TY - JOUR

T1 - Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential

AU - Vovchenko, Volodymyr

AU - Pásztor, Attila

AU - Fodor, Zoltán

AU - Katz, Sandor D.

AU - Stoecker, Horst

N1 - Funding Information:
We are grateful to Szabolcs Borsányi for stimulating discussions and for his help with the lattice data. This work was supported by HIC for FAIR within the LOEWE program of the State of Hesse. V.V. acknowledges the support from HGS-HIRe for FAIR . H.St. acknowledges the support through the Judah M. Eisenberg Laureatus Chair at Goethe University . This project was funded by the DFG grant SFB/TR55 . This research used resources of the Argonne Leadership Computing Facility , which is a DOE Office of Science User Facility supported under Contract DEAC02-06CH11357 . The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time for a GCS Large-Scale Project on the GCS share of the supercomputer JUQUEEN [70] at Jülich Supercomputing Centre (JSC), and at HazelHen supercomputer at HLRS, Stuttgart. Appendix A This appendix presents the calculation of the Fourier coefficients b k ( T ) in the Fourier expansion of the net baryon susceptibility χ 1 B at an imaginary baryochemical potential (4) for the vdW-HRG model [11] . In the vdW-HRG model, the attractive and repulsive baryonic interactions are described by the van der Waals equation, with common a and b parameters for all baryons. For a = 0 this model reduces to the EV-HRG model in Sec. 3.2 . Following results of Ref. [11] , in the Boltzmann approximation one has the following transcendental equations for n B vdw and n B ¯ vdw (24) n B vdw = ( 1 − b n B vdw ) λ B ϕ B ( T ) exp ( − b n B vdw 1 − b n B vdw ) × exp ( 2 a n B vdw T ) , (25) n B ¯ vdw = ( 1 − b n B ¯ vdw ) λ B − 1 ϕ B ( T ) exp ( − b n B ¯ vdw 1 − b n B ¯ vdw ) × exp ( 2 a n B ¯ vdw T ) . The calculation of the coefficients b k vdw proceeds in essentially the same way as it was done for the EV-HRG model. One assumes the fugacity expansions for n B ( B ¯ ) vdw in the form (11) – (12) , and calculates the b k vdw by plugging in the fugacity expansion into Eq. (24) . The result is (26) b 1 vdw ( T ) = 2 ϕ B ( T ) T 3 , (27) b 2 vdw ( T ) = − 4 ( b − a T ) ϕ B ( T ) ϕ B ( T ) T 3 , (28) b 3 vdw ( T ) = 9 ( b 2 − 8 3 a b T + 4 3 a 2 T 2 ) [ ϕ B ( T ) ] 2 ϕ B ( T ) T 3 , (29) b 4 vdw ( T ) = − 64 3 ( b 3 − 39 8 a b 2 T + 6 a 2 b T 2 − 2 a 3 T 3 ) × [ ϕ B ( T ) ] 3 ϕ B ( T ) T 3 .

PY - 2017/12/10

Y1 - 2017/12/10

N2 - The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potential – corresponding to the fugacity or virial expansion at real chemical potential – are calculated within this model, and compared with the Nt=12 lattice data. The lattice QCD behavior of the first four Fourier coefficients up to T≃185 MeV is described fairly well by an interacting HRG with a single baryon–baryon eigenvolume interaction parameter b≃1 fm3, while the available lattice data on the difference χ2 B−χ4 B of baryon number susceptibilities is reproduced up to T≃175 MeV.

AB - The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potential – corresponding to the fugacity or virial expansion at real chemical potential – are calculated within this model, and compared with the Nt=12 lattice data. The lattice QCD behavior of the first four Fourier coefficients up to T≃185 MeV is described fairly well by an interacting HRG with a single baryon–baryon eigenvolume interaction parameter b≃1 fm3, while the available lattice data on the difference χ2 B−χ4 B of baryon number susceptibilities is reproduced up to T≃175 MeV.

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U2 - 10.1016/j.physletb.2017.10.042

DO - 10.1016/j.physletb.2017.10.042

M3 - Article

AN - SCOPUS:85036629173

VL - 775

SP - 71

EP - 78

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

ER -