Topology in QCD and the axion abundance

Abstract

The temperature dependence of the topological susceptibility in QCD, χ 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 χ t encounter the serious problem of autocorrelation already at T ∼ 2 T c or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of χ 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 χ t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

“…In particular we checked that Q is compatible with zero and that the topological charge is not frozen. Indeed it is well known that, while approaching the continuum limit, the autocorrelation time of the topological charge increases very steeply until no tunneling events between different sectors happen anymore [28][29][30][31][32]. An example of this behavior can be observed in figure 1, where some time-histories for zero temperature runs are showed, for three different lattice spacings.…”

“…to different topological sectors, which can be hardly crossed by standard algorithms [28][29][30][31][32]. That causes a loss of ergodicity which, in principle, can spoil any effort to approach the continuum limit itself.…”

Topological critical slowing down: Variations on a toy model

“…This problem severely affects the study of θdependence in QCD [6][7][8] and in many QCD-like models [9][10][11][12], the most relevant case being the study of the axion potential at finite temperature [8,[13][14][15][16][17][18][19]. Several methods and new algorithms have been proposed to solve or at least alleviate this problem, however no comparative investigation of the efficiency of these proposals exists in the literature so far.…”

Lattice QCD on nonorientable manifolds

“…Additionally it is not clear if fixing the topological sector is compatible with ergodicity, and if not, it is an open question how the observables are affected. Let us also mention that there are recent Ansätze which increase tunneling between different topological sectors by modifying the original theory and applying a reweighting correction in the observables [13,14]. Here the efficiency of the reweighting might limit the applicability of these methods.…”