Determination of vector interaction from lattice QCD...
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0 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 μ [GeV] w/ G V w/o G V • The quark number density is normalized by the Stefan- Boltzmann (SB) limit. • The two arrows show the values of at T/T c =1.20 and 1.35 in the limit of μ q =0. Aim Determination of vector interaction from lattice QCD results at imaginary chemical potential Imaginary chemical potential region Lattice action - Renormalization group improved Iwasaki gauge action - Wilson + clover fermion action (two flavors) Set up - Lattice size : N x × N y × N z × N τ ＝8 × 8 × 16 × 4 - m ps /m v =0.8 line of constant physics [2] - Temperature : T/T c = 1.20, 1.35 - Imaginary chemical potential (μ I ) : μ I /T = 0〜π/3 - Configurations : 360 every 100 trajectories Lattice set up Two-phase model Summary Results Junichi Takahashi 1 , Junpei Sugano 1 , Masahiro Ishii 1 , Hiroaki Kouno 2 , Masanobu Yahiro 1 Kyushu University 1 , Saga University 2 [2]Y. Maezawa, et al. (WHOT-QCD Collaboration), Phys. Rev. D75 (2007) 074501. • LQCD has no sign problem at imaginary μ q . RW periodicity [1] QCD phase diagram at imaginary μ q ・The Roberge-Weiss (RW) transition line (blue solid lines) ・The RW endpoint (red points) ・The deconfinement transition line (blue dashed lines) ・The red arrows represent simulation points at this time. (Please see “Lattice set up” in detail.) confinement phase deconfinement phase • We construct a reliable effective model consistent with lattice QCD (LQCD) results at imaginary chemical potential (μ q ) in order to study high-density physics such as neutron stars (NSs). • The QCD phase diagram at high densities is quite sensitive to the strength (G V ) of the vector interaction. The strength G V is determined from the magnitude of the quark number density (n q ) which is finite only at finite μ q . • We then calculate n q with LQCD at imaginary μ q and determine the strength G V from the calculated n q . Finally, we predict the QCD phase diagram at high densities and the mass-radius relation of neutron stars. [1]A. Roberge and N. Weiss, Nucl. Phys. B275 (1986) 734. • In order to treat the quark-hadron phase transition, we take the two-phase model in which the EPNJL model is used for the quark phase and the Walecka model is taken for the hadron phase. In this model, the transition is assumed to be the first order phase transition. Quark phase Polyakov loop extended NJL model with entanglement vertex (EPNJL model) [3] - The effective potential is determined from pure gauge LQCD results. - The EPNJL model is consistent with LQCD results for the order parameter, the thermodynamic quantities [3,4,5] and the screening masses [6]. - In this work, is determined to reproduce n q calculated with LQCD. α 3 [3]Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, Phys. Rev. D82 (2010) 076003. [4]Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, J. Phys. G39 (2012) 035004. [5]R. Gatto and M. Ruggieri, Phys. Rev. D83 (2011) 034016. [6]M. Ishii, T. Sasaki, K. Kashiwa, H. Kouno, and M. Yahiro, Phys. Rev. D 89 (2014) 071901. [7]G. A. Lalazissis, J. Konig, and P. Ring, Phys. Rev. C 55 (1997) 540. Hadron phase Quantum hadrodynamics (QHD) model (Walecka model) [7] - The Walecka model reproduces nuclear saturation properties. μ I dependence of Mass-Radius relation of NSs QCD phase diagram • We have determined the strength of the vector interaction in the EPNJL model from calculated by LQCD simulations at imaginary μ q . • We have found that is most preferable to reproduce LQCD results for T dependence of in the limit of μ q =0. • At high density, the present model prediction is consistent with the 2M sol observations of NSs. • There may exist the quark-hadron mixed phase in the NS with two solar masses. • Using the present model, we have explored the hadron-quark phase transition in the μ B -T plane. The critical chemical potential at T=0 is μ B (c) ~ 1.6[GeV]. n q / n SB α 3 = 0.33 [8]S. Ejiri, et al.(WHOT-QCD Collaborations), Phys. Rev. D82 (2010) 014508. [9]B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, and J.W.T. Hessels, Nature 467 (2010) 1081. [10]T. Sasaki, N. Yasutake, M. Kohno, H. Kouno, and M. Yahiro, arXiv:1307.0681[hep-ph]. n q / n SB T dependence of in the limit of μ=0 n q / n SB Table 1 : The values of in the limit of μ q =0. n q / n SB n q / n SB • Our LQCD results are consistent with the previous results [8]. • The blue dotted line and the red line are the results of the EPNJL model without G V and with G V , respectively. • The EPNJL model with G V has good agreement with the LQCD results, when . α 3 = 0.33 n q / n SB 0.5 1 1.5 2 2.5 3 4 6 8 10 12 14 16 18 20 M/M sol R [km] Demorest w/o vector w/ vector 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1.6 1.8 2 T/T Ejiri, et al.(2010) Lattice data EPNJL w/ G V EPNJL w/o G V 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 μ /T T/T c =1.20 T/T c =1.35 • This relation is obtained by solving the Tolman-Oppenheimer-Volkoff equation with the equation of state calculated by the present model. • This result is consistent with the NS observations[9]. • There may exist the quark-hadron mixed phase in the NS with two solar masses. ※M sol : Solar mass • The red line and the blue dotted line are the results of the present calculations with and without G V , respectively, for the quark-hadron transition lines. • The critical chemical potential at T=0 is μ B (c) ~1.6[GeV] consistent with the previous study [10]. ※μ B : Baryon chemical potential, μ B =3μ q
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0
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
T [G
eV]
µB [GeV]
w/ GVw/o GV
• The quark number density is normalized by the Stefan-Boltzmann (SB) limit.
• The two arrows show the values of at T/Tc=1.20 and 1.35 in
the limit of µq=0.
Aim
Determination of vector interaction from lattice QCD results at imaginary chemical potential
Imaginary chemical potential region
Lattice action!- Renormalization group improved Iwasaki gauge action - Wilson + clover fermion action (two flavors)
Set up!- Lattice size : Nx × Ny × Nz × Nτ＝8 × 8 × 16 × 4 - mps/mv=0.8 line of constant physics [2]
- Temperature : T/Tc = 1.20, 1.35 - Imaginary chemical potential (µI) : µI/T = 0〜π/3
- Configurations : 360 every 100 trajectories
Lattice set up
Two-phase model
Summary
Results
Junichi Takahashi1, Junpei Sugano1, Masahiro Ishii1, Hiroaki Kouno2, Masanobu Yahiro1
Kyushu University1, Saga University2
[2]Y. Maezawa, et al. (WHOT-QCD Collaboration), Phys. Rev. D75 (2007) 074501.
• LQCD has no sign problem at imaginary µq.
RW periodicity [1]"
ü QCD phase diagram at imaginary µq ・The Roberge-Weiss (RW) transition line (blue solid lines) ・The RW endpoint (red points) ・The deconfinement transition line (blue dashed lines) ・The red arrows represent simulation points at this time. (Please see “Lattice set up” in detail.)
confinement phase
deconfinement phase
• We construct a reliable effective model consistent with lattice QCD (LQCD) results at imaginary chemical potential (µq) in order to study high-density physics such as neutron stars (NSs).
• The QCD phase diagram at high densities is quite sensitive to the strength (GV) of the vector interaction. The strength GV is determined from the magnitude of the quark number density (nq) which is finite only at finite µq.
• We then calculate nq with LQCD at imaginary µq and determine the strength GV from the calculated nq. Finally, we predict the QCD phase diagram at high densities and the mass-radius relation of neutron stars.
[1]A. Roberge and N. Weiss, Nucl. Phys. B275 (1986) 734.
• In order to treat the quark-hadron phase transition, we take the two-phase model in which the EPNJL model is used for the quark phase and the Walecka model is taken for the hadron phase. In this model, the transition is assumed to be the first order phase transition.
Quark phase!Polyakov loop extended NJL model with entanglement vertex (EPNJL model) [3] """
- The effective potential is determined from pure gauge LQCD results. - The EPNJL model is consistent with LQCD results for the order parameter, the
thermodynamic quantities [3,4,5] and the screening masses [6]. - In this work, is determined to reproduce nq calculated with LQCD. α3
[3]Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, Phys. Rev. D82 (2010) 076003. [4]Y. Sakai, T. Sasaki, H. Kouno, and M. Yahiro, J. Phys. G39 (2012) 035004. [5]R. Gatto and M. Ruggieri, Phys. Rev. D83 (2011) 034016. [6]M. Ishii, T. Sasaki, K. Kashiwa, H. Kouno, and M. Yahiro, Phys. Rev. D 89 (2014) 071901. [7]G. A. Lalazissis, J. Konig, and P. Ring, Phys. Rev. C 55 (1997) 540.
Hadron phase!Quantum hadrodynamics (QHD) model (Walecka model) [7]
- The Walecka model reproduces nuclear saturation properties.
μI dependence of ! !!
Mass-Radius relation of NSs"
QCD phase diagram"
• We have determined the strength of the vector interaction in the EPNJL model from calculated by LQCD simulations at imaginary µq.
• We have found that is most preferable to reproduce LQCD results for T dependence of in the limit of µq=0.
• At high density, the present model prediction is consistent with the 2Msol observations of NSs.
• There may exist the quark-hadron mixed phase in the NS with two solar masses. • Using the present model, we have explored the hadron-quark phase transition in the
µB-T plane. The critical chemical potential at T=0 is µB(c) ~ 1.6[GeV].
nq / nSBα3 = 0.33
[8]S. Ejiri, et al.(WHOT-QCD Collaborations), Phys. Rev. D82 (2010) 014508. [9]B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, and J.W.T. Hessels, Nature 467 (2010) 1081. [10]T. Sasaki, N. Yasutake, M. Kohno, H. Kouno, and M. Yahiro, arXiv:1307.0681[hep-ph].
nq / nSB
T dependence of! ! !in the limit of μ=0!
nq / nSB
Table 1 : The values of in the limit of µq=0. nq / nSB
nq / nSB• Our LQCD results are consistent
with the previous results [8]. • The blue dotted line and the red
line are the results of the EPNJL model without GV and with GV, respectively.
• The EPNJL model with GV has good agreement with the LQCD results, when . α3 = 0.33
nq / nSB
0.5
1
1.5
2
2.5
3
4 6 8 10 12 14 16 18 20
M/M
sol
R [km]
Demorestw/o vector
w/ vector
0
0.2
0.4
0.6
0.8
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2
n q/n
SB
T/Tc
Ejiri, et al.(2010)Lattice data
EPNJL w/ GVEPNJL w/o GV
0.4
0.5
0.6
0 0.2 0.4 0.6 0.8 1
n q/n
SB
µI/T
T/Tc=1.20T/Tc=1.35
• This relation is obtained by solving the Tolman-Oppenheimer-Volkoff equation with the equation of state calculated by the present model.
• This result is consistent with the NS observations[9].
• There may exist the quark-hadron mixed phase in the NS with two solar masses.
※Msol : Solar mass
• The red line and the blue dotted line are the results of the present calculations with and without GV, respectively, for the quark-hadron transition lines.
• The critical chemical potential at T=0 is µB
(c)~1.6[GeV] consistent with the previous study [10].
※µB : Baryon chemical potential, µB=3µq
