Abstract
In this work we compute the axion mass and, from this (exploiting a well-known relation), we also derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at ${T}_{c}$, making use of a chiral effective Lagrangian model which includes the axion, the scalar and pseudoscalar mesons and implements the $U(1)$ axial anomaly of the fundamental theory. We also provide a numerical estimate of the topological susceptibility at $T=0$ (in the physical case of three light quark flavors) and discuss the question of the temperature and quark-mass dependence of the topological susceptibility in the high-temperature regime.
Highlights
Among the possible solutions of the so-called “strongCP problem”, the most appealing is surely the one proposed by Peccei and Quinn (PQ) in 1977 [1] and developed by Weinberg and Wilczek in 1978 [2,3]
The results (3.10), (3.12), and (3.14) generalize the corresponding results found in Ref. [26], studying the θ dependence of the vacuum energy density and using the nonlinear versions of the various effective models, in which the scalar degrees of freedom had been integrated out, by taking the limit λ2π → ∞
In this paper we have computed the axion mass and, from this [exploiting the well-known formula (1.5), valid in the limit of very large fa, i.e., fa ≫ ΛQCD], we have derived an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at Tc, making use of a chiral effective Lagrangian model, the so-called interpolating model, which includes the axion, the scalar and pseudoscalar mesons and implements the Uð1Þ axial anomaly of the fundamental theory
Summary
Among the possible solutions of the so-called “strongCP problem” (that is, the experimental absence of CP violations in the strong-interaction sector), the most appealing is surely the one proposed by Peccei and Quinn (PQ) in 1977 [1] and developed by Weinberg and Wilczek in 1978 [2,3]. In this work we shall compute the axion mass and exploiting the relation (1.5), we shall derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at Tc, making use of a chiral effective Lagrangian model, the so-called “interpolating model,”. IV we shall briefly summarize the results obtained in this paper, giving some prospects and conclusions
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