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

May 17, 2022

Published in:

Phys.Rev.D 106 (2022) 3, 034504

Published: Aug 1, 2022

e-Print:

2205.08517 [hep-lat]

DOI:

10.1103/PhysRevD.106.034504 (publication)

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Abstract: (APS)

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential

μ_{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

μ_{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

μ_{B}

was proposed in [Phys. Rev. Lett. 128, 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

μ_{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

μ_{B} \neq 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.

Note:

References updated and manuscript revised to match the journal version

potential: chemical
quantum chromodynamics: equation of state
density: correlation function
isospin: density
potential: thermodynamical
charge: density
Taylor expansion
resummation
cumulant expansion
lattice field theory

References(43)

Figures(4)

[1]

Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium

- Phys.Rev.C 94 (2016) 2, 024907
•
e-Print:
- 1605.03954
•
DOI:
- 10.1103/PhysRevC.94.024907

[2]

QCD equation of state matched to lattice data and exhibiting a critical point singularity

Paolo Parotto
(
- Houston U. and
- Wuppertal U.
)
,
Marcus Bluhm
(
- Wroclaw U. and
- SUBATECH, Nantes
)
,
Debora Mroczek
(
- Houston U.
)
,
Marlene Nahrgang
(
- SUBATECH, Nantes
)
,
Jacquelyn Noronha-Hostler
(
- Illinois U., Urbana
)

et al.

- Phys.Rev.C 101 (2020) 3, 034901
•
e-Print:
- 1805.05249
•
DOI:
- 10.1103/PhysRevC.101.034901

[3]

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

Akihiko Monnai
(
- KEK, Tsukuba
)
,
Björn Schenke
(
- Brookhaven
)
,
Chun Shen
(
- Wayne State U. and
- RIKEN BNL
)

- Phys.Rev.C 100 (2019) 2, 024907
•
e-Print:
- 1902.05095
•
DOI:
- 10.1103/PhysRevC.100.024907

[4]

Multisystem Bayesian constraints on the transport coefficients of QCD matter

JETSCAPE

Collaboration

•

D. Everett
(
- Ohio State U.
)

et al.

- Phys.Rev.C 103 (2021) 5, 054904
•
e-Print:
- 2011.01430
•
DOI:
- 10.1103/PhysRevC.103.054904

[5]

Finite-density lattice QCD and sign problem: Current status and open problems

Keitaro Nagata
(
- Kyoto U., Yukawa Inst., Kyoto
)

- Prog.Part.Nucl.Phys. 127 (2022) 103991
•
e-Print:
- 2108.12423
•
DOI:
- 10.1016/j.ppnp.2022.103991

[5]

Simulating QCD at finite density

Philippe de Forcrand
(
- Zurich, ETH and
- CERN
)

- PoS LAT2009 (2009) 010
•
e-Print:
- 1005.0539
•
DOI:
- 10.22323/1.091.0010

[6]

Can complex Langevin dynamics evade the sign problem?

Gert Aarts
(
- Swansea U.
)

- PoS LAT2009 (2009) 024
•
e-Print:
- 0910.3772
•
DOI:
- 10.22323/1.091.0024

[7]

New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble

AuroraScience

Collaboration

•

Marco Cristoforetti
(
- ECT, Trento
)

et al.

- Phys.Rev.D 86 (2012) 074506
•
e-Print:
- 1205.3996
•
DOI:
- 10.1103/PhysRevD.86.074506

[8]

Controlling complex Langevin dynamics at finite density

Gert Aarts
(
- Swansea U.
)
,
Lorenzo Bongiovanni
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Denes Sexty
(
- Heidelberg U.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U. and
- Heidelberg, FEST
)

- Eur.Phys.J.A 49 (2013) 89
•
e-Print:
- 1303.6425
•
DOI:
- 10.1140/epja/i2013-13089-4

[9]

Simulating full QCD at nonzero density using the complex Langevin equation

Dénes Sexty
(
- U. Heidelberg, ITP
)

- Phys.Lett.B 729 (2014) 108-111
•
e-Print:
- 1307.7748
•
DOI:
- 10.1016/j.physletb.2014.01.019

[10]

Implementation of the HMC algorithm on the tempered Lefschetz thimble method

e-Print:
- 1912.13303

[11]

Higher order fluctuations and correlations of conserved charges from lattice QCD

Szabolcs Borsanyi
(
- Wuppertal U.
)
,
Zoltan Fodor
(
- Wuppertal U. and
- Eotvos U. and
- IAS, Julich
)
,
Jana N. Guenther
(
- Wuppertal U. and
- Regensburg U.
)
,
Sandor K. Katz
(
- Regensburg U.
)
,
Kalman K. Szabo
(
- Wuppertal U. and
- IAS, Julich
)

et al.

- JHEP 10 (2018) 205
•
e-Print:
- 1805.04445
•
DOI:
- 10.1007/JHEP10(2018)205

[12]

Lattice QCD and heavy ion collisions: a review of recent progress

Claudia Ratti
(
- Houston U.
)

- Rept.Prog.Phys. 81 (2018) 8, 084301
•
e-Print:
- 1804.07810
•
DOI:
- 10.1088/1361-6633/aabb97

[13]

The QCD Equation of State to $\mathcal{O}(\mu_B^6)$ from Lattice QCD

A. Bazavov
(
- Michigan State U.
)
,
H. -T. Ding
(
)
,
P. Hegde
(
- Bangalore, Indian Inst. Sci.
)
,
O. Kaczmarek
(
)
,
F. Karsch
(
- Bielefeld U. and
- Brookhaven
)

et al.

- Phys.Rev.D 95 (2017) 5, 054504
•
e-Print:
- 1701.04325
•
DOI:
- 10.1103/PhysRevD.95.054504

[14]

Second order cumulants of conserved charge fluctuations revisited: Vanishing chemical potentials

HotQCD

Collaboration

•

D. Bollweg
(
- Bielefeld U.
)

et al.

- Phys.Rev.D 104 (2021) 7, 074512
•
e-Print:
- 2107.10011
•
DOI:
- 10.1103/PhysRevD.104.074512

[15]

QCD at finite chemical potential with six time slices

R.V. Gavai
(
- Tata Inst.
)
,
Sourendu Gupta
(
- Tata Inst.
)

- Phys.Rev.D 78 (2008) 114503
•
e-Print:
- 0806.2233
•
DOI:
- 10.1103/PhysRevD.78.114503

[16]

Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD

P. Dimopoulos
(
- U. Parma (main) and
- INFN, Parma
)
,
L. Dini
(
- Bielefeld U.
)
,
F. Di Renzo
(
- U. Parma (main) and
- INFN, Parma
)
,
J. Goswami
(
- Bielefeld U.
)
,
G. Nicotra
(
- Bielefeld U.
)

et al.

- Phys.Rev.D 105 (2022) 3, 034513
•
e-Print:
- 2110.15933
•
DOI:
- 10.1103/PhysRevD.105.034513

[17]

Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials

HotQCD

Collaboration

•

D. Bollweg
(
- Columbia U.
)

et al.

- Phys.Rev.D 105 (2022) 7, 074511
•
e-Print:
- 2202.09184
•
DOI:
- 10.1103/PhysRevD.105.074511

[18]

Reliable estimation of the radius of convergence in finite density QCD

- Phys.Rev.D 99 (2019) 11, 114510
•
e-Print:
- 1904.01974
•
DOI:
- 10.1103/PhysRevD.99.114510

[19]

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions

- Phys.Rev.Lett. 128 (2022) 2, 022001
•
e-Print:
- 2106.03165
•
DOI:
- 10.1103/PhysRevLett.128.022001

[20]

Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

Swagato Mukherjee
(
- Brookhaven Natl. Lab.
)
,
Fabian Rennecke
(
- Brookhaven Natl. Lab. and
- Giessen U.
)
,
Vladimir V. Skokov
(
- North Carolina State U. and
- RIKEN BNL
)

- Phys.Rev.D 105 (2022) 1, 014026
•
e-Print:
- 2110.02241
•
DOI:
- 10.1103/PhysRevD.105.014026

[22]

QCD at finite isospin density

D.T. Son
(
- Columbia U. and
- RIKEN BNL
)
,
Misha A. Stephanov
(
- Illinois U., Chicago and
- RIKEN BNL
)

- Phys.Rev.Lett. 86 (2001) 592-595
•
e-Print:
- hep-ph/0005225
•
DOI:
- 10.1103/PhysRevLett.86.592

[23]

Magnetic structure of isospin-asymmetric QCD matter in neutron stars

G. Endrödi
(
- Regensburg U.
)

- Phys.Rev.D 90 (2014) 9, 094501
•
e-Print:
- 1407.1216
•
DOI:
- 10.1103/PhysRevD.90.094501

[24]

QCD phase diagram for nonzero isospin-asymmetry

- Phys.Rev.D 97 (2018) 5, 054514
•
e-Print:
- 1712.08190
•
DOI:
- 10.1103/PhysRevD.97.054514

[25]

Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

- Eur.Phys.J.C 81 (2021) 2, 173
•
e-Print:
- 2010.13655
•
DOI:
- 10.1140/epjc/s10052-021-08948-6

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