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Description
Nonrelativistic (NR) bound states have been at the root of the development of quantum physics and have triggered several revolutions. They are ubiquitous in physics from the high energy to the low energy domain and play a key role in several open challenges at the frontier of particle physics research. They are endowed with a pattern of separated energy scales that qualifies them as special probes for complex environments. This pattern of scales has made their description in quantum field theory particularly difficult up to the advent of Nonrelativistic Effective Field Theories (NREFT). In this talk, I present how to construct a pNREFT (potential Nonrelativistic Effective Field Theory) description that directly addresses the bound state dynamics, implements the Schroedinger equation as zero order problem, properly defines the potentials as matching coefficients, and allows to systematically calculate relativistic and retardation corrections. In this way, quantum mechanics can be properly reinterpreted as a pNREFT.
Focusing on QCD and heavy quarkonia, I show the impact of pNRQCD in allowing precise calculations of bound state properties and a systematic
factorization of short and long range contributions, the latest in the form of gauge-invariant correlators to be evaluated on the lattice.
Generalisations of the pNREFT description can be used to address exotics NR bound states like the X Y Z. Also the out-of-equilibrium evolution of NR bound states in a hot medium (quarkonium in the Quark Gluon Plasma, dark matter in the Early Universe) can be addressed combining the pNREFT with an open quantum system description.
