Partial wave effects in the heavy quarkonium radiative electromagnetic decays

Abstract

In a previous paper \cite{Bc}, it was pointed out that the wave functions of all particles are not pure waves, besides the main partial waves, they all contain {other partial waves}. It is very interesting to know what role these different partial waves play in particle transitions. Therefore, by using the Bethe-Salpeter equation method, we study the radiative electromagnetic decays $\psi \to \gamma {\chi }_{{}_{cJ}}$ and ${\rm Y}\to \gamma {\chi }_{{}_{bJ}}$ ($J=0,1,2$). We find that for the $S$ and $P$ wave dominated states, like the $\psi (2S)$, ${\rm Y}(2S)$, ${\chi }_{{}_{cJ}}(1P)$, and ${\chi }_{{}_{bJ}}(1P)$ etc., the dominant $S$ and $P$ waves provide main and nonrelativistic contrition to the decays; other partial waves mainly contribute to the relativistic correction. For the states like the $\psi (1D)$, ${\rm Y}(2D)$, ${\chi }_{c2}(1F)$, and ${\chi }_{b2}(1F)$ etc., they are the $S-P-D$ mixing state dominated by $D$ wave or the $P-D-F$ mixing state dominated by $F$ wave. Large decay widths are found in the transitions $\psi (2D)\to {\chi }_{c2}(1F)$, ${\rm Y}(1D)\to {\chi }_{bJ}(1P)$, and ${\rm Y}(2D)\to {\chi }_{bJ}(2P)$ etc., which may be helpful to study the missing states ${\chi }_{c2}(1F)$, ${\rm Y}(1D)$, and ${\rm Y}(2D)$.

31 pages, 19 tables

References in corpus (11)

• Heavy quarkonium: progress, puzzles, and opportunities
• Higher Charmonia and X,Y,Z states with Screened Potential
• Potential model calculations and predictions for heavy quarkonium
• Charmonium spectrum and their electromagnetic transitions with higher multipole contributions
• Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
• Decay constants of $P$-wave mesons
• The mass spectrum and wave functions of the $B_c$ system
• Measurement of $e^{+}{e}^{-}\to \gamma {\chi }_{c0,c1,c2}$ cross sections at center-of-mass energies between 3.77 and 4.60 GeV
• Open charm contributions to the E1 transitions of $\psi (3686)$ and $\psi (3770)\to \gamma {\chi }_{cJ}$
• The solution to the `$1/2$ vs $3/2$' puzzle
• Study of the dilepton electromagnetic decays of ${\chi }_{cJ}(1P)$