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Register a new userMulticanonical reweighting for the QCD topological susceptibility
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We introduce a reweighting technique which allows for a continuous sampling of temperatures in a single simulation and employ it to compute the temperature dependence of the QCD topological susceptibility at high temperatures. The method determines the ratio of susceptibility between any two temperatures within the explored temperature range. We find that the results from the method agree with our previous determination and that it is competitive with but not better than existing methods of determining the temperature derivative of the susceptibility. The method may also be useful in exploring the temperature dependence of other thermodynamical observables in QCD in a continuous way.
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We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperature. We discuss how these problems can be solved by two new techniques, the first one with reweighting using the quark zero modes and the second one with the integration method.
We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings, corresponding to temporal extent of the lattice, $N_tau=6,8,10$ and $12$. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below $250$ MeV. While for temperatures above $250$ MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant and the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.
We study the topological charge in $N_f=2$ QCD at finite temperature using Mobius domain-wall fermions. The susceptibility $chi_t$ of the topological charge defined either by the index of overlap Dirac operator or a gluonic operator is investigated at several values of temperature $T (>T_c)$ varying the quark mass. A strong suppression of the susceptibility is observed below a certain value of the quark mass. The relation with the restoration of $U_A(1)$ is discussed.
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.
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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