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Register a new userNew Insight about the Effective Restoration of U_A(1) Symmetry
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The effective restoration of the U_{A}(1) symmetry is revisited by implementing the functional renormalization group approach combining with the 2+1 flavor Polyakov-loop quark-meson model. A temperature-dependent t Hooft term is taken to imitate the restoration of the U_{A}(1) symmetry. Order parameters, meson spectrum and mixing angles, especially the pressure and the entropy density of the system are calculated to explore the effects of different U_{A}(1) symmetry restoration patterns. We show then that the temperature for the restoration of the U_{A}(1) symmetry is much higher than that for the chiral symmetry SU_{A}(3).
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The diquark is a strongly correlated quark pair that plays an important role in hadrons and hadronic matter. In order to treat the diquak as a building block of hadrons, we formulate an effective theory of diquark fields with $SU(3)_R times SU(3)_L$ chiral symmetry. We concentrate on the scalar ($0^+$) and pseudoscalar ($0^-$) diquarks and construct a linear-sigma-model Lagrangian. It is found that the effective Lagrangian contains a new type of chirally symmetric meson-diquark-diquark coupling that breaks axial $U_A(1)$ symmetry. We discuss consequences of the $U_A(1)$ anomaly term to the diquark masses as well as to the singly heavy baryon spectrum, which is directly related to the diquark spectrum. We find an inverse mass ordering between strange and nonstrange diquarks. The parameters of the effective theory can be determined by the help of lattice QCD calculations of diquarks and also from the mass spectrum of the singly heavy baryons. We determine the strength of the $U_A(1)$ anomaly term, which is found to give a significant portion of the diquark masses.
We study strong and radiative decays of excited singly heavy baryons (SHBs) using an effective chiral Lagrangian based on the diquark picture proposed in Ref. [1]. The effective Lagrangian contains a $U_A (1)$ anomaly term, which induces an inverse mass ordering between strange and non-strange SHBs with spin-parity $1/2^-$. We find that the effect of the $U_A (1)$ anomaly combined with flavor-symmetry breaking modifies the Goldberger-Treiman relation for the mass difference between the ground state $Lambda_Q (1/2^+)$ and its chiral partner $Lambda_Q (1/2^-)$, and $Lambda_Q (1/2^-) Lambda_Q (1/2^+) eta$ coupling, which results in suppression of the decay width of $Lambda_Q (1/2^-) to Lambda_Q (1/2^+) eta$. We also investigate the other various decays such as $Lambda_Q (1/2^-) to Sigma_Q (1/2^+, , 3/2^+) pi pi$, $Lambda_Q (1/2^-) to Sigma_Q (1/2^+) pi$, $Lambda_Q (1/2^-) to Sigma_Q (1/2^+, , 3/2^+) gamma$, and $Lambda_Q (1/2^-) to Lambda_Q (1/2^+) pi^0$ for wide range of mass of $Lambda_Q (1/2^-)$.
The nature and location of the QCD phase transition close to the chiral limit restricts the phase structure of QCD with physical pion masses at non-vanishing density. At small pion masses, explicit $U(1)_{rm A}$-breaking, as induced by a non-trivial topological density, is of eminent importance. It triggers the t Hooft interactions and also manifests itself in the interplay of four-quark interactions at low momentum scales. In the present work, we perform a Fierz-complete analysis of the emergence of four-quark interactions from the QCD dynamics at finite temperature, subject to a given t Hooft coupling at large momentum scales. The variation of the latter allows us to test the robustness of our findings. Taking an estimate of the effect of the topological running of the t Hooft coupling into account, our analysis suggests that the chiral transition in QCD with two massless quark flavours falls into the $O(4)$ universality class.
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.
Properties of cold nuclear matter are studied within a generalized Nambu-Jona-Lasinio model formulated on the level of constituent nucleons. The model parameters are chosen to reproduce simultaneously the observed nucleon and pion masses in vacuum as well as saturation properties of nuclear matter. The strongest constraints on these parameters are given by the empirical values of the nucleon effective mass and compression modulus at nuclear saturation density. A preferable value of the cut-off momentum, determining density of active quasinucleon states in the Dirac sea, is estimated to about 400 MeV/c. With the most reasonable choice of model parameters we have found a first order phase transition of the liquid-gas type at subsaturation densities and the gradual restoration of chiral symmetry at about 3 times the saturation density. Fluctuations of the scalar condensate around its mean-field value are estimated and shown to be large in the vicinity of chiral transition.
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