Abstract
QCD topological susceptibility at high temperature, $\chi_t(T)$, provides an important input for the estimate of the axion abundance in the present Universe. While the model independent determination of $\chi_t(T)$ should be possible from the first principles using lattice QCD, existing methods fail at high temperature, since not only the probability that non-trivial topological sectors appear in the configuration generation process but also the local topological fluctuations get strongly suppressed. We propose a novel method to calculate the temperature dependence of topological susceptibility at high temperature. A feasibility test is performed on a small lattice in the quenched approximation, and the results are compared with the prediction of the dilute instanton gas approximation. It is found that the method works well especially at very high temperature and the result is consistent with the instanton calculus down to $T\sim 2\, T_c$ within the statistical uncertainty.
Highlights
The PQ mechanism is attractive because it provides a candidate for the dark matter of the Universe through the misalignment mechanism for the axion generation [9,10,11]
While the model independent determination of χt(T ) should be possible from the first principles using lattice QCD, existing methods fail at high temperature, since the probability that non-trivial topological sectors appear in the configuration generation process and the local topological fluctuations get strongly suppressed
It is found that the method works well especially at very high temperature and the result is consistent with the instanton calculus down to T ∼ 2 Tc within the statistical uncertainty
Summary
The calculation of the topological susceptibility in the dilute instanton-gas approximation (DIGA) [14] is briefly reviewed. Where z and ρ are the position and the size of the instanton, respectively, and n(ρ, T ) is factorized into the gauge (nG), the fermionic part (nF ) and the finite temperature effect (nT ). After the explicit calculation of ZQ=1 [12, 25], the gauge contribution to the instanton density is found to be nG(ρ) = CI (μρ)β0. While the ρ integral diverges at zero temperature, it becomes finite at finite temperature [14] since the Debye screening exponentially suppresses the large size instanton. This effect is embedded in nT , which is known to be nT (λ) = exp 1 −
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