Regularization dependence of pion generalised parton distributions

Pion generalised parton distributions are calculated within the framework of the Nambu--Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three dimensional momentum cutoff scheme, the four dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalised parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalised parton distributions, which related to the electromagnetic and gravitational form factors of pion. Pion generalised parton distributions are continuous but not differential at $x=\pm \,\xi$, when considering the effect of D-term, generalised parton distributions become not continuous at $x=\pm \,\xi$ in all the four regularization schemes. Generalised parton distributions in impact parameter space are considered, the width distribution of $u$ quark in the pion and the mean-squared $\langle \mathbf{b}_{\bot}^2\rangle_{\pi}^u$ are calculated. The light-front transverse-spin distributions are studied, when quark polarized in the light-front-transverse $+\,x$ direction, the transverse-spin density is no longer symmetric around $(b_x=0,b_y=0)$, the peaks shift to $(b_x=0,b_y>0)$, we compare the average transverse shift $\langle b_{\bot}^y\rangle_1^u$ and $\langle b_{\bot}^y\rangle_2^u$ in different regularization schemes. The light-cone energy radius $r_{E,LC}$ and the light-cone charge radius $r_{c,LC}$ are also evaluated, we find that in the proper time regularization scheme the values of these quantities are the largest, in the three dimensional momentum cutoff scheme they are the smallest.Comment: 34 pages, 39 figure

Which Constituent Quark Model Is Better?

A comparative study has been done by calculating the effective baryon-baryon interactions of the 64 lowest channels consisting of octet and decuplet baryons with three constituent quark models: the extended quark gluon exchange model, the Goldstone boson exchange model and the quark gluon meson exchange hybrid model. We find that these three models give similar results for 44 channels. Further tests of these models are discussed.Comment: 6pp., 3 figs., Asia-Pacific Few-Body Conf. II (Shanghai, Aug.25-30 2002), to appear in MPLA; references adde

Study of qqqqˉQqqq\bar{q}Q pentaquark system in the Chiral Quark Model

With the discovery of some hidden-charm pentaquark resonances by the LHCb Collaboration, investigations of pentaquark states containing heavy quarks have aroused the interest of theorists. We study herein $qqq\bar{q}Q$ ($q = u$ or $d$, $Q=c$ or $b$) pentaquark system, in the framework of the chiral quark model. In consequence, some charmed and bottomed pentaquarks are considered to exist by five-body dynamical calculations. In the charm sector, $\Sigma_c\pi(IJ^P=0\frac{1}{2}^-)$ and $\Sigma_c^*\pi(IJ^P=0\frac{3}{2}^-)$ are possible candidates of $\Lambda_c(2595)$ and $\Lambda_c(2625)$, respectively. Besides, two high-spin states, $\Sigma_c^*\rho(IJ^P=0\frac{5}{2}^-)$ and $\Delta D^*(IJ^P=1\frac{5}{2}^-)$, are also found in the energy region of $3.2 \sim 3.3$ GeV. In the bottom sector, $\Sigma_b\pi(IJ^P=0\frac{1}{2}^-)$, $\Sigma_b^*\pi(IJ^P=0\frac{3}{2}^-)$ could be candidates of $\Lambda_b(5912)$ and $\Lambda_b(5920)$, respectively. And $\Sigma_b^*\rho(IJ^P=0\frac{5}{2}^-)$ and $\Delta B^*(IJ^P=1\frac{5}{2}^-)$ are found in the energy region of $6.5 \sim 6.6$ GeV. $\Sigma_c^{(*)}\pi$ and $\Sigma_b^{(*)}\pi$ are expected as compact states, while $\Sigma_c^*\rho$, $\Sigma_b^*\rho$, $\Delta D^*$ and $\Delta B^*$ are expected as molecular states.Comment: 11 pages, 1 figur

Contact interaction analysis of pion GTMDs

A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction's simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions (GPDs), it is found that the pion's mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion's core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions (TMDs), their magnitude and domain of support decrease with increasing twist. The simplest Wigner distribution associated with the pion's twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.Comment: 20 pages, 12 figures, 1 tabl