1202.4775 (Zhi-Guo He)

Investigating the heavy quarkonium radiative transitions with the
effective Lagrangian method    [PDF]

Zhi-Guo He

In this work, we study the radiative decay of heavy quarkonium states by
using the effective Lagrangian approach. Firstly, we construct the
spin-breaking terms in the effective Lagrangian for the $nP\leftrightarrow mS$
transitions and determine the some of the coupling constants by fitting the
experimental data. Our results show that in $\chi_{cJ}$, $\psi(2S)$,
$\Upsilon(2S)$, and $\Upsilon(3S)$ radiative decays, the spin-breaking effect
is so small that can be ignored. Secondly, we investigate the radiative decay
widths of the $c\bar{c}(1D)$ states and find the if $\psi(3770)$ is a pure
$^3D_1$ state its radiative decay into $\chi_{cJ}+\gamma$ roughly preserve the
heavy-quark spin symmetry, while if it is a $S-D$ mixing state with mixing
angel $12^{\circ}$ the heavy quark-spin symmetry in its radiative decay and in
the radiative decay of $\psi(3686)$ will be largely violated. In the end, we
show that combining the radiative decay and the light hadron decay of $P$-wave
$\chi_{bJ}(1,2P)$ can provide another way to extract the information of the
color-octet matrix element in the context of non-relativistic QCD (NRQCD)
effective theory, and our result is consistent with potential NRQCD hypothesis.

View original: http://arxiv.org/abs/1202.4775