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Register a new userTemperature-dependence of the QCD topological susceptibility
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Authors
Tamas G. Kovacs
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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.
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We study temperature dependence of the topological susceptibility with the $N_{f}=2+1$ flavors Wilson fermion. We have two major interests in this paper. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Two definitions are related by the chiral Ward-Takahashi identity but their coincidence is highly non-trivial for the Wilson fermion. By applying the gradient flow both for the gauge and quark fields we find a good agreement of these two measurements. The other is a verification of a prediction of the dilute instanton gas approximation at low temperature region $T_{pc}< T<1.5T_{pc}$, for which we confirm the prediction that the topological susceptibility decays with power $chi_{t}propto(T/T_{pc})^{-8}$ for three flavors QCD.
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 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.
The behaviour of the topological susceptibility chi in QCD with two colours and 8 flavours of quarks is studied at nonzero temperature on the lattice across the finite density transition. It is shown that the signal of chi drops abruptly at a critical chemical potential mu_c, much as it happens at the finite temperature and zero density transition. The Polyakov loop and the chiral condensate undergo their transitions at the same critical value mu_c. At a value mu_s of the chemical potential, called saturation point, which in our case satisfies mu_s > mu_c, Pauli blocking supervenes and consequently the theory becomes quenched.
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