The role of $U(1{)}_A$ symmetry breaking in the QCD corrections to the pion mass difference

Abstract

The charged and neutral pion mass difference can be attributed to both the QED and QCD contributions. The current quark mass difference ($\Delta m$) is the source of the QCD contribution. Here, in a two-flavour non-local NJL model, we try to estimate the QCD contribution. Interestingly, we find that the strength of the $U(1{)}_A$ symmetry-breaking parameter $c$ plays a crucial role in obtaining the pion mass difference while intertwined with the current quark mass difference. To obtain the QCD contribution for the pion mass difference, we scan the parameter space in $\{\Delta m,c\}$, and by comparing this with the existing results, we constrained the parameter space. Further, using a fitted value of $c$, we determine the allowed range for the $\Delta m$ in the model. The model estimated $\Delta m$ ranges enable us to extract the chiral perturbation theory low-energy constant, $l_7$ and verify the dependence of the pion mass difference on $\Delta m$. We also find out its dependence on $c$ \textemdash\, it increases with the decreasing value of $c$, i.e., toward an axial anomaly restored phase.

12 pages, 6 captioned figures, discussion on l7 has been added, accepted in JPG

References in corpus (8)

• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• On covariant nonlocal chiral quark models with separable interactions
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Strong magnetic fields in nonlocal chiral quark models
• Electromagnetic effects in the pion dispersion relation at finite temperature
• Transport regimes for exciton-polaritons in disordered microcavities
• Studying explicit $U(1{)}_A$ symmetry breaking in hot and magnetised two flavour non-local NJL model constrained using lattice results
• First direct lattice calculation of the chiral perturbation theory low-energy constant ${\ell }_7$

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• Strongly interacting matter in extreme magnetic fields
• Vector interaction bounds in NJL-like models from LQCD estimated curvature of the chiral crossover line
• Thermal Field Theory in the Presence of a Background Magnetic Field and its Application to QCD