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Register a new userRadiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
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In this work we study the radiative decays of heavy-light quarkonia through M1 and E1 transitions, that involve quark-triangle diagrams with two hadron vertices, and are difficult to evaluate in BSE-CIA. We have expressed the transition amplitude, $M_{fi}$ as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadron, with coefficients being related to results of pole integrals over complex $sigma$- plane. We evaluate the decay widths for $M1$ transitions ($^3S_1 rightarrow ^1S_0 +gamma$), and $E1$ transitions ($^3S_1 rightarrow ^1P_0 +gamma$ and $^1P_0 rightarrow ^3S_1 +gamma$). We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $0^{++},1^{--}$, and $0^{-+}$ heavy-light quarkonia in approximate harmonic oscillator basis, to calculate their decay widths. The input parameters used by us were obtained by fitting to their mass spectra. We have compared our results with experimental data and other models, and found reasonable agreements.
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This work is an extension of our previous work in cite{bhatnagar20} to calculate M1 transitions, $0^{-+}rightarrow 1^{--} gamma$, and E1 transitions involving axial vector mesons such as, $1^{+-} rightarrow 0^{-+}gamma$, and $0^{-+}rightarrow 1^{+-} gamma $ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work, we make use of leading Dirac structures in the hadronic Bethe-Salpeter wave functions of the involved hadrons, which makes the formulation more rigorous. We evaluate the decay widths for both the above mentioned $M1$ and $E1$ transitions. We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $1^{--}$,$0^{-+}$ and $1^{+-}$ heavy-light quarkonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. We have compared our results with experimental data, where ever available, and other models.
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.
In this paper we study the properties of diquarks (composed of $u$ and/or $d$ quarks) in the Bethe-Salpeter formalism under the covariant instantaneous approximation. We calculate their BS wave functions and study their effective interaction with the pion. Using the effective coupling constant among the diquarks and the pion, in the heavy quark limit $m_Qtoinfty$, we calculate the decay widths of $Sigma_Q^{(*)}$ ($Q=c,b$) in the BS formalism under the covariant instantaneous approximation and then give predictions of the decay widths $Gamma(Sigma_b^{(*)}toLambda_b+pi)$.
We investigate the properties of mesons with the exotic J^PC = 1^-+ quantum numbers. Starting out from the light-quark domain, where the pi_1 states are used as references, we predict the masses of analogous quarkonia for cbar{c} and bbar{b} configurations. We employ a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach with a rainbow-ladder truncated model of quantum chromodynamics.
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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