Topology in QCD and the axion abundance

The temperature dependence of the topological susceptibility in QCD, chi_t, essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heatbath algorithm. We obtain an indication that unquenched calculations of chi_t encounter the serious problem of autocorrelation already at T~2Tc or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of chi_t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where chi_t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.Comment: 18 pages, 3 figures, discussion on autocorrelation and references adde

θ=π\theta=\pi in SU(N)/ZNSU(N)/\mathbb{Z}_N gauge theories

In $SU(N)$ gauge theory, it is argued recently that there exists a "mixed anomaly" between the CP symmetry and the 1-form $\mathbb{Z}_N$ symmetry at $\theta=\pi$, and the anomaly matching requires CP to be spontaneously broken at $\theta=\pi$ if the system is in the confining phase. In this paper, we elaborate on this discussion by examining the large volume behavior of the partition functions of the $SU(N)/\mathbb{Z}_N$ theory on $T^4$ a la 't Hooft. The periodicity of the partition function in $\theta$, which is not $2\pi$ due to fractional instanton numbers, suggests the presence of a phase transition at $\theta=\pi$. We propose lattice simulations to study the distribution of the instanton number in $SU(N)/\mathbb{Z}_N$ theories. A characteristic shape of the distribution is predicted when the system is in the confining phase. The measurements of the distribution may be useful in understanding the phase structure of the theory.Comment: 18 pages, 1 figure, reference added, typo fixe

Topological susceptibility with a single light quark flavour

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping $m_d$ finite. The $\theta$ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the $m_u=0$ point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does. We will present our recent progresses on the empirical check of this property using $N_f=1+2$ flavours of clover fermions, where the lightest fermion is tuned very close to $m^{PCAC}_u$=0 and the mass of the other two is kept of the order of magnitude of the physical $m_s$. This choice is indeed expected to amplify any unknown non-perturbative effect caused by $m_u\not=m_d$. The simulation is repeated for several $\beta$s and those results, although preliminary, give a hint about what happens in the continuum limit.Comment: 8 pages, 3 figures, Presented at Lattice2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017

Topological susceptibility with a single light quark flavour

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping md finite. The θ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the mu = 0 point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does. We will present our recent progresses on the empirical check of this property using Nf = 1 + 2 flavours of clover fermions, where the lightest fermion is tuned very close to muPCAC=0 and the mass of the other two is kept of the order of magnitude of the physical ms. This choice is indeed expected to amplify any unknown non-perturbative effect caused by mu ≠ md. The simulation is repeated for several βs and those results, although preliminary, give a hint about what happens in the continuum limit

Instanton effects on CP-violating gluonic correlators

In order to better understand the role played by instantons behind nonperturbative dynamics, we investigate the instanton contributions to the gluonic two point correlation functions in the SU(2) YM theory. Pseudoscalar-scalar gluonic correlation functions are calculated on the lattice at various temperatures and compared with the instanton calculus. We discuss how the instanton effects emerge or disappear with temperature and try to provide the interpretation behind it