The QCD topological charge and its thermal dependence: the role of the η′

Abstract

We analyze the contribution of the η (958) meson in the first two non-trivial moments of the QCD topological charge distribution, namely, the topological susceptibility and the fourth-order cumulant of the vacuum energy density. We perform our study within U(3) Chiral Perturbation Theory up to next-to-next-to-leading order in the combined chiral and large-Nc expansion. We also describe the temperature dependence of these two quantities and compare them with previous analyses in the literature. In particular, we discuss the validity of the thermal scaling of the topological susceptibility with the quark condensate, which is intimately connected with a Ward Identity relating both quantities. We also consider isospin breaking corrections from the vacuum misalignment at leading order in the U(3) framework.

Addendum to: Aspects of the QCD θ-vacuum

“…(2.23) and (2.29)) by calculating this quantity using the full NLO Lagrangian, as well as the Kaiser-Leutwyler δ-expansion. However, while this result was confirmed recently in [2], the authors of this particular paper also recognized that in contrast to our original statements in section 2.4, this scaling behavior does not hold to higher orders in chiral perturbation theory. In fact, the NNLO Lagrangian involving a term C 4 (θ + Ψ) 4 adds a contribution of O N −2 c to the fourth cumulant c 4 [2], since the LEC C 4 is of the same order, which follows from eq.…”

Light- and strange-quark mass dependence of the ρ(770) meson revisited

“…Thus, for a qualitative description it is sufficient to approximate the left-hand cut using ChPT. At NLO, one finds 30) which stands for the well-known equation of the IAM method. The IAM was derived first in [46,47] using only unitarity for ππ scattering.…”

“…The contribution of the ρ(770) is also important for the hadronic total cross section σ(e + e − → hadrons) [9][10][11], which explains applications that go well beyond low-energy meson physics, ranging from the hadronic-vacuum polarization and the light-by-light contributions to the anomalous magnetic moment of the muon (see, for instance, [12][13][14][15]) to the electromagnetic and tensor-nucleon form factors [16][17][18][19]. Furthermore, it also plays a crucial role in the analysis of heavy meson decays [20,21] and in the restoration of chiral symmetry at high temperatures [22][23][24][25][26][27][28][29][30].…”

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

“…Following the pioneering work in [58,97,98], there has been considerable work in the chiral perturbation theory of the U (3) nonet both on the phenomenology [99] of η mixings and decays and on high order precision computations in this framework [100]. With regard to the latter, finite temperature computations are especially relevant [101].…”