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Register a new userThe fate of pion condensation in quark matter: from the chiral limit to the physical pion mass
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We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu--Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion $(pi^c)$ condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, $mu_{e}=M_{pi^-}$, as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass $m$, and is ruled out for $m$ larger than the order of 10 keV.
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We explore the link between the chiral symmetry of QCD and the numerical results of the light-front quark model, analyzing both the two-point and three-point functions of the pion. Including the axial-vector coupling as well as the pseudoscalar coupling in the light-front quark model, we discuss the implication of the chiral anomaly in describing the pion decay constant, the pion-photon transition form factor and the electromagnetic form factor of the pion. In constraining the model parameters, we find that the chiral anomaly plays a critical role and the analysis of $F_{pigamma}(Q^2)$ in timelike region is important. Our results indicate that the constituent quark picture is effective for the low and high $Q^2$ ranges implementing the quark mass evolution effect as $Q^2$ grows.
The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe-Salpeter amplitude combined with Euclidean Lattice QCD results for the running quark mass. In the present work, a pion model previously proposed, which allows for a Nakanishi integral representation, is studied in order to verify the sensitivity of the pion electromagnetic form factor to small variations of the quark self-energy. In addition, we extend the previous work, providing the Nakanishi integral representation for the invariants associated with a decomposition of the pion Bethe-Salpeter amplitude.
Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $Delta$(1232) resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the $ u_mu nto mu^-npi^+$ channel, where higher-order contributions might still be significant. The $Delta$ resonance mechanisms lead to sizeable contributions in all channels, especially in $ u_mu pto mu^- ppi^+$, even though the considered energies are close to the production threshold. The present study provides a well founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments.
We study the pion Distribution Amplitude (pi DA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained pi DA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This pi DA is applied to leading order and next-to-leading order calculations of the pion-photon transition form factor. Implications of the results are discussed.
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