$E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation

Abstract

This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\to 1^{--}\gamma$, and E1 transitions involving axial vector mesons such as, $1^{+-}\to 0^{-+}\gamma$, and $0^{-+}\to 1^{+-}\gamma$ 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.

arXiv comment26 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:2004.12444

References in corpus (35)

• Big-Bang Nucleosynthesis
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Higher Charmonia
• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Mesons with Beauty and Charm: Spectroscopy
• Quarkonia and their transitions
• $B_c$ spectroscopy
• Evidence of Two Resonant Structures in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$
• Precision tests of the J/ψ from full lattice QCD: mass, leptonic width and radiative decay rate to η_c
• q\bar q$ bound states in the Bethe-Salpeter formalism
• Decay constants and radiative decays of heavy mesons in light-front quark model
• Charmonium spectrum and their electromagnetic transitions with higher multipole contributions
• Model-independent Study of Magnetic Dipole Transitions in Quarkonium
• Observation of h_c(^1P_1) State of Charmonium
• Quarkonium mass splittings in three-flavor lattice QCD
• Lattice QCD study of the radiative decays $J/\psi \to {\eta }_c\gamma$ and $h_c\to {\eta }_c\gamma$
• $B_c$ Spectroscopy from Lattice QCD
• Improved determination of Heavy Quarkonium magnetic dipole transitions in pNRQCD
• Mass spectra and decay properties of $D_s$ Meson in a relativistic Dirac formalism
• Radiative transitions between $0^{-+}$ and $1^{--}$ heavy quarkonia on the light front
• Spectroscopy of ground and excited states of pseudoscalar and vector charmonium and bottomonium
• A Dynamical Principle For 3D-4D Interlinkage In Salpeter-like Equations
• Generalized structure of hadron-quark vertex function in Bethe-Salpeter framework: Applications to leptonic decays of V-mesons
• Relevance of various Dirac covariants in hadronic Bethe-Salpeter wave functions in electromagnetic decays of ground state vector mesons
• Arranging Dirac covariants in hadronic Bethe-Salpeter wave functions for pseudoscalar meson decays
• Bethe-Salpeter study of radially excited vector quarkonia
• Analytic approach to calculations of mass spectra and decay constants of heavy-light quarkonia in the framework of Bethe-Salpeter equation
• Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach
• An approach to calculation of mass spectra and two-photon decays of $c\overline{c}$ mesons in the framework of Bethe-Salpeter Equation
• The Electromagnetic Decays of $B_c^{\pm }(2S)$
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation
• Potential description of the charmonium from lattice QCD
• Revisiting radiative decays of $1^{+-}$ heavy quarkonia in the covariant light-front approach