steps for matching the Fermilab E989 experimental precision.
I revisit the proposal that colour confinement in non-Abelian gauge theories is related to the dynamics of Abelian magnetic monopoles using methods derived from Topological Data Analysis, which provide a mathematically rigorous characterisation of topological properties of fields defined on a lattice. After introducing homology, I shall discuss how this concept can be used to quantitatively...
The orbifold lattice formulation provides a framework for quantum simulation of lattice gauge theories, enabling the explicit and analytical construction of quantum circuits whose computational cost scales polynomially with the number of qubits. This cost can be further reduced by neglecting selected terms and degrees of freedom in the original formulation, leading to two simplified versions....
This talk will be a follow up of Latham Boyle’s talk on discretizing a chiral gauge theory on the lattice. Building up on the natural geometrical discretization of Kahler-Dirac fermions with different polyforms fields (and the tetrad and spin-connection one forms), we will further see how this geometrical picture also suggests a novel formulation of Einstein gravity on the lattice. We will...
Unnormalized probability distributions are fundamental in modelling complex physical systems, especially in lattice field theory. Traditionally, Markov Chain Monte Carlo (MCMC) methods used to study these systems often exhibit slow convergence, critical slowing down, and poor mixing, resulting in highly correlated samples. Machine learning–based sampling approaches, such as normalising flows...
We investigate the mixing between S-wave flavor-singlet light meson and charmonium operators in two $N_f = 3 + 1$ ensembles at different pion masses ($m_{\pi} \approx 420, 800$ MeV). By solving a GEVP we find both types of operators have non-zero overlaps with all states we look at. We also compare the resulting spectrum with the one coming from separate GEVPs including either only light meson...
We present a qubit-based approach for simulating Quantum Electrodynamics (QED), extending the well-established quantum algorithm for scalar field theory to gauge fields. Our method ensures gauge invariance, which automatically enforces Gauss’s law, and is formulated in the lattice framework akin to Wilson or Kogut-Susskind theory. The qubit representation is designed to align with finite Weyl...
In the recent muon g-2 white paper update, the hadronic vacuum polarization (HVP) contribution⸺which dominates the theoretical uncertainty⸺is evaluated as an average of different lattice QCD calculations. Since lattice simulations are mostly carried out in isospin symmetric QCD, corrections due to the mass difference of the up and down quarks and the coupling to photons have to be accounted...
We report recent results on the finite-temperature chiral phase transition in (2+1)-flavor QCD with physical quark masses, using the Möbius domain wall fermion (MDWF) action to preserve chiral symmetry to a high precision. Our simulations cover a temperature range from 140 to 250 MeV for two lattice spacings, corresponding to temporal extents of $N_t = 12$ and $16$, with aspect ratios...
In recent years, flow-based samplers have emerged as a promising alternative to traditional sampling methods in lattice gauge theory. In this talk, we will introduce a class of flow-based samplers known as Stochastic Normalizing Flows (SNFs), which combine neural networks with non-equilibrium Monte Carlo algorithms. We will show that SNFs exhibit excellent scaling with the volume in lattice...
I will summarize various lattice investigations of charmed and charmonium tetraquarks using CLS lattice QCD ensembles that we have performed in the past one year.
Lattice simulations based on importance sampling suffer from the infamous sign problem when applied to certain physical systems of interest, such as QCD at finite baryon density or real-time quantum field theories. A possible way out is provided by the complex Langevin approach, which is based on a stochastic evolution of complexified degrees of freedom in an auxiliary time direction. However,...
We present updated results for the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment. The calculations are based on ETMC's $N_f = 2+1+1$ Wilson-clover twisted-mass ensembles at the physical point. We perform continuum extrapolations for the strange- and charm-quark connected contributions, and report on our results for the light-quark connected and light-light...
The type IIB matrix model has been proposed as a non-perturbative formulation of string theory. Its partition function is divergent due to the non-compactness of the Lorentz group. This has led to a new definition of the type IIB matrix model with the Lorentz symmetry fixed by the Faddeev-Popov procedure in a non-perturbative manner. We study this model using the complex Langevin method, and...
The existence of an approximate spectrum-generating algebra in the PXP model has been extensively studied as a mechanism underlying quantum many-body scars. Since the PXP model can be mapped to a gauge theory in one spatial dimension, a natural question arises: can similar algebraic structures and scar-like dynamics occur in higher-dimensional gauge theories? In this work, we show that this is...
In this work, we investigate the possible existence of a strange partner of the $T_{cc}$ tetraquark with flavor content $cc\bar{u}\bar{s}$ using lattice QCD. We determine the coupled-channel $DD_s^* - D^*D_s$ scattering amplitudes in the axialvector ($J^P = 1^+$) channel, as well as the elastic $DD_s$ scattering amplitude in the scalar ($J^P = 0^+$) channel. The calculations are performed on...
Abstract:
We present a multilevel generative sampler for lattice field theories that combines local upsampling with normalizing flows (NFs). At each level, new sites are first sampled independently from Gaussian mixture models and then refined with NFs to introduce correlations, while the coarse sites remain embedded in the finer lattice. Our results show that hierarchical generative sampling...
Precise determination of the strong coupling, $\alpha_s$, at the electroweak scale $m_Z$ is crucial for high-energy phenomenology and precision QCD tests. We apply the continuous $\beta$-function method to four-flavor lattice QCD with highly improved staggered quarks. This approach defines the coupling via gradient flow and allows direct determination of the $\beta$-function in the infinite...
Computations at imaginary values of chemical potential is one of the most popular ways to tackle the sign problem in lattice simulations.
For this reason, it is important to study different ways to perform the analytic continuation to the real axis.
In the context of the Bielefeld-Parma collaboration, we have been generating data which fed our multi-point Padé analysis of the QCD phase...
The doubly charmed tetraquark $T_{cc}(3875)^+$ observed at LHCb has attracted considerable interest in recent years. To accurately determine its finite-volume spectrum, a variational analysis using a large basis of operators, including bilocal scattering operators but also local tetraquark operators, should be used. Using Wilson-clover fermions at the $SU(3)$-flavour-symmetric point, we...
Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. This approach has close ties to trivializing maps and numerical stochastic perturbation theory, in which field transformations are defined by integrating flow fields that exactly solve a local transport problem. In this talk, I will discuss a new Monte Carlo...
We present a lattice calculation of the parton distribution function (PDF) of the lightest positronium system employing the 1+1D Schwinger model in the Hamiltonian formulation, implemented within a quantum computational framework on an IBM quantum computer. Our setup employs a total of 11 qubits: 10 qubits represent stagger fermions sites, which correspond to five spatial lattice sites and one...
An ongoing project of the Fermilab Lattice, HPQCD, and MILC collaborations is the precision calculation of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. In this talk, we present the isospin breaking corrections to the connected and disconnected contributions to HVP with a focus on the dominant, long-distance contributions to these correction....
The recent discovery of $T_{cc}$ has attracted several lattice QCD
as well as other studies of $T_{cc}$ pole. Though for $T_{bb}$ there
is a consensus about the existence of a deeply bound state, no such
consensus have been reached for $T_{cc}$. On top of that the discovery
of Left Hand Cut made the pole analysis using Lüscher’s method
difficult. In this situation it is desirable to study...
The main contribution to the cost of Lattice QCD calculations typically comes from solving the Dirac equation. Using preconditioners such as multigrid, this computational cost can be reduced significantly. We introduce a novel gauge-equivariant neural network architecture for preconditioning the Dirac equation. We study the behavior of this preconditioner as a function of topological charge...
Electromagnetic corrections to n-point functions on the lattice can be calculated by using a position space photon propagator. In this representation the propagator depends on the difference between the two vertices connected by the internal photon, leading to a volume square sum. The sum can be avoided by fixing one of the vertices to a single point with the downside of drastically reducing...
Quantum simulations of fundamental gauge theories require a thorough understanding of non-unitary dynamics that arise from interactions with an environment, including measurements. This talk focuses on the one-dimensional Z₂ gauge theory, a foundational model for probing such effects. Using tensor network calculations, we investigate the dynamics of entanglement entropy when physical...
Mapping the QCD phase structure at finite baryon density remains a challenging problem because direct simulations are hindered by the sign problem. By analyzing results at vanishing and purely imaginary chemical potentials, we identified strangeness susceptibility, in the case of strangeness neutrality, as a proxy for the chiral transition. We exploit this observation to investigate the QCD...
The QCD axion is one of the most promising solutions to the strong CP problem, as it is also a viable dark matter candidate. Moreover, a large fraction of the current experimental searches focus on its coupling to photons. In this talk, we present the first determination of the QCD corrections to the model-independent part of the axion–photon coupling from a first-principles lattice QCD...
We build an EFT which accurately captures low energy physics of the chiral sector of QCD. When fitted to properties of pions at finite temperature obtained from lattice simulations of 2+1 flavour QCD, it accurately reproduces the crossover temperature seen in the simulations. Its predictions for other quantities are shown. The EFT can then be used for analytic continuation to real time. An...
We present results by ETMC on the leading-order hadronic vacuum polarisation (LO-HVP) contribution to the muon anomalous magnetic moment within isospin symmetric $N_f=2+1+1$ QCD. In our computation, we use Wilson–clover twisted-mass quarks in a sequence of simulations at large volumes, realistic pion masses, four lattice spacings and two different valence-quark regularisations for the...
We present new results from our lattice investigations of maximally supersymmetric Yang--Mills theory in three dimensions, focusing on its nonperturbative phase diagram. Using a lattice formulation that preserves part of the supersymmetry algebra at finite lattice spacing, we study the spatial deconfinement transition, which holography relates to the transition between localized and...
We present our recent investigation on doubly bottom and bottom-strange tetraquarks in the isoscalar channel in search of a possible tetraquark bound state. The calculations are performed on four ensembles with dynamical quark fields up to the charm quark generated by the MILC Collaboration with various lattice spacings. Multiple volumes have been used to account for finite volume effects....
In many modern machine learning applications, models are often trained
to near zero "training loss" (in other words, to interpolate the
training data), while also having far more training parameters than the
"number of data points". This appears to violate traditional
rules-of-thumb for avoiding overfitting, and considerable work has thus
been devoted to gain a better understanding of...
I will review the status of lattice QCD in extreme conditions—finite temperature, nonzero baryon chemical potential, and strong magnetic fields. Emphasis will be on the QCD phase structure and bulk thermodyanmics.
We will survey how RHIC and LHC measurements constrain the properties of QCD matter when interpreted with lattice-QCD inputs. The talk will: (i) present hydrodynamic descriptions of momentum and angular distributions using a lattice-anchored equation of state at μB≈0 and its finite-density extensions relevant to the RHIC Beam Energy Scan; (ii) confront fluctuation measurements with lattice...
Dynamical probes such as thermal photons and quarkonia provide valuable insight into the properties of the quark-gluon plasma (QGP) created in heavy-ion collisions. The relevant information is encoded in their spectral functions. Extracting these spectral functions from lattice correlators is a challenging task due to the ill-posed nature of the inverse problem, which requires additional...
Studying the behavior of QCD at high temperatures is essential for understanding the properties of strongly interacting matter and its role in the evolution of the early Universe. A key quantity in this context is the QCD Equation of State. I present a non-perturbative determination with three massless quark flavors, covering a wide range of temperatures, from the electroweak scale down to 3...
Gauge fixing is an essential step in lattice QCD calculations, particularly when studying gauge-dependent observables. Traditional iterative algorithms for gauge fixing are computationally expensive and often suffer from critical slowing down near fixed points, as well as scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, in which...
We study conserved charges for the 3+1 D staggered fermion Hamiltonian.
In addition to $\mathrm{U}(1)_V$ charge $Q_0$, we find that the system has three independent non-singlet charges $Q_{x_i}$ $(i=x,y,z)$ that generate axial $\mathrm{SU}(2)_A$ transformations in the continuum limit. On the lattice, these charges do not commute with $Q_0$, signaling a mixed anomaly between...
Hadronic vacuum polarization is a key observable in low-energy QCD, and is famously the greatest contributor to theoretical uncertainty in the muon magnetic moment. Its long-distance part in particular is a weak point of the current best lattice QCD computations. We compute it to next-to-next-to-next-to-leading order in chiral perturbaion theory, capturing the lowest-energy hadronic...
We present our latest results on charmonium states $J/\psi(1S)$, $\psi(2S)$, $\eta _c(1S)$, $\eta _c(2S)$, $\chi _{c0}(1P)$ and $\chi _{c1}(1P)$ above the pseudo-critical temperature, using extended operators [1] on $N_x=64$, $N_\tau =16-32$ HISQ lattices using Wilson Clover fermions.
The charmonium states at zero temperature are well described by the heavy quark anti-quark potential. At...
By employing K-theory to classify the Wilson Dirac operator on a lattice, we give a comprehensive formulation for various indices via its spectral flow. While the index of the overlap Dirac operator, which utilizes the Ginsparg-Wilson relation, is limited to flat tori in even dimensions, our formulation offers several key advantages: 1)It is straightforward to apply to the Atiyah-Patodi-Singer...
We present progress towards a new determination of the hadronic vacuum polarization (HVP) function $\Pi(Q^2)$ relevant for the running of the electromagnetic coupling and the electroweak mixing angle. In the conventional time–momentum representation, strong correlations induced by the kernel prevent reliable continuum extrapolations. To address this issue, we reconstruct smeared spectral...
Investigating the critical endpoint of the finite-temperature QCD phase transition requires higher-order cumulants of the chiral condensate. These, in turn, involve traces of inverse Dirac operator powers $\text{Tr}\,M^{-n}$ ($n=1,2,3,4$). Because direct computation with the Conjugate Gradient method is computationally expensive, we adopted a machine-learning strategy using gradient-boosted...
The hadronic tensor is the central non-perturbative object in the calculation of the cross section of lepton-hadron interactions like neutrino-nucleon scattering. It is usually parameterized in terms of structure functions, which encode all necessary information independently of the kinematic region. Moreover, the hadronic tensor can be factorized in terms of parton distribution functions...
In this work we investigate the time-like pion form factor from lattice QCD, a quantity interesting for its physics content and its phenomenological reach. This observable can be calculated in the elastic region using the finite-volume approach, up to the first (four-particle) open channel. With the goal of accessing the exclusive two-pion form factor in the inelastic region, starting from a...
In this work we calculate the non-perturbative potential between a heavy quark and an anti-quark pair in a QCD plasma at finite temperature. Extracting the leading order static potential $V_s(r)$ from the temporal Wilson line correlators we then calculate the spin dependent component $V_{ss}(r)$ at $\mathcal{O}(1/M^2)$, using color-magnetic field insertions. The computations have been...
Isospin-breaking corrections to the HVP are among the leading sources of uncertainty in the Standard Model prediction of the muon g−2 [1]. In recent work by the RC* collaboration [1], we compute the intermediate window contribution for a flavour non-singlet current using two strategies to include isospin-breaking corrections: the RM123 approach and a fully dynamical QCD+QED simulation. In both...
We study the problem of defining and computing entanglement entropy in lattice gauge systems using a dual loop formulation. The main idea is to apply a sequence of canonical transformations that rewrite the standard link variables of $SU(2)$ and $U(1)$ lattice gauge theories in terms of the loop variables. This allows an easier handling of gauge-invariant degrees of freedom and gives a cleaner...
Using forward matrix elements of local leading twist operators, we present a determination of the third Mellin moments $\left< x^2 \right>$ of nucleon's unpolarized, polarized and transversity parton distribution functions.
Two lattice QCD ensembles at the physical pion mass are used: these were generated using a tree-level Symanzik-improved gauge action and $2+1$ flavor tree-level improved...
Topological invariants and their associated anomalies have played a crucial role in understanding low-energy phenomena in quantum field theories. In lattice gauge theory, the standard $\mathbb{Z}$-valued Atiyah–Singer index is formulated via the overlap Dirac operator through the Ginsparg–Wilson relation, but extensions to more general topological invariants have remained limited. In this...
Domain-wall fermions provide a good lattice realization of chiral fermions by introducing an additional fifth dimension. Achieving improved chiral symmetry typically necessitates increasing the extent of this dimension at the expense of significantly higher computational cost. We propose a machine-learning-based parameter-optimization approach that emulates the effect of a longer fifth...
Scattering processes featuring the strong interactions can be studied using lattice QCD by means of the Lüscher formalism. This approach relies on analyticity and unitarity of the $S$-matrix to relate infinite-volume scattering amplitudes to finite-volume energy levels. However, lattice QCD simulations employing rooted staggered fermions manifest unitarity violation as an $\mathcal{O}(a^2)$...
In this talk, we discuss tests of the Hybrid Monte Carlo algorithm using four dimensional pure SU(3) gauge theory when the conjugate momenta are not chosen as random Gaussian variables of uniform variance for each lattice site, but instead are represented as different normal modes across the lattice volume, with variable variance. Generically, this involves simulating in a fixed gauge. One...
It has been predicted that the CP symmetry of the 4D SU(3) Yang-Mills theory at $\theta = \pi$ is spontaneously broken in the confined phase, and it is recovered precisely at the deconfining temperature.
The direct simulation of the theory at $\theta = \pi$ is, however, difficult due to the sign problem.
Thus, we simulate the theory with an imaginary theta parameter and perform analytic...
We investigate how quarkonium states are affected by a medium with non-zero isospin chemical potential at near zero temperature. We obtain quarkonium correlators from heavy quark propagators which are calculated via lattice Non-Relativistic QCD (NRQCD) on the gauge field ensembles simulated with non-zero isospin chemical potential. Here, the gauge field ensemble with $\mu_I a = 0.000, 0.048,...
Minimally doubled fermions realize one pair of Dirac fermions on the lattice. Similarities to staggered fermions exist, namely, spin and taste degrees of freedom become intertwined, and a peculiar nonsinglet chiral symmetry and ultralocality are maintained. However, charge conjugation, some space-time reflection symmetries and isotropy are broken by the cutoff.
We address the most simple...
The deconfined quantum critical point (DQCP) exemplifies a phase transition beyond the Landau paradigm, yet its true nature remains debated. We investigate a candidate for the $SU(2)$ QCD$_3$ theory with $N$ fermions and a $Sp(N)/\mathbb{Z}_2$ global symmetry, which is a possible effective description of the DQCP—using the recently proposed fuzzy sphere regularization. This method offers a...
The HadStruc collaboration is pursuing a program aimed at understanding the three-dimensional internal structure of the nucleon encapsulated in the Generalized Parton Distributions (GPDs) and Generalized Form Factors (GFFs) within the short-distance factorization approach. I present recent work by HadStruc on the isovector GFFs of the nucleon, including those corresponding to non-zero...
The modification of heavy-quark interactions in hot and dense QCD matter plays a central role in understanding the fate of quarkonium in heavy-ion collisions. While lattice QCD studies at zero chemical potential have established the temperature dependence of the static quark–antiquark potential and its spectral properties, the finite baryon density regime remains largely unexplored. In this...
Resonant hadrons, and some loosely bound states, can be studied by looking at the energy dependence of the reaction rate of the multi-particle asymptotic states associated to them. For instance, the form factors of these states can be found via analytic continuation of the two-particle transition rate induced by the current of interest. These transitions, in turn, can be constrained from...
We report on the continued efforts to measure the glueball and meson spectra of Yang-Mills lattice gauge theories based on the gauge group $SU(N_c)$ in the t’Hooft limit.
We employ a multilevel sampling algorithm to measure glueball correlators to reduce statistical noise in the large time separation limit. The gluon operator basis is composed of spatial Wilson loop with vanishing momentum...
Trace estimation in lattice QCD benefits from two complementary variance-reduction techniques: probing methods that exploit operator structure, and multigrid multilevel Monte Carlo, an efficient deflation technique. We propose a unified framework that combines these ideas and evaluate it on three representative targets: the trace of the inverse of the Dirac operator, traces entering the...
We present a novel procedure for analyzing the lattice-QCD spectrum via the finite-volume formalism to obtain constraints on multi-hadron scattering amplitudes at both real and complex energies. This approach combines a Bayesian reconstruction of the scattering amplitude on the real axis with Nevanlinna interpolation for analytic continuation to complex-valued energies. The method is...
The Thirring model in 2+1d with $N$ flavors can exhibit spontaneous
U(2$N)\to\,$U($N)\otimes$U($N$) breaking through fermion - antifermion condensation in the limit $m\to0$. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for $N=1$...
We propose a novel approach to directly simulate the 't Hooft partition function and revisit the (de)confining phase structure of an $SU(N)$ gauge theory with the $\mathbb{Z}_N$ $1$-form symmetry. We develop a hybrid Monte Carlo algorithm (the halfway HMC) for the $SU(N)/\mathbb{Z}_N$ gauge theory. The usual partition function $\mathcal{Z}[B]$ with 't Hooft flux $B$ can be numerically computed...
The conjugate gradient (CG) algorithm, employing mixed precision and even-odd preconditioning, is typically used when computing propagators for highly improved staggered quarks (HISQ). However, its performance degrades due to critical slowing down as the light quark mass approaches its physical value. In previous work, we addressed this issue using deflation, which significantly reduced solve...
The light-cone distribution amplitude (LCDA) is a fundamental non-perturbative quantity for understanding hadron structure. We report on our calculation of the pion and kaon LCDAs using the heavy-quark operator product expansion (HOPE) framework. This method employs an OPE analysis of hadronic amplitudes through the inclusion of a fictitious valence heavy quark, and has previously been shown...
Lattice quantum chromodynamics (LQCD) calculations are pushing the limits of today’s most powerful supercomputers. Since most resources are consumed in solving large systems of linear equations, efficient solvers, such as those based on adaptive multigrid methods, are essential. However, with the slowdown of Moore’s Law, it is uncertain whether traditional architectures can deliver the...
I will present new non-perturbative results about the meson spectrum and the low-energy constants of QCD in the 't Hooft large-$N$ limit, $N \to \infty$ with $N_{\rm f}/N \to 0$. These are obtained from lattice Monte Carlo simulations of the Twisted Eguchi-Kawai (TEK) model up to $N=841$.
More precisely, I will discuss the determination of radial Regge trajectories in the $\pi$ and $\rho$...
We study spectral reconstruction techniques to obtain the electric conductivity coefficient at non-zero external magnetic fields for Wilson fermions in quenched QCD from the euclidean correlator. Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the euclidean correlator to the spectral function via an inhomogenous Fredholm equation of...
Four-particle intermediate and final states pose major challenges for lattice calculations of scattering and decay amplitudes, as well as long-distance matrix elements. As a step toward addressing these challenges, we present preliminary results from a perturbative study of four-pion effects in finite-volume spectra and in the relation between finite-volume matrix elements and decay...
We present the results of lattice QCD calculation of all leading-twist x-dependent Light-cone Distribution Amplitudes (LCDAs) for baryons in light octet, within the framework of Large-momentum Effective Theory (LaMET). We implement a novel Hybrid renormalization scheme for baryon nonlocal operators, and perform simulations at 4 different lattice spacings a = {0.052, 0.068, 0.077, 0.105} fm,...
The rich internal structure of hadrons is encoded in partonic functions, such as parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs), which are crucial in collider experiments and decay processes. Calculating them from first principles remains a major challenge: they require matrix elements with a Wilson line along a light-like direction, which is not directly...
Cuprate superconductors, the most commonly known class of high-$T_c$ superconductors, have much richer properties than the conventional superconductors, yet much of it is not well-understood. To explain their physical origin, many theories involving emergent gauge fields have been put forth in recent years. Focusing on the theory developed in Christos et al., PNAS 120(21) e2302701120 (2023), ...
We report on our ongoing lattice QCD computation of antistatic-antistatic-light-light potentials using the CLS $N_f=2$ gauge configurations and the OpenQ*D codebase. We improve on previous work by calculating the correlation matrices for all three attractive ground state potentials previously characterized, to mitigate excited state contributions and further probe the vague indication of...
Centre vortices have been shown to underpin confinement and dynamical chiral symmetry breaking. Here we consider the centre vortex geometry of dynamical QCD at finite temperature using the anisotropic FASTSUM ensembles and uncover evidence for two transition temperatures. The first corresponds to the established chiral transition $T_c$ while the second occurs at $T_d\simeq 2\,T_c$. Drawing...
The covariant coordinate space (CCS) method for hadronic vacuum polarization calculations has been developed as an alternative to the established time-momentum representation (TMR) and is particularly promising for its potential to mitigate statistical noise. Our investigations further reveal that this framework exhibits a favorable continuum limit. We provide an extensive analysis of the...
We construct an exact dual formulation of pure SU(N) Hamiltonian lattice gauge theory with local dual dynamics in (2+1) dimensions. The dual model is obtained by making a series of iterative canonical transformations on the electric field operators and their conjugate vector potentials associated with the links around each plaquette. This transformation maps the original gauge degrees of...
We present an analysis of deflation and low-mode averaging techniques applied to two- and three-point correlation functions of mesons and baryons at the physical point. The focus is on improving the signal quality at large Euclidean time separations, where statistical noise typically dominates. We quantify the computational cost and statistical gains across several ensembles, identifying the...
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating distinct sectors. With appropriately constructed bias potentials, Metadynamics and related enhanced sampling techniques can mitigate this problem and...
Recent advances in numerical algorithms for matrix function evaluations have significantly improved the stability and efficiency of large-scale computations in quantum field theory. In this study, we investigate their applicability to the calculation of the quark propagator in lattice QCD. The quark propagator, which involves the inversion and functional evaluation of large sparse matrices...
For nearly two decades, the highly improved staggered quark (HISQ) discretization of the Dirac operator has enabled fast and accurate simulations of (2+1)- and (2+1+1)-flavor QCD, particularly at the physical point. Over this period, numerous code bases targeting both CPU and GPU architectures have implemented HISQ through a variety of methods that optimize for low communication overhead,...
We present initial results for the application of a novel relativistic heavy-quark action in the charm sector on 2+1-flavor lattice ensambles produced by the CLS consortium. The five parameter action was tuned non-perturbatively using a neural network and experimental continuum charmonium ground state masses. We investigate effective masses of $D$ meson correlators produced on CLS ensambles...
In this work, we investigate discretization effects proportional to the quark mass, $O(a m)$, on the QCD beta-function within lattice perturbation theory. Using the background field method and improved lattice actions, we compute the renormalization factor of the coupling constant and thus determine the beta-function. In this framework, we calculate, up to two-loop order, the contributions...
Despite their simplicity, O(N) scalar field theories, or O(N) models for short, allow for the investigation of several interesting phenomena such as asymptotic freedom and spontaneous symmetry breaking. On the lattice, O(N) models can be represented in terms of integer-valued flux variables, which allow for efficient Monte Carlo (MC) simulations both at zero and non-zero densities with a worm...
In two dimensions, the phi4 theory exhibits a non-trivial infrared fixed
point that governs the continuum limit and connects to the Ising universality class. I will present the investigation of RG flow of 2D phi4 theory using gradient flow techniques, with smooth lattice configurations and allow for a non-perturbative definition of scale-dependent observables. By tracking the evolution of...
We study the phase diagram of massless staggered fermions with two distinct four-fermion couplings, U and U′, on a three-dimensional Euclidean lattice using the fermion-bag Monte Carlo method. The model exhibits three distinct phases: a massless fermion phase, a symmetry-broken massive phase with a fermion bilinear condensate, and a symmetric massive phase where fermions acquire mass without...
We present results from our DEI surveys conducted in 2023 and 2024, focusing on whether workshops should be held online or in person. Surprisingly, we find no correlation between diversity criteria and a preference for online conferences, including care responsibilities. The only numerically significant predictors that lead scientists to prefer an online conference, as shown in new survey data...
The sensible application of the Hybrid Monte Carlo (HMC) method to the Hubbard model is hindered by the emergence of infinite potential barriers due to a vanishing fermion determinant, resulting in an ergodicity problem that needs to be resolved. This can be achieved by augmenting the HMC algorithm with radial updates, which refer to multiplicative Metropolis-Hastings updates in a radial...
We present results on the pion and kaon decay constants determined on a set of over 50 coordinated lattice simulations (CLS) gauge ensembles with $N_f=2+1$ sea quark flavours of non-perturbatively improved Wilson fermions. This is part of a project to explore the range of validity of SU(3) chiral perturbation theory (ChPT) in the meson sector and to determine its low energy constants (LECs)....
The conjugate gradient is the standard technique for computing propagators in lattice QCD. Preconditioning the Dirac Operator makes this method faster. The goal of our project is to develop Neural Networks to predict preconditioners for the Dirac operator with the gauge configuration as input.
Our approach closely follows recent successes from MIT[1], where traditional neural networks have...
The sign problem is a major obstacle for lattice studies of spontaneous supersymmetry breaking (SSB). Quantum computing provides a promising alternative approach. In particular, properties of supersymmetry relate SSB to the ground-state energy, which can be probed using hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE). I will present VQE analyses for...
We present numerical results of staggered fermions with a
taste splitting mass term on dynamical configurations. The rise of gluonic counterterms from rotational symmetry breaking is studied for a single taste operator and the pion propagator is computed. Preliminary numerical results are given for lattice sizes up to $16^4$
We use variational methods to numerically study the matrix model for two-color QCD coupled to a single quark (matrix-QCD(_{2,1})) in the ultra-strong Yang--Mills coupling ((g = \infty)). The model's spectrum is divided into superselection sectors characterized by baryon number (B) and spin (J). Our analysis focuses on the sectors (B = 0, 1, 2) and (J = 0, 1), which correspond to...
The complex Langevin method (CLM) is a promising tool to address the sign problem in quantum field theories with complex actions. However, it can converge to incorrect results even when simulations appear stable, highlighting the need for robust diagnostics. Existing checks, such as monitoring drift distributions, are useful but indirect. We propose a complementary test based on the...
We study the theta dependence of the deconfining temperature in SU(3) Yang-Mills theory. Simulation at real theta causes the sign problem, while simulations at imaginary theta are feasible but suffer from topological freezing that becomes severe at large imaginary theta. We mitigate the topological freezing using two-dimensional parallel tempering technique with replica exchanges across...
Accurately simulating long-time dynamics of quantum many-body systems—whether in real or imaginary time—is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables and ground state properties. I will present a...
We present recent progress towards continuum estimates of cumulants of conserved charges in (2+1)-flavor QCD with Möbius Domain Wall fermions (MDWF). Simulations are performed at the physical quark-mass point on lattices with temporal extent $N_\tau=12,16$ and aspect ratio $N_{\sigma}/N_{\tau}=3$, enabling a controlled study of cutoff effects. We focus on second- and fourth-order cumulants of...
The Ising model serves as a model for simple magnetic systems and as a testing ground for the study of strongly-coupled systems. The model is exactly solvable in two dimensions and can be simulated with relatively small computing resources. We investigate the phase transition of the Ising model through a novel scaling procedure first proposed to explore the phase structure of a theory with...
Normalizing flows provide a framework to learn statistically exact machine-learned maps between different lattice field theories. Flows constructed to map from QCD to the same theory with a (possibly localized) operator insertion provide a general tool to construct unbiased reduced-variance estimators for lattice QCD correlation functions. Building on previous applications to Feynman-Hellmann...
Understanding a hadron’s electric and magnetic polarizabilities allows one to access internal structural information. Traditionally, the external field two-point function method has been used to calculate polarizabilities. However, recent work has demonstrated the effectiveness of using four-point functions for computing polarizabilities of charged and neutral hadrons. Our previous study on...
We present results for $f_K/f_{\pi}$ in pure QCD with $N_f=2+1$ flavors, along with a determination of $|V_{us}|$ and a study on the unitarity of the first row of the Cabibbo-Kobayashi-Maskawa (CKM) matrix after introducing strong isospin-breaking and QED effects.
The results obtained are based on a combination of a Wilson unitary action and a mixed action setup using Wilson twisted mass...
We present a new Monte Carlo sampling method to calculate the rate at which probability flows out of a meta-stable regime in a complex system. In field theory, this method could be used to calculate false vacuum decay rates. The original probability distribution of the system is multiplied by a simple re-weighting function which guarantees that the system transitions between the meta-stable...
We show preliminary results for the nonperturbative Renormalization Group (RG) running of the full $\Delta F=2$ four-fermion operators basis in QCD with $N_f=3$ massless dynamical flavours. The perturbative part of the running is obtained extending the conventional approaches in the literature, employing the Poincaré–Dulac theorem. The nonperturbative computations employ...
We show that the tensor renormalization group offers a consistent framework in which twisted partition functions can be employed as order parameters to study critical phenomena. Investigating the two-dimensional Ising model and the three-dimensional $O(2)$ model as concrete examples, we demonstrate that critical points associated with spontaneous symmetry breaking can be located solely from...
The approach to the continuum of a given discretization of a quantum field theory is understood within the framework of Symanzik Effective Field Theory. It explains the concept of universality whereby dimensionless renormalized observables approach the same continuum value in any discretization. The functional form of these observables as functions of the lattice spacing depends on the...
The precision of current lattice QCD calculations of the direct CP-violating parameter $\varepsilon’$ now requires the inclusion of $\Delta I = \frac{1}{2}$ rule-enhanced, isospin-breaking effects. Here we give an update on the program to include electromagnetism and quark mass differences in a first-principles calculation of $\varepsilon’$. We combine finite-volume hadronic matrix elements...
Instanton liquid model is believed to capture the main features of vacuum QCD dynamics. Recently, multiple predictions for hadron structure functions have been derived and compared with experimental measurements and lattice QCD calculations, finding a general agreement. In order to explore the precision of the instanton liquid model, one has to compare its predictions with non-perturbative...
We demonstrate, for the first time, that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model—a central framework for understanding the electronic structure of graphene and related materials. Conventional approaches such as Hybrid Monte Carlo often encounter ergodicity breakdowns near the time-continuum limit, introducing systematic biases. By...
We calculate spatial string tension in 2+1 flavour QCD in (3,1)
dimensions within temperature range of [166MeV, 1000MeV] using spatial
Wilson Loops with HYP smearing. We used Highly Improved Staggered Quark
action for
fermions and tree level Symanzik improved gauge action for gluons at two
lattice spacings corresponding to temporal extent $N_{\tau}=8,10$. We
then compare our results...
We present the entanglement entropy for the two-dimensional real scalar φ^4 theory using a higher-order tensor renormalization group algorithm. This quantity is employed to identify a critical point of the system. We will also discuss the continuum limit of the critical point.
Tensor Renormalization Group (TRG) is a promising numerical
method for systems with the sign problem. However, the computational
cost increases exponentially with the dimension, which makes the
development of effective algorithms for three-dimensional or
four-dimensional models a crucial challenge. As a first step toward
addressing this, we study the three-dimensional finite-density...
Novel theoretical and computational strategies have opened the possibility of exploring QCD thermodynamics at the non-perturbative level at unprecedented temperatures, reaching from the GeV scale up to the electroweak scale.
A number of observable quantities are now being investigated in this regime.
Key ones are the hadronic screening masses, which encode the correlation length of the...
Current precision tests of the Standard Model (SM) show a deficit in the first row unitarity of the CKM matrix. At the current level of precision, the only relevant CKM matrix elements that contribute to first row unitarity are $|V_{ud}|$ and $|V_{us}|$. Without resorting on nuclear inputs, those can be extracted from the experimental decay width of kaon and pion leptonic decays along with the...
We report on the status of an update of our previous computation of light and strange quark masses in QCD with $N_f=2+1$ dynamical flavour. Bare quark masses are extracted from CLS ensembles, using $\mbox{O}(a)$-improved Wilson fermions, and the mass renormalization is performed non-perturbatively in the Schrödinger functional scheme over a wide range of scales to make safe contact with...
The calculation of the hadronic form factors on the lattice provides important information about the internal structure of the corresponding states. However, calculating the form factor for unstable states, viz. resonances, is not as straightforward, both from the conceptual point of view and in terms of technical implementation. In this work, we specifically consider the electromagnetic form...
Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. We further present the scaling...
A while ago, the generalised density-of-states method was proposed to address the sign problem that arises in systems with a complex action. More recently, with the advent of normalising flows and their ability to model complicated target densities, a flow-based density-of-states approach was developed. This method has been shown to successfully reconstruct the partition function of 0D, 1D,...
We develop a computational scheme based on the tensor renormalization group method to investigate the multi-particle state of the (1+1)d Ising model. The scheme is started by representing the system as a tensor network and coarse-graining it with the higher-order tensor renormalization group algorithm. Thereafter, we construct the corresponding numerical transfer matrix from the coarse-grained...
The $U(1)_A$ symmetry of the massless QCD Lagrangian is broken in the quantised theory but may be effectively restored at some finite temperature with important consequences on the order of the chiral transition and the QCD phase diagram in the chiral limit. It has been argued in the literature that one way to probe the effective restoration of $U(1)_A$ is to check for the degeneracy of...
We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $\theta=\pi$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value,...
First-principles prediction of inclusive heavy-particle decay is key to interpreting experimental data and testing the Standard Model. However, lattice QCD data requires ill-posed analytic continuation before such predictions can be made. Bergamaschi, et al. proposed using Nevanlinna-Pick interpolation to address this inverse problem which provides rigorous bounds on the continued results. ...
We present the results of the nucleon axial-vector charge based on PACS10 gauge ensembles. These ensembles are generated by PACS Collaboration using stout-smeared O(a) improved Wilson-clover quark action and Iwasaki gauge action, and they are characterized by the spatial extent of 10 fm and three lattice spacings 0.09 fm, 0.06 fm and 0.04 fm. In particular, the latest update at 0.04 fm is...
The discovery of XYZ exotic states in the hadronic sector, particularly those containing two heavy quarks, remains one of the most intriguing open problems in particle physics. In this talk, I present the Born-Oppenheimer Effective Field Theory (BOEFT), a framework derived from QCD, capable of describing exotic hadrons of any composition. I present results on the key nonperturbative...
This work is motivated by the limitations of conventional Euclidean Monte Carlo methods, particularly the sign problem, which hinder the exploration of physically rich regimes such as nonzero chemical potential, topological terms, and real time dynamics. To address this challenge, we present a Hamiltonian-based variational approach for numerical simulations of quantum mechanical systems. We...
The SU(2) gauge symmetry of the weak sector implies that the Higgs vacuum expectation value has to be gauge variant and hence cannot be a physical observable, even though it is generally regarded as such. The standard perturbative expansion, therefore, has a conceptual flaw that can be resolved using the Fröhlich-Morchio-Strocchi mechanism. In this presentation, we explore the mechanism on the...
In this work, we calculate the eigenvalues of the probe (overlap) Dirac operator on thermal gauge ensembles of 2+1 flavor QCD generated using domain wall fermions as well as pure SU(3) gauge theory on the lattice. Focusing on the infrared part of the eigenspectrum that lies within the non-perturbative magnetic scale, we propose suitable observables that allow us to categorize different regions...
We present an update on the Los Alamos collaborations' calculations of the spectrum, charges, form-factors, and electric dipole moments of nucleons using lattice QCD. Our calculations are done using Wilson-Clover fermions on both Clover and MILC collaboration's HISQ gauge configurations. These ensembles include multiple lattice spacings down to 0.04 fm, and multiple isospin-symmetric pion...
We introduce an all-mode extension of the Higher-Order Tensor Renormalization Group (HOTRG) by using a squeezer transformation at the coarse-graining step. This all-mode framework eliminates systematic errors, leaving only statistical uncertainties, enabling direct comparison with exact results. We demonstrate the method on the two- and three-dimensional Ising models, obtaining results in...
Many hadronic observables are nowadays computed in lattice QCD with a sub-percent precision which requires the inclusion of isospin-breaking and electromagnetic effects. Most of the methods that implement the photon propagator in finite-volume lead to power-law suppressed finite size effects. These are due to the long-range nature of electromagnetism and make reliable predictions...
The determination of the lattice scale with high precision is a prerequisite for extracting reliable physical results from lattice QCD. We present an analysis of scale setting using 2+1-flavor Wilson–clover ensembles generated by the JLab/W&M/LANL/MIT/Marseille collaborations with the Hybrid Monte Carlo algorithm. These ensembles span a broad range of lattice spacings ($0.056 \leq a \leq...
The topological susceptibility is one of the quantities that has a large discretization error, and the error can be sensitive to the choice of fermion action. We report on our results from physical point simulations with 2+1 flavor Moebius domain wall fermion at finite temperature. The temporal lattice size is Nt=12 and 16, and the temperature range is around 140 MeV to 250 MeV. We also...
I will briefly review how machine learning can be used in lattice gauge theory simulations and what approaches are currently available. I will then dicuss one specific application in more detail, namely the machine learning of RG-improved gauge actions using gauge-equivariant convolutional neural networks. In particular, I will present scaling results for a machine-learned fixed-point action...
I will review the current generation of exascale supercomputers and present performance results for lattice applications. On the software side, I will discuss strategies for achieving performance portability across heterogeneous architectures. I will conclude with an outlook on architectures now under development.
Despite the impressive success of the lattice-gauge-theory program in enabling first-principles predictions in particle, hadronic, and nuclear physics over the years, a range of systems and phenomena will remain out of reach of our current computational paradigm. These include studies of large atomic nuclei and their properties, of phases of matter at finite density, and of the nonequilibrium...
Gauge theories are the cornerstone of our description of nature. At the theoretical level, many of their fascinating aspects - from real time dynamics, to regimes of finite density of baryon matter - represent some of the most notable and fascinating challenges for computational methods. Over the last decade, this has stimulated a broad effort to understand how to quantum simulate gauge...
We present a method based on the bootstrap to determine $p$-values from Monte Carlo data, in particular those generated in a lattice QCD calculation, where we make no assumptions about the underlying distribution. By generating samples from the underlying data, we are able to naturally incorporate the effects of autocorrelations and non-normally-distributed samples, both of which skew the...
We present progress towards a high-precision lattice QCD study of the nucleon’s isovector vector form factors, which encode key aspects of the nucleon’s spatial structure and its response to electromagnetic probes. We utilize the Coordinated Lattice Simulations (CLS) ensembles generated with $N_f =2+1$ non-perturbatively $O(a)$ improved Wilson fermions and a tree-level Symanzik-improved gauge...
We discuss the calculation of the inclusive semileptonic decay for the process $B_s \to X_c \, l\nu_l$ using lattice QCD, which could be decisive in understanding the long-standing tension between inclusive and exclusive determinations of the CKM matrix element, $|V_{cb}|$. In this talk, we investigate the main sources of systematic uncertainty in these decays, including the impact of Jacobi...
We present our work on the computation of the axial form factor of the nucleon from lattice QCD. We employ a set of $N_f=2+1$ CLS ensembles with $O(a)$-improved Wilson fermions and the Lüscher-Weisz gauge action, with lattice spacings ranging from $0.05\,\text{fm}$ to $0.086\,\text{fm}$ and pion masses spanning between $130\,\text{MeV}$ and $350\,\text{MeV}$. To control excited-state effects,...
The unitarity of the CKM matrix is a fundamental property of the Standard Model, and leptonic decays of pseudoscalar mesons $P \to \ell\nu(\gamma)$ are an important avenue to probe this experimentally. The theoretical prediction of the decay rate depends on a number of form factors, which can be calculated using lattice QCD. We present an approach to compute them using a JLQCD domain-wall...
The pole structure of the $\Lambda(1405)$ has been a topic of debate for a long time. Chiral perturbation theory predicts that its experimental spectrum may be explained by a two pole structure originating in the $SU(3)$ chiral dynamics of the baryon-meson interaction. The $SU(3)$-symmetric flavor point is readily accessible in lattice QCD, in this work we study the baryon-meson states...
A new method to approximate Euclidean correlation functions by exponential sums is introduces. The truncated Hankel correlator (THC) method builds a Hankel matrix from the full correlator data available and truncates the eigenspectrum of said Hankel matrix. It proceeds by applying the Prony generalised eigenvalue method to the thus obtained low-rank approximation. A large number of algebraic...
We determine the role of topology from the eigenmodes, and extract the chiral condensate from the eigenvalue density of minimally doubled fermions (MDF), namely in Karsten-Wilczek (KW) and Borici-Creutz (BC) formulations. We employ MILC asqtad ensembles with $N_f=2+1$ dynamical flavors of quarks [1] as backgroud gauge fields. Using flavored mass terms [2,3], we find that the spectral flow of...
The double-pole structure of the strangeness S=-1 isoscalar baryon resonance has become a poster child for the complicated, non-perturbative structure of QCD at low energies. Traditionally, the most successful theoretical approach to study this state has been based on the extensions of Chiral Perturbation Theory. This remains so far the primary methodology underlying the pole positions quoted...
Computing derivatives of observables with respect to parameters of the theory is a powerful tool in lattice QCD, as it allows the study of physical effects not directly accessible in the original Monte Carlo simulation. Prominent examples of this include the impact of the up-down quark mass difference and electromagnetic corrections. In this talk, I will present a new approach based on...
We present new results for Sp(4) Yang-Mills theory around its first-order thermal phase transition by reconstructing the density of states via the LLR algorithm. We show results on different space and time extents, as well as aspect ratios, and estimate discretization artifacts. We see clear signatures of the first-order transition and determine the critical coupling, the specific heat and set...
A first-principles computation of the inclusive semi-leptonic decay rates of heavy mesons from lattice QCD has a great phenomenological relevance since the comparisons of the theoretical results with the corresponding experimental data allows for stringent Standard Model tests in the sector of Flavour physics. In this talk we present the first fully non-perturbative computation of the $D_s \to...
We discuss the extraction of form factors for heavy-light pseudo-scalar to light pseudo-scalar decay form factors from finite time correlation functions. Particular emphasis is placed on controlling the contamination from excited-states using also the information from chiral perturbation theory to isolate the ground-state contribution. The analysis is performed on CLS ensembles with $N_f =...
Methods based on analyticity, such as Nevanlinna-Pick interpolation, have the promise of providing rigorous constraints on real-time observables (e.g. spectral functions), assuming only causal consistency of the underlying euclidean data. In this talk, I will review recently discovered connections between Nevanlinna-Pick interpolation and moment problems, which provide a discrete euclidean...
We present the strange electromagnetic form factors of the nucleon using lattice QCD with $N_f=2+1+1$ twisted mass clover-improved fermions and quark masses tuned to their physical values. Using four ensembles with lattice spacings of $a=0.080$ fm, $0.068$ fm, $0.057$ fm and $0.049$ fm, and similar physical volume, we obtain the continuum limit directly at the physical point. The disconnected...
Recent advances such as multigrid and deflation have significantly accelerated Dirac operator solves in lattice QCD. However, the substantial setup costs of these methods have impeded their application in the repeated Dirac inversions required for HMC ensemble generation. Building on earlier work at Columbia University, which showed that renormalization-group (RG) blocked coarse lattices with...
Isospin-breaking corrections pose a significant challenge to lattice simulations, both because of the splitting between the up and down quark masses and, in particular, the need to include QED effects. The RC$*$ collaboration has developed the openQxD code, based on openQCD, which enables fully dynamical QCD+QED simulations through the implementation of C-periodic boundary conditions.
We use...
We present a new temperature estimator for lattice gauge theories. This estimator is based on the gradient and Hessian of the Euclidean action. It draws inspiration from geometric methods in statistical mechanics. This approach provides a gauge-invariant and momentum-free way to check thermodynamic consistency in Monte Carlo simulations. Unlike traditional methods, which control temperature...
The R-ratio is a phenomenological observable of great relevance, both in itself and in applications such as the dispersive approach to the muon anomalous magnetic moment. It can be investigated from first-principles in lattice QCD by introducing an arbitrary smearing kernel and employing the well-known Hansen-Lupo-Tantalo method to perform spectral reconstruction with controlled statistical...
We investigate the critical behaviour of a $\mathbb{Z}_2$-symmetric scalar field theory defined on Bethe lattices (the tree limit of regular hyperbolic tessellations) using both lattice perturbation theory and the non-perturbative functional renormalization group. Owing to the hyperbolic nature of such graphs, the Laplacian lacks a zero mode and exhibits a spectral gap, which is an external...
Preliminary results are presented for an implementation of the overlap Dirac operator in lattice QCD based on the diagonal Kenney-Laub (KL) rational approximation to the matrix sign function. Both the Wilson and Brillouin Dirac operators are tested as kernels. As in any other rational approximation, the diagonal KL iterates of order (n,n) can be decomposed into partial fractions with n poles,...
We present the first lattice QCD determination of the Λ→N vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay Λ→pℓνˉ. This channel provides a clean, theoretically controlled avenue for extracting the CKM matrix element ∣Vus∣ from the baryon sector. Our analysis uses a gauge ensemble with physical light, strange, and charm quark masses and yields...
Many observables used to extract Standard Model parameters and to
constrain New Physics in the quark-flavour sector rely on lattice inputs.
I will review the current status and recent developments in these
determinations, with emphasis on controlling dominant sources of
systematic uncertainties.
I will review recent progress in our understanding of hadron structure, with emphasis on lattice-QCD calculations that directly support the scientific goals of the upcoming Electron-Ion Collider (EIC). I will discuss results for pion, kaon, and proton form factors, the computation of Mellin moments, and recent advances in the direct calculation of generalized parton distributions (GPDs). These...
Ensemble generation remains a central challenge in lattice field theory simulations, as traditional MCMC algorithms suffer from long autocorrelation times. Recent advances in generative modeling, including diffusion models, offer accelerated approaches for sampling complicated probability distributions. In this work, we present a diffusion-based framework for sampling ${\rm SU}(N)$ degrees of...
We present new results on semileptonic decays of B-mesons using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. Our calculation uses lattice spacings ranging from 0.12 fm down to 0.03 fm, including several ensembles with physical-mass pions. The focus on the talk will be on the vector and scalar form factors for the decay $B\to\pi\ell\nu$.
The loop-string-hadron (LSH) formulation for lattice gauge theories has been developed in the Hamiltonian framework for application in quantum simulation and tensor-network calculations. A major driver of its development has been eventual application to QCD. The LSH formalism for SU(2) gauge fields was quickly developed for coupling to staggered quarks, in 1D space, and in multidimensional...
The quantum imaginary time evolution (QITE) is a quantum algorithm that approximates imaginary-time evolution using unitary operators.
We apply the QITE to the two-dimensional pure $\mathbb{Z}_2$ lattice gauge theory to obtain the ground state energy. In addition, we estimate the algorithmic and statistical errors and computational costs via classical simulation. It was also shown in the...
The nature of the finite temperature phase transition of QCD depends on the particle density and the mass of the dynamical quarks. It is known that the transition is first order in the region of zero density and heavy quark mass, and also first order in the region of light quark mass when the number of flavors is large. The intermediate region is the crossover region, and numerical simulations...
We present first-principles lattice QCD results for the strangeness $S = -1$ sector of baryon-baryon interactions with the physical masses for the first time. Employing the (2+1)-flavor gauge configurations (HAL-conf-2023) [1] generated on the physical point, $(m_\pi , m_K) = (137, 502)~\mathrm{MeV}$, we calculate baryon-baryon correlation functions using the supercomputer Fugaku and extract...
We present a calculation of the form factors for $B_{(s)} \to D_{(s)} \ell \nu$ decay using the highly improved staggered quark action for both valence and sea quarks on the MILC collaboration’s $2+1+1$-flavor ensembles with lattice spacings ranging from 0.09fm to 0.03fm, many with physical pion masses. On our finest ensembles, we can compute the form factors directly at the physical $b$-quark...
We study the ground state energy of a two-dimensional pure $\mathbb{Z}_2$ lattice gauge theory (LGT) on a triangular lattice by applying the sample-based quantum Krylov diagonalization. Moreover, an error detection and mitigation method based on Gauss’s law constraints is incorporated. We demonstrate this method in the $\mathbb{Z}_2$ LGT using the IBM quantum hardware and classical tensor...
Quantum Link Models with dynamical matter coupled to spin-1/2 U(1) gauge fields in d=2+1 and 3+1 can give rise to phases expected in QED and beyond. Using exact diagonalization techniques, we show that the ground state is always the sector which satisfies (G_e,G_o) = (d,-d), where d is the spatial dimension and e and o are even and odd sites. It can be analytically proven that this sector is...
Real time evolution in QFT poses a severe sign problem, which may be alleviated via a complex Langevin approach.
However, so far simulation results consistently fail to converge with a large real-time extent. A kernel in a complex Langevin equation is known to influence the appearance of the boundary terms and integration cycles, and thus kernel choice can improve the range of real-time...
We present preliminary results on the $I=0$, $S=-2$ $H$ dibaryon in $N_f=2+1$ QCD. The calculation is performed with heavier-than-physical quarks ($m_\pi \approx 280$ MeV) on a single CLS ensemble. Correlation matrices are constructed using the distillation technique and the three relevant channels, $\Lambda\Lambda$, $N\Xi$, $\Sigma\Sigma$, are investigated to determine the interacting...
Strong magnetic fields can profoundly affect the equilibrium properties, characterized by the equation of state and bulk thermodynamics of strongly interacting matter. Although such fields are expected in off-central heavy-ion collisions, directly measuring their experimental imprints remains extremely challenging. To address this, in this talk we propose the baryon-electric charge...
The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. However, its effectiveness relies not only on accessing ground-state energies but also on preparing accurate eigenvectors, and the later is particularly challenging in degenerate and strongly entangled regimes. We investigate this problem using the...
We construct quantum Monte Carlo methods for simple qubit regularized gauge theories in various dimensions that do not suffer from sign problems. Results from these calculations suggest that these theories contain both confined and deconfined phases. Finite temperature phase transitions between these phases show the expected universality classes of traditional gauge theories in various...
We investigate the static-quark entropy in QCD in the presence of external magnetic fields, using its temperature peak as a pseudocritical deconfinement indicator. Our calculations employ HISQ fermions with a tree-level improved Symanzik gauge action at physical quark masses, on lattices with temporal extents $N_\tau = 8, 12$ and fixed aspect ratio $N_\sigma/N_\tau = 4$. A two-dimensional $(T,...
Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavour universality.
Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic
$B_s\to D_s^*\ell\nu_\ell$
decays using the narrow width approximation....
Complex langevin for theories with a sign problem effectively sample from a real-valued probability distribution that is a priori unknown and notoriously hard to predict. In generative AI, diffusion models can learn distributions from data. In this contribution, we investigate their ability to capture the distributions sampled by a complex Langevin process, comparing score-based and...
Excited-state effects lead to hard-to-quantify systematic uncertainties in spectroscopy calculations when imaginary times are smaller than inverse excitation gaps. The recently proposed Lanczos/Rayleigh-Ritz framework provides a set of two-sided constraints on energy levels that hold regardless of the size of excited-state effects. In this talk I discuss the application of these newly...
We employ the wavelet formalism of quantum field theory to study field theories in the nonperturbative Hamiltonian framework. Specifically, we make use of Daubechies wavelets in momentum space. These basis elements are characterised by a resolution and a translation index that provides for a natural nonperturbative infrared and ultraviolet truncation of the quantum field theory. As an...
Approaching the continuum limit in a lattice field theory is an important but computationally difficult problem. Here, on the one side, most traditional Monte Carlo methods suffer from critical slowing down. On the other side, generative models find it increasingly difficult to learn the map from a simpler to the targeted theory.
To tackle this problem, we construct a generative model using...
Theoretical predictions for heavy meson lifetimes require high-precision determinations of the matrix elements involving four-quark operators using non-perturbative methods.
While similar operators relevant for neutral meson mixing have become standard for lattice QCD calculations, these lifetime operators suffer from complications in renormalisation where the dimension-six operators of...
The Harrow–Hassidim–Lloyd (HHL) algorithm offers an exponential quantum speedup for solving sparse, well-conditioned linear systems of equations. We have implemented the HHL algorithm and evaluated its performance across systems of varying sparsity and recorded each class separately with sizes upto $N=1024$.
The principal bottleneck of HHL lies in Quantum Phase Estimation. To address...
We present preliminary results from a lattice QCD study of the lowest energy levels of light nuclei—specifically the deuteron, dineutron, helium-3, and helium-4 systems—and compare those with their respective thresholds for investigating their binding energies. We utilize a set of $N_f=2+1$ flavor gauge ensembles, generated by the HotQCD Collaboration with the HISQ action at the physical sea...
The QCD Anderson transition is believed to be connected to both, confinement and chiral symmetry breaking. We investigate the latter relation by studying the low-lying eigenmodes of the overlap operator in the background of gauge configurations with 2+1+1 quark flavors of twisted-mass Wilson fermions. The mobility edge, below which eigenmodes are localized, is estimated by the inflection point...
Entanglement calculations in quantum field theories are extremely challenging and typically rely on the replica trick, where the problem is rephrased in a study of defects. We demonstrate that the use of deep generative models drastically outperforms standard Monte Carlo algorithms. Remarkably, such a machine-learning method enables high-precision estimates of Rényi entropies in three...
We present an extended version of the k-Shape method, originally developed for time-series clustering, and apply it to lattice simulations of the finite-temperature and finite-density (1+1)-dimensional Gross–Neveu model. The method has been generalized from real to complex scalar fields and from one-dimensional to multidimensional configurations, allowing a detailed analysis of spatially...
In a recent paper [1], we introduced a simplified Lattice Field Theory framework that allows experimental observations from major Brain-Computer Interfaces (BCI) to be interpreted in a simple and physically grounded way. From a neuroscience point of view, our method modifies the Maximum Entropy Model for Neural Networks so that also the time evolution of the system is taken into account, and...
In this talk I will review the status of a calculation of the form factors of the most relevant heavy-to-heavy decay channels. Using seven N_f=2+1+1 HISQ ensembles, with lattice spacings ranging from 0.15 fm down to 0.06 fm, we calculate the form factors of the $B_{(s)}\to D_{(s)}^{(\ast)}\ell\nu$ decays, including correlations among them. More than half of our ensembles feature physical pion...
Drawing upon well established zero-temperature techniques, we present, for the first time, insight into the fate of the $1^{-+}$ exotic charmonium state at finite temperature using anisotropic FASTSUM ensembles. Specifically, we use distillation with a wide operator basis which has been extensively used at zero-temperature by the Hadron Spectrum Collaboration to study the charmonium spectrum....
We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $\pi^+$ and $K^+$, at a lattice spacing $a = 0.063 ,\text{fm}$, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson...
Higher-twist effects reflect the physics of quark-quark and quark-gluon correlations that provide unique insights into the dynamics inside hadrons that goes beyond the parton model. These effects are sub-leading (suppressed by powers of $1/Q^2$) but crucial for quantitative analyses and precision tests of QCD. By their nature higher-twist contributions are non-perturbative. In this...
We present Symplectic Quantization, a novel functional approach to quantum field theory that allows us to sample quantum fluctuations directly in Minkowski space–time, bypassing the limitations of traditional importance sampling techniques restricted to imaginary time. Our method is based on a deterministic dynamics governed by Hamilton-like equations in an auxiliary time parameter $\tau$. We...
Accurately simulating long-time dynamics of quantum many-body systems—whether in real or imaginary time—is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables and ground state properties. I will present a...
Simulating the real-time dynamics of SU(3) strings is one of the major near-term goals for the quantum simulation community. We propose a protocol for an analog quantum simulation of this non-Abelian physics using cold atoms. Based on the Loop-String-Hadron (LSH) framework, our approach maps the SU(3)-invariant dynamics of strings and hadrons onto an SU(3) ionic Fermi-Hubbard model with three...
We present our recent calculation of radiative leptonic decay
rates of the kaon, based on twisted clover simulations at the physical
point carried out by ETM collaboration. The calculation improves
substantially our previous estimate, by improving the stastistcs,
including electrounquenched diagrams, carrying out the continuum
extrapolation on three different lattice spacings and...
The Collins-Soper (CS) kernel may be obtained through the TMD soft function by formulating the Wilson line in terms of 1-dimensional auxiliary fermion fields on the lattice. Our computation takes place in the region of the lattice that corresponds to the “spacelike” region in Minkowski space, i.e., Collins' scheme. We explore two methods for obtaining the CS kernel. The "ratio method"; which...
We introduce Symplectic Quantization, a functional approach to quantum field theory that samples quantum fluctuations directly in Minkowski space–time, bypassing the traditional importance sampling techniques that are restricted to imaginary-time. Our method evolves fields via deterministic Hamilton-like equations in an auxiliary time parameter $\tau$. We prove that the microcanonical...
In this talk, I discuss an ongoing first lattice study of the doubly-charmed tetraquark $T_{cc}^+(3875)$ via a fully three-body approach. We investigate the $DD\pi$ system in the $I = 0$, $C = 2$ sector, where the $T_{cc}^+$ appears as a pole in the $J^P = 1^+$ $DD\pi$ elastic scattering amplitude. The approach automatically incorporates two-body $DD^*$ and three-body $DD\pi$ effects and...
We demonstrate the chaoticity inherent in SU(2) gauge theory consisting of soft momentum modes both in and out-of-thermal equilibrium conditions using lattice techniques. The non-equilibrium state has been realized starting from an over-occupied initial condition for low momentum soft gluons whereas the thermal state comprises of strongly interacting soft gluons at temperatures where these are...
In this work, we explore a numerical approach to performing the inverse Laplace transformation, with an emphasis on stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data smoothing, optimization techniques, and various approaches to regularizing ill-conditioned systems. Together, these elements enable consistency checks that enhance the...
We present an update of the ongoing computation of the isospin-breaking effects in the Pion Decay Constant from the BMW Collaboration. The calculation is carried out with N$_f$=2+1+1 staggered quarks with a near-physical pion mass and QED$_L$. We present some preliminary results of the valence-valence contribution to the axial-pseudoscalar correlator for different volumes $L=4.2, 6.3, 8.4$ fm...
We discuss how a systematic partitioning of the terms in a lattice gauge theory Hamiltonian, with regard to electric-basis discretization, can be done so as to dramatically reduce the number of terms to be simulated in product-formula-based quantum simulation protocols (including Trotterization). Compared to another frequently cited proposal, this simple regrouping can immediately drop at...
We describe the extension of the relativistic field theoretic finite-volume formalism to $N \pi \pi$ scattering states at maximal isospin, $I=5/2$, focusing on the new features that arise in this system.
We illustrate the application of the formalism by providing a sample numerical application that includes the $\Delta$ resonance in the $N\pi$ subchannel.
We study the singularities in...
Quantum simulation of non-Abelian gauge theories like QCD requires an efficient encoding of physical degrees of freedom that respects gauge invariance. The Loop-String-Hadron (LSH) formulation offers a promising path, significantly reducing the number of qubits required to represent the SU(3) invariant states in 1+1 dimensions compared to traditional approaches. While the LSH basis...
Recent software advances now allow large-scale lattice studies of the Corrigan–Ramond large-$N_c$ limit of Yang-Mills theory coupled with a two-index antisymmetric fermion, providing a path to SUSY Yang-Mills. We are currently generating ensembles for $N_c=4,5,6$ for lattice spacings in the range $0.1 - 0.08 \,\mathrm{fm}$, enabling a careful study of cutoff effects and lattice topological...
What is the pattern and mechanisms behind the labyrinthine spectrum of excited hadrons?
Many open questions in this regard hinge on a precise understanding of the three-body dynamics in continuum and in finite-volume settings. One curious case is that of the lightest hadron — the pion — with the mass of 1/7th of that of the nucleon. Its excited state (pi(1300)) is nearly as heavy as the...
We present a lattice QCD calculation of the Collins-Soper kernel, which governs the rapidity evolution of transverse-momentum-dependent (TMD) distributions, using Large Momentum Effective Theory (LaMET). Quasi-TMD wave functions are computed with three meson momenta on CLQCD configurations (multiple lattice spacings) employing clover quarks and varied hadronic states. HYP smearing is applied...
We propose a new and simple method for determining the renormalized quark masses from lattice simulations. Renormalized quark masses are an important input to many phenomenological applications, including searching/modeling physics beyond the Standard Model. The non-perturbative renormalization is performed using gradient flow combined with the short-flow-time expansion that is improved by...
Simulating the real-time dynamics of non-Abelian lattice gauge theories in more than 1+1 dimensions presents a significant computational challenge. We present an exact diagonalization study of 2+1-dimensional SU(2) lattice gauge theory, leveraging the gauge-invariant Loop-String-Hadron (LSH) framework. By harnessing GPU-based computation, we have successfully pushed the classical simulation...
The nature of low-lying scalar and axial-vector charmed mesons has long been debated, specifically whether they are best explained by hadronic molecular or compact tetraquark models. These two models predict quite different features for the accessible SU(3) multiplets in the scalar and axial-vector sectors.
We performed N_f=3+1 lattice simulations and calculate the energy levels of of the...
For decades, the lattice community has successfully extracted fundamental properties of non-abelian gauge theories, like QCD, using the Euclidean path integral formalism and Monte Carlo methods. However, the advent of quantum computation, quantum simulation, and advanced tensor network methods has created new opportunities and demands for a Hamiltonian approach, which is better suited for...
Tensor networks provide novel formulations of lattice field theories, which in turn enable the development of practically efficient renormalization group methods. Unlike conventional Monte Carlo methods, tensor networks are free from the sign problem in principle and can be straightforwardly extended to fermionic systems. We present recent progress in these formulations and numerical...
Special classes of non-supersymmetric, strongly interacting gauge theories provide ultraviolet completions for new physics extensions of the Standard Model that offer potential solutions to key open problems in the energy frontier, including the absence of new physics signatures at energies just above the electroweak scale, the anomalously heavy mass of the top quark, the absence of new flavor...
I review recent progress in calculating scattering amplitudes and resonance properties involving three particles using lattice QCD results for the finite-volume spectrum, coupled with solutions to the associated integral equations. I describe the outlook for future extensions of this work.
