A new way of determining the Lattice QCD equation of state at a finite chemical potential

TL;DR

This paper introduces an unbiased cumulant expansion method for resumming Taylor series in lattice QCD at finite chemical potential, improving accuracy and reliability over previous biased resummation techniques.

Contribution

It presents a novel cumulant expansion approach that regulates biased estimates and exactly reproduces Taylor series, enhancing the calculation of thermodynamic observables in lattice QCD.

Findings

Unbiased estimates capture genuine stochastic fluctuations.

The formalism exactly reproduces Taylor series to desired order.

Reweights and properties of the partition function are recovered.

Abstract

The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $\mu_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision in calculating these high-ordered Taylor coefficients, it becomes essential to look for various resummation schemes which can mitigate the computational cost, besides providing trustworthy estimates of different thermodynamic observables. Recently, a way to exponentially resum the contribution of the first $N$ charge density correlation functions $D_1,\dots,D_N$ to the Taylor series to all orders in $\mu_B$ was proposed in Phys. Rev. Lett. 128, 2, 022001 (2022). Since the correlation functions $D_n$ are calculated stochastically using estimates from different random volume sources, the resummation formulation gets affected by the biased estimates. These estimates can become very drastic and can radically misdirect the calculations for large values of $N$ and $\mu$ and also for observables which are higher order $\mu$ derivatives of free energy, specially at lower temperatures. In this work, we present a cumulant expansion procedure that allows to investigate and regulate these biased estimates at different orders in $\mu$. 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 by the exponential resummation formulation. Finally, we discover an unbiased formalism of the exponential resummation, which when expanded in a series, can exactly reproduce the Taylor series upto a desired power in $\mu$. We are also able to regain the knowledge of reweighting factor and many other important properties of the partition function, which got entirely lost through the implementation of cumulant expansion scheme.