New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential

Abstract

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential ${\mu }_B$ is a well-known method to bypass the Sign Problem of Lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of ${\mu }_B$. Recently, a way to 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). The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large $N$ and ${\mu }_B$. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order $M$, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for ${\mu }_B\ne 0$, here we present it for the simpler case of a finite isospin chemical potential ${\mu }_I$ for which there is no Sign Problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

References updated and manuscript revised to match the journal version

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• Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice
• A new way of determining the Lattice QCD equation of state at a finite chemical potential
• The phases of QCD reached in terrestrial and cosmic colliders