Chiral symmetry restoration effects onto the meson spectrum from a Dyson-Schwinger/Bethe-Salpeter approach

Abstract

Light meson spectra are studied in a Dyson-Schwinger/Bethe-Salpeter approach to QCD. By varying the interaction strength of three sets of models for the quark-antiquark interaction, the transition from the chiral symmetric to the chirally broken regime in the vacuum is studied. The simplest type of these models leads to degenerate meson spectra for a large domain of the strength parameter. The more sophisticated and thus more realistic models show significantly smaller parameter domains for which degenerate meson spectra are obtained. The underlying mechanism for obtaining and then lifting degeneracies is traced back to the location of the quark propagators' poles, in particular, whether they are beyond or within the domain of integration in the Bethe-Salpeter equation. In view of this mechanism the potential relation of the obtained degeneracies to the dynamical emergence of symmetries is discussed, adding thereby another point of view on the conjectured chiral spin symmetry of QCD in the temperature domain right above the crossover.

Figures (7)

• Figure 1: (left) The location of the poles of the function $\sigma(p^2)$\ref{['sigmaA']} for model I in the complex $p^2$-plane as a function of $D_I$, cf. table \ref{['tab:param_W']}. (right) Position of the poles of $\sigma (p^2)$ along the real axis as a function of $D_I$. When the two low-lying poles cross they generate a pair of complex conjugate poles, cf. the left panel. Note, that we also observe a crossing of two real valued poles that does not lead to the formation of a complex pole pair.
• Figure 2: (left) Displayed is the infrared value of the quark mass function $M(0)$, as a proxy for the strength of dynamical chiral symmetry breaking, for model I as function of $D_I$ in the chiral limit and for a small quark current mass. (right) The parameter $\mathcal{M}$ determined by the largest parabola with apex $-\mathcal{M}^2/4$ that is free of poles for the given coupling strength $D_I$. In the presence of non-vanishing current quark masses, the second-order transition, visible in both variables, is smoothened into a crossover behavior.
• Figure 3: Pole structure emerging from model II as a function of the strength parameter $D_{II}$ for fixed $\omega_{II} = 0.4$ GeV. We observe a pattern similar to the one of model I.
• Figure 4: Masses of mesons with quantum numbers $J^{PC} = 0^{-+}, 0^{++}, 1^{--}, 1^{++}, 1^{+-}$ as functions of the strength parameters $D_{I,II,III}$ of models I-III. In all cases we obtain the same pattern of degeneracy at small interaction strengths. Shown is furthermore the parameter $\mathcal{M}$ characterizing the largest parabolic region symmetric to real $p^2$ with apex $-\mathcal{M}/4$.
• Figure 5: Dressing function $\sigma(p)$ for model III based on the ghost and gluon propagators on the real axis for various strength parameters $D_{III}$. The plot shows the largest parabola for which we could solve the complex quark DSEs self-consistently, as well as the parabolas associated with the meson masses as determined through their respective BSEs.