New way to resum the lattice QCD Taylor series equation of state at finite chemical potential

A new way to resum Lattice QCD equation of state at finite chemical potential

“…1, the biased and unbiased results of pressure and number density are in good agreement with the resummed and QNS results of similar orders respectively. The unbiased cumulants managed to capture more higher-order fluctuations, which got suppressed by the exponential behaviour of the resummed series [28]. The unbiased cumulant expansion results hence, demonstrated that the difference between the resummed and QNS results is attributable to the difference between biased and unbiased estimates.…”

“…We then comprehensively discuss about the emergence of biased estimates in exponential resummation, which has the potential to become highly problematic in the regime of large values and higher orders of 𝜇. We then come across the formulation of cumulant expansion [28][29][30][31][32], which allows an order-by-order analysis of biased estimates, but unfortunately at the cost of the reweighting factor and hence, the invaluable partition function itself. Finally, we present an unbiased formulation of exponential resummation, which reproduces the Taylor (QNS) expansion upto a given order of 𝜇 apart from a newly defined reweighting factor and partition function altogether.…”

The isentropic equation of state of (2+1)-flavor QCD: An update based on high precision Taylor expansion and Pade-resummed expansion at finite chemical potentials

“…The 's and 's (where = 1, 3, 5) can be used to create all expansion coefficients of the bulk thermodynamic observables, as shown by Eq. (9)(10)(11)(12). The functional forms of the 's and 's are defined as follows:…”

“…Currently, the most commonly used methods for determining the EoS at non-vanishing chemical potentials are Taylor expansion and analytic continuation, both of which have their own strengths and limitations. Taylor expansion, analytic continuation and various resummation technique have been used recently to analyze the EoS at non-vanishing values of the chemical potentials for baryon number, electric charge, and strangeness in previous lattice QCD calculations [8][9][10][11][12][13][14].…”

QCD thermodynamics: an overview of recent progress

“…Moreover, several resummation schemes for the Taylor expansion with (empirically observed) better convergence properties have been proposed. There were several contributions at this year's lattice conference reporting progress in these directions [68,69] and results are published in several papers [66,[70][71][72][73][74]. In Fig.…”