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Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow

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 Added by Kazuyuki Kanaya
 Publication date 2017
  fields
and research's language is English




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We study the energy-momentum tensor and the equation of state as well as the chiral condensate in (2+1)-flavor QCD at the physical point applying the method of Makino and Suzuki based on the gradient flow. We adopt a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. At Lattice 2016, we have presented our preliminary results of our study in (2+1)-flavor QCD at a heavy u, d quark mass point. We now extend the study to the physical point and perform finite-temperature simulations in the range T simeq 155--544 MeV (Nt = 4--14 including odd Nts) at a simeq 0.09 fm. We show our final results of the heavy QCD study and present some preliminary results obtained at the physical point so far.



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We study thermodynamic properties of 2+1 flavor QCD applying the Small Flow-time eXpansion (SFtX) method based on the gradient flow. The method provides us with a general way to compute correctly renormalized observables irrespective of explicit violation of symmetries due to the regularization, such as the Poincare and chiral symmetries on the lattice. We report on the status of our on-going project to compute the energy-momentum tensor and the chiral condensate at the physical point with improved Wilson quarks, extending our previous study with slightly heavy u and d quarks. We also report on our test of two-loop matching coefficients recently calculated by Harlander et al., revisiting the case of QCD with slightly heavy u and d quarks. Our results suggest that the SFtX method is powerful in extracting physical observables on the lattice.
The energy-momentum tensor and equation of state are studied in finite-temperature (2+1)-flavor QCD with improved Wilson quarks using the method proposed by Makino and Suzuki based on the gradient flow. We find that the results of the gradient flow are consistent with the previous results using the $T$-integration method at $T mathrel{rlap{raise 0.511ex hbox{$<$}}{lower 0.511ex hbox{$sim$}}} 280$ MeV ($N_tmathrel{rlap{raise 0.511ex hbox{$>$}}{lower 0.511ex hbox{$sim$}}}10$), while a disagreement is found at $T mathrel{rlap{raise 0.511ex hbox{$>$}}{lower 0.511ex hbox{$sim$}}} 350$ MeV ($N_t mathrel{rlap{raise 0.511ex hbox{$<$}}{lower 0.511ex hbox{$sim$}}} 8$) presumably due to the small-$N_t$ lattice artifact. We also report on the results on the renormalized chiral condensate and its disconnected susceptibility using the method of Hieda and Suzuki. The results show a clear signal of the expected chiral restoration crossover even with Wilson-type quarks which violate the chiral symmetry explicitly.
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We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-$N_t$ approach, it is easy to keep scaling violations small at low temperature in the fixed scale approach. We study 2+1 flavor QCD at light quark mass corresponding to $m_pi/m_rho simeq 0.63$, while the strange quark mass is chosen around the physical point. Although the light quark masses are heavier than the physical values yet, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large $N_t$.
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