Speaker
Description
The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $\mu_B$ is a well-known approach to circumvent the fermion sign problem. The reliability of a Taylor estimate is determined by the radius of convergence, a reasonable estimate of which requires sufficiently higher order calculations in $\mu_B$. But, owing to the associated difficulty and limitations of precision in calculating these higher-order Taylor coefficients, it becomes essential to look for various alternative expansion schemes. Exponential Resummation to all orders in $\mu_B$ is one such promising alternative scheme, which has been recently proposed in Phys. Rev. Lett. 128, 022001 (2022). Unfortunately, the resummation formulation gets affected by the appearance of biased estimates. The effects from these estimates can become very drastic and can radically misdirect the calculations for higher values and orders of $\mu$ and also with increasing order of $\mu$ derivatives of free energy. In this work, we present a cumulant expansion procedure that allows to investigate and regulate these biased estimates at different orders in isospin chemical potential $\mu_I$. We find that the unbiased estimates in the cumulant expansion can truly capture the genuine higher order stochastic fluctuations of the higher order correlation functions, which got suppressed in exponential resummation. Finally, we discuss an unbiased formalism of the exponential resummation, which when expanded in form of a series, can exactly replicate the Taylor series up to a desired power in $\mu_B$. This enables us to regain the knowledge of reweighting factor and most importantly, retrieve back the partition function and many of its important properties, which got entirely lost while implementing the cumulant expansion scheme.
| Session | Heavy Ions and QCD |
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