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Register a new userLight-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
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We investigate the light quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass of sbars exotic 1-+ states, and identify orbital angular momentum content in the excitations of the rho meson. Comparing our covariant model results, the rho and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of $m_pi$ ~ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of $m_pi$.
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In this work, we employ the Bethe-Salpeter (B-S) equation to investigate the spectra of free diquarks and their B-S wave functions. We find that the B-S approach can be consistently applied to study the diqaurks with two heavy quarks or one heavy and one light quarks, but for two light-quark systems, the results are not reliable. There are a few free parameters in the whole scenario which can only be fixed phenomenologically. Thus, to determine them, one has to study baryons which are composed of quarks and diquarks.
Using a well-established effective interaction in a rainbow-ladder truncation model of QCD, we fix the remaining model parameter to the bottomonium ground-state spectrum in a covariant Bethe-Salpeter equation approach and find surprisingly good agreement with the available experimental data including the 2^{--} Upsilon(1D) state. Furthermore, we investigate the consequences of such a fit for charmonium and light-quark ground states.
We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.
This work is an extension of the work in cite{bhatnagar18} to ground and excited states of $0^{++}, 0^{-+}$, and $1^{--}$ of heavy-light ($coverline{u}, coverline{s}, boverline{u}, boverline{s}$, and $boverline{c}$) quarkonia in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure $(gamma_{mu}bigotimesgamma_{mu})$ in the interaction kernel, in contrast to the approximate treatment of the same in our previous works cite{hluf16, bhatnagar18}), which is a substantial improvement over our previous works cite{hluf16,bhatnagar18}. In this $4times 4$ BSE framework, the coupled Salpeter equations for $Qoverline{q}$ (that are more involved than the equal mass ($Qoverline{Q}$) mesons) are first shown to decouple for the confining part of interaction, under heavy-quark approximation, and analyically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of $0^{-+}$, and $1^{--}$ as a test of these wave functions and the over all framework.
The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.
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