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Register a new userTopological susceptibility in 2+1-flavor QCD with chiral fermions
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We compute the topological susceptibility $chi_t$ of 2+1-flavor lattice QCD with dynamical Mobius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a slab sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass $M_pi$ and decay constant $F_pi$, we obtain $chi_t$ = 0.227(02)(11)$M_pi^2 F_pi^2$ at the physical point, where the first error is statistical and the second is systematic.
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We determine the topological susceptibility chi_t in the topologically-trivial sector generated by lattice simulations of N_f = 2+1 QCD with overlap Dirac fermion, on a 16^3 x 48 lattice with lattice spacing ~ 0.11 fm, for five sea quark masses m_q ranging from m_s/6 to m_s (where m_s is the physical strange quark mass). The chi_t is extracted from the plateau (at large time separation) of the 2-point and 4-point time-correlation functions of the flavor-singlet pseudoscalar meson eta, which arises from the finite size effect due to fixed topology. In the small m_q regime, our result of chi_t agrees with the chiral effective theory. Using the formula chi_t = Sigma(m_u^{-1} + m_d^{-1} + m_s^{-1})^{-1} by Leutwyler-Smilga, we obtain the chiral condensate Sigma^{MSbar}(2 GeV) = [249(4)(2) MeV]^3.
We compute the topological charge and its susceptibility in finite temperature (2+1)-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quarks, we perform simulations on a fine lattice with~$asimeq0.07,mathrm{fm}$ at a heavy $u$, $d$ quark mass with $m_pi/m_rhosimeq0.63$ but approximately physical $s$ quark mass with $m_{eta_{ss}}/m_phisimeq0.74$. In a temperature range from~$Tsimeq174,mathrm{MeV}$ ($N_t=16$) to $697,mathrm{MeV}$ ($N_t=4$), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in $T$ which is consistent with the predicted $chi_mathrm{t}(T) propto (T/T_{rm pc})^{-8}$ for three-flavor QCD even at low temperature $T_{rm pc} < Tle1.5 T_{rm pc}$.
We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two degenerate, massless quarks and a physical strange quark mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of $58~{rm MeV}lesssim m_pilesssim 163~{rm MeV}$. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. Finite volume effects are controlled by extrapolating to the thermodynamic limit using spatial lattice extents in the range of $2.8$-$4.5$ times the inverse of the pion mass. Continuum extrapolations are carried out by using three different values of the lattice cut-off, corresponding to lattices with temporal extent $N_tau=6, 8$ and $12$. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature $T_c^0=132^{+3}_{-6}$ MeV.
We calculate chiral susceptibilities in (2+1)-flavour QCD for different masses of the light quarks using the functional renormalisation group (fRG) approach to first-principles QCD. We follow the evolution of the chiral susceptibilities with decreasing masses as obtained from both the light-quark and the reduced quark condensate. The latter compares very well with recent results from the HotQCD collaboration for pion masses $m_{pi}gtrsim 100,text{MeV}$. For smaller pion masses, the fRG and lattice results are still consistent. In particular, the estimates for the chiral critical temperature are in very good agreement. We close by discussing different extrapolations to the chiral limit.
We compute the topological susceptibility $chi_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the Mobius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab sub-volume of the simulated lattice using the method proposed by Bietenholz {it et al.} The quark mass dependence of $chi_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $Sigma^{overline{rm MS}} (mbox{2GeV}) = [274(13)(29)mbox{MeV}]^3$, where the first error is statistical and the second one is systematic. Combining the results for the pion mass $M_pi$ and decay constant $F_pi$, we obtain $chi_t = 0.229(03)(13)M_pi^2F_pi^2$ at the physical point.
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