The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Chiral phase transition and axion mass

2009/08/31 by Olivier Wantz, E. P. S. Shellard · 2 citations
Physics and Astronomy · #Axion #Combinatorics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Grand canonical ensemble #Instanton #Lambda #Mathematical physics #Monte Carlo method #Particle physics #Particle physics theoretical and experimental studies #Phase transition #Physics #Quantum mechanics #Quark #Topology (electrical circuits) #astro-ph.CO #hep-lat #hep-ph

paper · pdf · doi:10.1016/j.nuclphysb.2009.12.005

published as Nucl.Phys.B829:110-160,2010 · 65 pages, 36 figures. As accepted by Nucl.Phys.B

openalex publication_date 2009/12/15 · arxiv created 2010/01/14 · arxiv updated 2010/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, m²_a f²_a = 1.46 10^-3Λ⁴ \frac1+0.50 T/Λ1+(3.53 T/Λ)^7.48. It connects smoothly to the high temperature dilute gas approximation; the latter is improved by including quark threshold effects. To compare with earlier studies, we also provide the usual power-law m²_a = (α_a Λ⁴)/(f_a² (T/Λ)ⁿ), where Λ=400\unitsMeV, n=6.68 and α=1.68 10^-7.

Citations

• Topological susceptibility at zero and finite T in SU(3) Yang-Mills theory
• The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Zero temperature calibrations and numerical framework
• A simple solution to the strong CP problem with a harmless axion
• The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Strongly associating fluids and biased Monte Carlo
• Parity Conservation in Quantum Chromodynamics
• QCD matching conditions at thresholds
• Pseudoparticle solutions of the Yang-Mills equations
• QCD and instantons at finite temperature
• Periodic Euclidean solutions and the finite-temperature Yang-Mills gas

Cited by

• The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Zero temperature calibrations and numerical framework
• The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Strongly associating fluids and biased Monte Carlo
• Strong CP problem with low-energy emergent QCD: The 4321 case
• QCD axions and axionlike particles in a two-inflation scenario