• axion
• Hasenbusch parallel tempering
• Hybrid Monte Carlo
• Lattice QCD
• Monte Carlo Methods
• QCD
• topological susceptibility
• topology
• θ-dependence

The dependence of Quantum Chromodynamics (QCD) on the θ-parameter, coupling
the topological charge to QCD, is extremely relevant for the so-called strong CP problem.
Since no violation of the CP symmetry from strong interactions has ever been observed,
experimental bounds on the θ-parameter introduce a fine-tuning problem. A possible
solution is the Peccei-Quinn model, which includes a new particle called the axion. A
precise knowledge of the QCD topological susceptibility χ is fundamental to compute
accurately the axion mass ma and the axion relic abundance, which could explain a
fraction of the observed Dark Matter.
A natural non-perturbative approach to study QCD topology is represented by numerical
lattice simulations using Monte Carlo methods. Many studies have been carried
out to tackle the problem of computing , but several non-trivial computational problems
have been identified, especially when considering the full theory with dynamical fermions.
One of the main algorithmic problems is the so-called topological freezing, due to standard
sampling algorithms becoming less and less capable of exploring different topological
sectors as the continuum limit is approached (lattice spacing a -> 0).
A recent promising solution to mitigate this problem is the proposal introduced by M.
Hasenbusch for large-N 2d CP^(N-1) models, recently applied also in 4d large-N pure-SU(N)
gauge theories. If periodic boundary conditions (pbc) are put aside and replaced by open
boundary conditions in at least one of the space-time directions, as suggested by Lüscher
and Schaefer, the barriers among topological sectors are eliminated allowing standard
sampling methods to easily explore non-integer values of the lattice topological charge
during the Monte Carlo evolution. However, by choosing open boundary conditions (opc)
any physical notion of global topological charge is lost. To bypass this issue, Hasenbusch
proposal combines pbc and obc in a parallel tempering framework.
Our main goal is to extend the Hasenbusch parallel tempering to the case of full QCD
to improve the computation of  at high temperatures, which has important implications
for the axion dynamics in the early Universe. Since so far this algorithm has been employed
at zero temperature and in the large-N limit in pure gauge theories, our investigation
starts from the study of the SU(3) pure gauge theory at finite temperature. Most of our
parallel tempering simulations were carried on by adopting local updating algorithms like
the heat-bath algorithm, but for one of the explored temperatures we also performed a
preliminary study adopting the Hybrid Monte Carlo (HMC), which is the standard choice
in the presence of dynamical fermions.
Preliminary results about the improvements yielded by the Hasenbusch algorithm in
finite-temperature quenched QCD obtained from these simulations are promising and encourage
further studies in the near future. In particular, we plan to perform a more
systematic study of pure-glue QCD with the HMC algorithm and the parallel tempering.
Moreover, since we also implemented a working code for full QCD, we also plan to
systematically study the performances of this algorithm in this case.