Pion and kaon valence quark distribution functions from Dyson-Schwinger equations

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 NLO DGLAP 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 be resolved by incorporating gluon contributions into the mesons if the pion hosts more gluons than kaon nonperturbatively

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness.Comment: 9 pages, 3 figure

Limits on the Dark Matter from AMS-02 antiproton and positron fraction data

We derive limits on the dark matter annihilation cross section and lifetime using measurements of the AMS-02 antiproton ratio and positron fraction data. In deriving the limits, we consider the scenario of secondary particles accelerated in supernova remnants (SNRs) which has been argued to be able to reasonably account for the AMS-02 high energy positron/antiproton fraction data. We parameterize the contribution of secondary particles accelerated in SNRs and then fit the observational data within the conventional cosmic ray propagation model by adopting the GALPROP code. We use the likelihood ratio test to determine the 95$\%$ confidence level upper limits of the possible dark matter (DM) contribution to the antiproton/positron fractions measured by AMS-02. Our limits are stronger than that set by the Fermi-LAT gamma-ray Pass 8 data of the dwarf spheroidal satellite galaxies. We also show that the solar modulation (cosmic ray propagation) parameters can play a non-negligible role in modifying the constraints on the dark matter annihilation cross section and lifetime for $m_\chi100$ GeV), where $m_\chi$ is the rest mass of the dark matter particles. Using this results, we also put limits on the effective field theory of dark matter

Nature of chiral phase transition in QED3_3 at zero density

Based on the feature of chiral susceptibility and thermal susceptibility at finite temperature, the nature of chiral phase transition around the critical number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a fixed fermion flavors number in massless QED$_3$ are investigated. It is showed that, at finite temperature the system exhibits a second-order phase transition at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1, while it reveals a higher-order continuous phase transition around $N_c$ at zero temperature.Comment: Accepted by PHYSICAL REVIEW

Finite volume effects with stationary wave solution from Nambu--Jona-Lasinio model

In this paper, we use the two-flavor Nambu-Jona-Lasinio (NJL) model with the proper time regularization to study the finite-volume effects of QCD chiral phase transition. Within a cubic volume of finite size $L$, we choose the stationary wave condition (SWC) as the real physical spatial boundary conditions of quark fields and compare our results with that by means of commonly used (anti-)period boundary condition (APBC or PBC). It is found that the results by means of SWC are obviously different to the results from the APBC or PBC. Although the three boundary conditions give the same chiral crossover transition curve in the infinite volume limit, the limit size $L_0$ (when $L\geq L_{0}$, the chiral quark condensate $-\left\langle { \bar \psi \psi} \right\rangle_L$ is indistinguishable from that at $L=\infty$) using SWC is $L_0\approx 500$ fm which is much larger than the results obtained using APBC or PBC. More importantly, $L_0\approx 500$ fm is also much large than the typical size of the quark-gluon plasma produced by the relativistic heavy ion collisions. This means that the finite volume effects play a very important role in Relativistic Heavy Ion Collisions. In addition, we also found that when $L\leq 2$ fm, even at zero temperature the chiral symmetry is effectively restored. Furthermore, to quantitatively reflect the finite volume effects on the QCD chiral phase transition, we introduce a new vacuum susceptibility, $\chi_{1/L}(T)=-\frac{\partial \left\langle { \bar \psi \psi} \right\rangle}{\partial (1/L)}$. With this new vacuum susceptibility, it is very interesting to find $\chi_{1/L}(T=0)=\chi_{1/L}(T=1/L)$ for SWC

Nonperturbative solutions of Dyson-Schwinger equations in QED3_3

The studies of Dyson-Schwinger Equations (DSEs) provide us with insights into nonperturbative phenomenon of quantum field theory. However, DSEs are essentially an infinite set of coupled Green's functions, it's necessary to decouple parts of the equations which are thought of major physical importance to make the solution of these equations possible. Although the results are model-dependent, no qualitative deviations from exact solutions are expected with properly chosen truncation scheme. In this article, a globally convergent numerical method for the solution of the DSEs of QED$_3$ in Euclidean space is presented. This method can be adapted for more complex problems, however, it also shows its limitations when adopted in problems such as the searching for Wigner solutions.Comment: 17 pages, 11 figure

Modelling the Multi-band Afterglow of GRB 091127: Evidence of a Hard Electron Energy Spectrum with an Injection Break

The afterglow of GRBs is believed to originate from the synchrotron emission of shock-accelerated electrons produced by the interaction between the outflow and the external medium. The accelerated electrons are usually assumed to follow a power law energy distribution with an index of $p$. Observationally, although most GRB afterglows have a $p$ larger than 2, there are still a few GRBs suggestive of a hard ($p<2$) electron spectrum. GRB 091127, with well-sampled broad-band afterglow data, shows evidence of a hard electron spectrum and strong spectral evolution, with a spectral break moving from high to lower energies. The spectral break evolves very fast and cannot be explained by the cooling break in the standard afterglow model, unless evolving microphysical parameters are assumed. Besides, the multi-band afterglow light curves show an achromatic break at around 33 ks. Based on the model of a hard electron spectrum with an injection break, we interpret the observed spectral break as the synchrotron frequency corresponding to the injection break, and the achromatic break as a jet break caused by the jet-edge effect. It is shown that the spectral evolution and the multi-band afterglow light curves of GRB 091127 can be well reproduced by this model.Comment: 25 pages, 2 figure

On the morphology of γ−\gamma-ray emission induced by e±e^{\pm} from annihilating self-interacting dark matter

With the Fermi-LAT data quite a few research groups have reported a spatially extended GeV $\gamma$-ray excess surrounding the Galactic Center (GC). The physical origin of such a GeV excess is still unclear and one interesting possibility is the inverse Compton scattering of the electrons/positrons from annihilation of self-interacting dark matter (SIDM) particles with the interstellar optical photons. In this work we calculate the morphology of such a kind of $\gamma$-ray emission. For the annihilation channel of $\bar{\chi}\chi\rightarrow \phi\phi\rightarrow e^{+}e^{-}e^{+}e^{-}$, the inverse Compton scattering (ICS) dominates over the bremsstrahlung on producing the GeV $\gamma$-ray emission. For the SIDM particles with a rest mass $m_\chi \sim$ tens GeV that may be favored by the modeling of the Galactic GeV excess, the ICS radiation at GeV energies concentrates along the Galactic plane. The degrees of asymmetry high up to $\geq 0.3$ are found in some regions of interest, which in turn proposes a plausible test on the SIDM interpretation of the GeV excess.Comment: 9 pages, 6 figures, Phys. Rev. D in pres

New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the (2+1)-flavor NJL model

In this paper, we study the pseudo-Wigner solution of the quark gap equation with a recently proposed algorithm in the framework of the (2+1)-flavor Nambu-Jona-Lasinio (NJL) model. We find that for the current quark mass $m_{\rm u,d}=5.5$ MeV and chemical potential $\mu<\mu_{\rm TCP}=272.5$ MeV, the Nambu solution and the positive pseudo-Wigner solution obtained via this algorithm is consistent with the physical solution obtained with the iterative method. Furthermore, the algorithm we used can help to illustrate the evolution of the solutions of the gap equation from the chiral limit to non-chiral limit and gives a prediction where the crossover line is located in the phase diagram for $\mu<272.5$ MeV. In addition, we also study the chiral susceptibilities as well as the loss of solutions for different chemical potentials.Comment: 9 pages, 12 figure

The chiral phase transition of QED3_3 around the critical number of fermion flavors

At zero temperature and density, the nature of the chiral phase transition in QED$_3$ with $\textit{N}_{f}$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors $\textit{N}_{f}$ reaches the critical number $\textit{N}_{f,c}$, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball-Chiu vertex.Comment: 9 pages, 9 figure