The QCD equation of state at finite density from analytical continuation

We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness based on the results of lattice QCD simulations and the hadron resonance gas model. The situation of strangeness neutrality and a fixed charge-to-baryon ratio, which resembles that of heavy nuclei, is considered for the application to relativistic heavy-ion collisions. This increases the values of baryon chemical potential compared to the case of vanishing strangeness and electric charge chemical potentials, modifying the fireball trajectory in the phase diagram. We perform viscous hydrodynamic simulations and demonstrate the importance of multiple chemical potentials for identified particle production in heavy-ion collisions at the RHIC and SPS beam energy scan energies.

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“…GeV, respectively [11]. One can see that the region of least reliability where µ B /T > 3 above T c tends to be avoided.…”

Section: Numerical Resultsmentioning

confidence: 88%

Equation of state at finite densities for QCD matter in nuclear collisions

2019

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“…While a solution of the sign problem is still lacking, several techniques have been developed to bypass it, including Taylor expansion at µ B = 0 [8][9][10][11][12][13][14][15][16], analytic continuation from imaginary chemical potential [17][18][19][20][21][22][23][24][25][26][27][28][29][30], and reweighting methods [31][32][33][34][35][36]. The basic idea of these methods is to reconstruct the behavior of the theory at finite real chemical potential, where standard simulations are not feasible, by extrapolating from zero or purely imaginary chemical potential, where the sign problem is absent.…”

Section: Introductionmentioning

confidence: 99%

Radius of convergence in lattice QCD at finite μB with rooted staggered fermions

et al. 2020

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In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity e µ T . The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around µ = 0. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We show that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted staggered operator. We suggest a new definition of the rooted staggered determinant at finite chemical potential that allows for a definition of a Lee-Yang polynomial, and therefore of the numerical study of Lee-Yang zeros. We also describe an algorithm to determine the Lee-Yang zeros and apply it to configurations generated with the 2-stout improved staggered action at Nt = 4. We perform a finite volume scaling study of the leading Lee-Yang zeros and estimate the radius of convergence of the Taylor expansion extrapolated to an infinite volume. We show that the limiting singularity is not on the real line, thus giving a lower bound on the location of any possible phase transitions at this lattice spacing. In the vicinity of the crossover temperature at zero chemical potential, the radius of convergence turns out to be at µ B T ≈ 2 and roughly temperature independent.

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“…The next step in our investigation of the phase diagram is the determination of the equation of state [9,10]. In [11] the coefficients c 2 to c 6 were presented on N t = 6 and N t = 8 lattices.…”

Section: The Equation Of Statesmentioning

confidence: 99%

“…. One option to account for this terms is the use of different fit functions as done in our original analysis in [9,10]. However to…”

Section: The Equation Of Statesmentioning

confidence: 99%