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Abstract
With analyzing the mass function obtained by solving Dyson-Schwinger Equations, we propose a cut-off independent definition of quark condensate beyond chiral limit. With this well-defined condensate, we then analyze the evolution of the condensate and its susceptibility with the current quark mass. The susceptibility shows a critical mass in the neighborhood of the s-quark current mass, which defines a transition boundary for internal hadron dynamics.
Highlights
Chiral symmetry and its breaking plays significant roles in QCD phase structure as well as hadron dynamics
In order to describe the transition from a dynamical chiral symmetric (DCS) phase to a dynamical chiral symmetry breaking (DCSB) phase, the chiral condensate, i.e., the expectation value of the composite operator qq, is usually applied as the order parameter, and the chiral condensate is related to many important problems such as the pion-nucleon sigma term [23], the cosmological constant [24], and thermodynamic quantities [25]
In case of a finite current quark mass, the ultraviolet contribution to the condensate is much smaller than that from the current quark mass, and the fitting process needs to be extremely careful. Inspired by these earlier works, if one takes the first subtraction scheme mentioned above to eliminate the contribution of the current quark mass, and fits the ultraviolet behavior of the condensate, we can extract the quark condensate from the quark propagator while avoiding both the logarithm and the quadratic divergences [35]. This process can be extended to large current quark mass since it does not require the existence of multisolutions of the DysonSchwinger equations (DSEs); i.e., we verify a well-defined and divergence-free quark condensate beyond the chiral limit directly in terms of the dressed quark propagator
Summary
Chiral symmetry and its breaking plays significant roles in QCD phase structure as well as hadron dynamics. It is, in principle, difficult to separate the DCSB effect from the explicit mass scale arising from the ECSB term To solve these problems, one needs to determine appropriately the quark condensate in the case of both light flavor and heavy flavor quarks. Inspired by these earlier works, if one takes the first subtraction scheme mentioned above to eliminate the contribution of the current quark mass, and fits the ultraviolet behavior of the condensate, we can extract the quark condensate from the quark propagator while avoiding both the logarithm and the quadratic divergences [35] This process can be extended to large current quark mass since it does not require the existence of multisolutions of the DSEs; i.e., we verify a well-defined and divergence-free quark condensate beyond the chiral limit directly in terms of the dressed quark propagator.
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