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 μ_{B} is a wellknown 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 μ_{B}. Recently, a way to resum the contribution of the first N charge density correlation functions D_{1},…,D_{N} to the Taylor series to all orders in μ_{B} was proposed in [Phys. Rev. Lett. 128, 022001 (2022), 10.1103/PhysRevLett.128.022001]. 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 μ_{B}. In this paper, we present a new method to calculate the QCD equation of state based on the wellknown 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 μ_{B}≠0 , here we present it for the simpler case of a finite isospin chemical potential μ_{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.
 Publication:

Physical Review D
 Pub Date:
 August 2022
 DOI:
 10.1103/PhysRevD.106.034504
 arXiv:
 arXiv:2205.08517
 Bibcode:
 2022PhRvD.106c4504M
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Nuclear Experiment;
 Nuclear Theory
 EPrint:
 References updated and manuscript revised to match the journal version