Electromagnetic decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3823</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> state and its radial excited states
Wei Li, Su-Yan Pei, Tianhong Wang, Yinglong Wang, Tai-Fu Feng, Guo‐Li Wang
Abstract
We study the electromagnetic (EM) decays of $X(3823)$ as the ${\ensuremath{\psi}}_{2}(1{^{3}D}_{2})$ state by using the relativistic Bethe-Salpeter method. Our results are $\mathrm{\ensuremath{\Gamma}}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c0}\ensuremath{\gamma}]=1.2\text{ }\text{ }\mathrm{keV}$, $\mathrm{\ensuremath{\Gamma}}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}\ensuremath{\gamma}]=265\text{ }\text{ }\mathrm{keV}$, $\mathrm{\ensuremath{\Gamma}}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}\ensuremath{\gamma}]=57\text{ }\text{ }\mathrm{keV}$, and $\mathrm{\ensuremath{\Gamma}}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}\ensuremath{\gamma}]=1.3\text{ }\text{ }\mathrm{keV}$. The ratio $\mathcal{B}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}\ensuremath{\gamma}]/\phantom{\rule{0ex}{0ex}}\mathcal{B}[X(3823)\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}\ensuremath{\gamma}]=0.22$, agrees with the experimental data. Similarly, the EM decay widths of ${\ensuremath{\psi}}_{2}({n}^{3}{D}_{2})$, $n=2$, 3, are predicted, and we find the dominant decays channels are ${\ensuremath{\psi}}_{2}(n{^{3}D}_{2})\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}(nP)\ensuremath{\gamma}$, where $n=1$, 2, 3. The wave function include different partial waves, which means the relativistic effects are considered. We also study the contributions of different partial waves.