Working in the linear sigma model with quarks, we compute the finite-temperature effective potential in the presence of a weak magnetic field, including the contribution of the pion ring diagrams and considering the sigma as a classical field. In the approximation where the pion self-energy is computed perturbatively, we show that there is a region of the parameter space where the effect of the ring diagrams is to preclude the phase transition from happening. Inclusion of the magnetic field has small effects that however become more important as the system evolves to the lowest temperatures allowed in the analysis.
We apply the approximating chiral quark model. This chiral quark model is based on an effective Lagrangian which the interactions between quarks via sigma and pions mesons. The field equations have been solved in the mean field approximation for the hedgehog baryon state. Good results are obtained for nucleon properties in comparison with original model.
We study the structure of the sigma meson, the lowest-lying resonance of the pi pi scattering in the scalar-isoscalar channel, through the softening phenomena associated with the partial restoration of chiral symmetry. We build dynamical chiral models to describe the pi pi scattering amplitude, in which the sigma meson is described either as the chiral partner of the pion or as the dynamically generated resonance through the pi pi attraction. It is shown that the internal structure is reflected in the softening phenomena; the softening pattern of the dynamically generated sigma meson is qualit…
The S-wave Sigma_c Dbar and Lambda_c Dbar states with isospin I=1/2 and spin S=1/2 are dynamically investigated within the framework of a chiral constituent quark model by solving a resonating group method (RGM) equation. The results show that the interaction between Sigma_c and Dbar is attractive, which consequently results in a Sigma_c Dbar bound state with the binding energy of about 5-42 MeV, unlike the case of Lambda_c Dbar state, which has a repulsive interaction and thus is unbound. The channel coupling effect of Sigma_c Dbar and Lambda_c Dbar is found to be negligible due to the fact t…
We consider a globally invariant chiral Lagrangian that contains vector and axial-vector mesons. We compute the f0(600) decay width into two pions and pion-pion scattering lengths and compare with the corresponding results in which the (axial-)vector degrees of freedom decouple. We show that the role of vector mesons has a great impact on these quantities.
Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
在O（4）线性西格玛模型和U（N_f）_r x U（N_f）_l线性西格玛模型（N_f= 2，3，4夸克味）的框架下，研究了非零温度下的手征对称性恢复.我们调查的标量和赝标量介子的质量的温度依赖性，和非奇怪的，奇怪的，和魅力凝聚的Hartree近似内从Cornwall-Jackiw-Tomboulis形式主义。我们发现非零温度下非奇异介子和奇异介子的质量敏感地依赖于模型的特殊对称性和轻夸克味数N_f。另一方面，由于大的粲夸克质量，粲介子既不显着影响其他介子的性质，也没有明显的变化，在手征对称性恢复温度附近的温度范围内，他们的质量。在手征极限下，手征对称性恢复的跃迁温度与格点量子色动力学中的跃迁温度非常接近。
The pi pi scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the sigma meson which is observed as the lowest scalar-isoscalar resonance. We compare several models with different origins of the sigma meson, such as the chiral partner of the pion and the dynamically generated pi pi molecule. We find that the dynamically generated sigma meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. Thi…
The spontaneous breaking of chiral symmetry is examined by chiral effective theories, such as the linear sigma model and the Nambu Jona-Lasinio (NJL) model. Indicating that sufficiently large contribution of the UA(1) anomaly can break chiral symmetry spontaneously, we discuss such anomaly driven symmetry breaking and its implication. We derive a mass relation among the SU(3) flavor singlet mesons, eta0 and sigma0, in the linear sigma model to be satisfied for the anomaly driven symmetry breaking in the chiral limit, and find that it is also supported in the NJL model. With the explicit breaki…
We present a two-flavour linear sigma model with global chiral symmetry and (axial-)vector mesons as well as an additional glueball degree of freedom. We study the structure of the well-established scalar resonances f0(1370) and f0(1500): by a fit to experimentally known decay widths we find that f0(1370) is predominantly a \bar{q}q state and f0(1500) is predominantly a glueball state. The overall phenomenology of these two resonances can be well described. Other assignments for our mixed quarkonium-glueball states are also tested, but turn out to be in worse agreement with the phenomenology. …
We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions …
We studied the chiral phase transition for small $|1-q|$ within the Tsallis nonextensive statistics of the entropic parameter $q$, where the quantity $|1-q|$ is the measure of the deviation from the Boltzmann-Gibbs statistics. We adopted the normalized $q$-expectation value in this study. We applied the free particle approximation and the massless approximation in the calculations of the expectation values. We estimated the critical physical temperature, and obtained the chiral condensate, the sigma mass, and the pion mass, as functions of the physical temperature $T_{\mathrm{ph}}$ for various…
We present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, sigma and pion. The chiral Lagrangian also includes a logarithmic potential, associated with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. We show that the model can reach higher densities respect to the Linear-sigma model, up to approximately 3 rho_0 for m_sigma=1200 MeV.
We present a two-flavour linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate pion-pion scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We inv…
The chiral symmetry breaking in the presence of external magnetic field is studied in the framework of logarithmic quark-sigma model. The effective logarithmic mesonic potential is employed and is numerically solved in the mean-field approximation. We find that the chiral symmetry breaking enhances in comparison with the original sigma model. Two sets of parameterization are investigated in the present model. We find that increasing coupling constant enhances the breaking symmetry while increasing sigma mass inhibits enhancing chiral broken vacuum state. A comparison with the Numbu-Jona-Lasini…
We report a new analysis of lattice simulation results for octet baryon masses in 2+1-flavor QCD, with an emphasis on a precise determination of the strangeness nucleon sigma term. A controlled chiral extrapolation of a recent PACS-CS Collaboration data set yields baryon masses which exhibit remarkable agreement both with experimental values at the physical point and with the results of independent lattice QCD simulations at unphysical meson masses. Using the Feynman-Hellmann relation, we evaluate sigma commutators for all octet baryons. The small statistical uncertainty, and considerably smal…
We discuss the description of chiral imbalance imprint in pion matter. It is based on the Chiral Perturbation Theory supplemented by medium induced chiral chemical potential in the covariant derivative. Such an implementation of chiral imbalance recently was explored in linear sigma model inspired by QCD. The relationship between two sigma models is examined. A possible experimental detection of chiral imbalance in charged pion decays inside the fireball is pointed out.
Sigma-term physics in the perturbative chiral quark model
本文应用微扰手征夸克模型（PCQM）分析了介子-重子σ项。这些量的解析表达式得到的基本参数的低能π介子核子物理（弱π衰变常数，轴向核子耦合，强π介子核子形状因子）和只有一个模型参数（半径的核子三夸克核心）。我们的结果为约45 MeV的π N σ项是在良好的协议与Gasser，Leutwyler和Sainio使用色散关系技术和利用手征对称性约束推导出的值。
We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of th…
We investigate the scalar meson mass dependence on the chiral phase transition in the framework of an SU(3), (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops. We determine the parameters of the Lagrangian at zero temperature in a hybrid approach, where we treat the mesons at tree-level, while the constituent quarks at 1-loop level. We assume two nonzero scalar condensates and together with the Polyakov-loop variables we determine their temperature dependence according to the 1-loop level field equations.
The chiral symmetry breaking in the presence of an external magnetic field is studied in the framework of logarithmic quark-sigma model with three flavors (u,d,s). The effective logarithmic mesonic potential is extended to strange quark and is numerically solved in the mean-field approximation. The present results show that the chiral symmetry breaking is sensitive for the strange quark flavour in the presence an external magnetic field. In addition, the effect of the free parameters is studied. A comparison with original sigma model is discussed.
We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM) as realizations of low energy QCD for light mesons in a chirally imbalanced medium. The relations between the low-energy constants of the Chiral Lagrangian and the corresponding constants of the Linear Sigma Model are established as well as the expressions for the decay constant of the $π$-meson in the medium and the mass of the $a_0$. In the large $N_c$ count taken from QCD the correspondence of ChPT and LSM is remarkably good and give a solid ground for search of chiral imbalance manifestation in pion physics. A po…
We report an analysis of the octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order with and without the virtual decuplet contributions. Particular attention is paid to the finite-volume corrections and the finite lattice spacing effects on the baryon masses. A reasonable description of all the publicly available $n_f=2+1$ lattice QCD data is achieved.Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as $σ_{πN}=55(1)(4)$ MeV and $σ_{sN}=27(27)(4)$ MeV.
We study the production of non-strange mesons in proton-proton scattering reactions within an effective model of mesons and baryons with global chiral symmetry. The model includes the nucleon ($N$) and its chiral partner ($N^{\ast}$) and their couplings to the $N_{f}=2$ multiplets of (pseudo-)scalar and (axial-)vector mesons. Results for the production of $ω$ and $η$ mesons are presented.
We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.
We present an overview of modern approaches to low-energy baryon structure based on baryon chiral perturbation theory. These are driven by the emergence of Lorentz covariant schemes and the systematic consideration of the effects of the lowest-lying decuplet resonances. In order to illustrate the progress recently achieved in this field, we present the last developments on our understanding of the nucleon sigma terms along these lines. In particular, we will show how these methods, in SU(2) or SU(3) settings, are reliable tools to process and maximize the information on the physical structure …
