The structure of a light quark star is studied within a new two-flavor Nambu–Jona-Lasinio model. By retaining the contribution from the vector term in the Fierz-transformed Lagrangian, a two-solar-mass pure quark star is achieved. To overcome the disadvantage of three-momentum truncation in the regularization procedure, we introduce the proper-time regularization. We also employ the newly proposed definition of vacuum pressure [ J. Phys. G 45, 105001 (2018)], in which the quasi-Wigner vacuum (corresponding to the quasi-Wigner solution of the gap equation) is used as the reference ground state. The free parameters include only a mixing constant $\alpha$ which weighs the contribution from the Fierz-transformed Lagrangian. We constrain $\alpha$ to be around 0.9 by the observed mass of pulsars PSR $\mathrm{J}0348+0432$ and PSR $\mathrm{J}1614\text{−}2230$. We find that the calculated surface energy density meets the requirement ($>2.80\times {10}^{14}\mathrm{g}/{\mathrm{cm}}^3$) [ Phys. Rev. D 99, 043001 (2019)]. Besides, for a 1.4-solar-mass star, the deformability $\mathrm{\Lambda }$ is calculated, which is consistent with a recent analysis on the binary neutron star merger GW170817 with $\mathrm{\Lambda }$ in (0,630) for large component spins and ${300}_{-230}^{+420}$ when restricting the magnitude of the component spins [ Phys. Rev. X 9, 011001 (2019)], and satisfies the constraints $200<\mathrm{\Lambda }<800$ of early works.

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: $⟨{\mathit{b}}_T^2{⟩}_u^{\pi }=0.11{\mathrm{fm}}^2$, $⟨{\mathit{b}}_T^2{⟩}_s^K=0.08{\mathrm{fm}}^2$, and $⟨{\mathit{b}}_T^2{⟩}_u^K=0.13{\mathrm{fm}}^2$, and therefore the $s$ quark in the kaon is much closer to the center of transverse momentum than the $u$ quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

Using realistic quark propagators and meson Bethe-Salpeter amplitudes based on the Dyson-Schwinger equations, we calculate the pion and kaon’s valence parton distribution functions (PDF) through the modified impulse approximation. The PDFs we obtained at hadronic scale have the purely valence characteristic and exhibit both dynamical chiral symmetry breaking and $SU(3)$ flavor symmetry breaking effects. A new calculation technique is introduced to determine the valence PDFs with precision. Through next-to-leading order (NLO) evolution, our result is compared with pion and kaon valence PDF data at experimental scale. Good agreement is found in the case of pion, while deviation emerges for kaon. We point out this situation can potentially be resolved by incorporating gluon contributions into the mesons if the pion hosts more gluons than kaon nonperturbatively.

We study the chiral phase transition inside a rotating cylinder within the framework of the Nambu–Jona-Lasinio model. A spectral boundary condition is imposed to avoid faster than light. We investigate how the geometry of the cylinder and rotation influence the chiral phase transition at finite temperature and chemical potential. The inhomogeneous effects caused by the finite size and rotation are also taken into account. It is found that finite size will reduce the chiral transition temperature and raises the chiral transition chemical potential, while the rotation reduces both the chiral transition temperature and chemical potential. In addition, we discuss the implications of our results in heavy-ion collisions and equation of states of neutron star.

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ ₅. The chiral quark condensate $$ \left\langle \overline{\psi}\psi \right\rangle $$ ψ ¯ ψ is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ ₅ is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μ _E , T _E ) shifts toward larger T _E but constant μ _E as μ ₅ increases. A technique is then introduced to compute the chiral charge density n ₅ from the fully dressed quark propagator. We find the n ₅ generally increases with temperature T , quark number chemical potential μ and μ ₅. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n ₅ and find an increase in n ₅ with smaller system size.

We study the leading-twist time-reversal even transverse momentum-dependent parton distribution functions (TMDs) of light and heavy vector mesons, i.e., the $\rho$, $J/\psi$ and $\mathrm{\Upsilon }$. We employ the leading Fock-state light front wave functions (LF-LFWFs) of $\rho$ and $J/\psi$ from our recent study, and supplement with $\mathrm{\Upsilon }$’s LF-LFWFs. These LF-LFWFs are extracted from dynamically solved Bethe-Salpeter wave functions. The vector meson TMDs are then studied with the light front overlap representation at leading Fock-state. All the obtained TMDs are nonvanishing and evolve with current quark mass, in particular the tensor polarized TMDs $f_{1LT}$ and $f_{1TT}$ which undergo a sign flip. The $\rho$ TMDs are compared with other model studies and agreement is found, aside from $f_{1LT}$ and $f_{1TT}$. Finally, the collinear PDFs of vector mesons are studied. The $\rho$’s valence PDFs $f_{1,v}(x)$ and $g_{1L,v}(x)$ are evolved to the scale of 2.4 GeV, with their first three moments compared to the lattice QCD prediction. The qualitative behavior of tensor polarized PDF $f_{1LL}(x)$ in $\rho$ at large $x$ is also discussed.