Radiative E1 decays of X(3872)

TL;DR

This paper calculates the radiative E1 decay widths of X(3872) assuming it is the $ m ext{chi}_{c1}(2P)$ state using the relativistic Salpeter method, finding results consistent with some experimental data and making predictions for related bottomonium states.

Contribution

It is the first to calculate X(3872)'s E1 decay widths under the $ m ext{chi}_{c1}(2P)$ assumption using the relativistic Salpeter method, aligning well with experimental ratios.

Findings

Decay width for X(3872) to $ m ext{J}/ ext{psi}$ is 33.0 keV.

Decay width for X(3872) to $ m ext{psi}(2S)$ is 146 keV.

Predicted decay widths for bottomonium states are provided.

Abstract

Radiative E1 decay widths of $\rm X(3872)$ are calculated through the relativistic Salpeter method, with the assumption that $\rm X(3872)$ is the $\chi_{c1}$(2P) state, which is the radial excited state of $\chi_{c1}$(1P). We firstly calculated the E1 decay width of $\chi_{c1}$(1P), the result is in agreement with experimental data excellently, then we calculated the case of $\rm X(3872)$ with the assignment that it is $\chi_{c1}$(2P). Results are: ${\Gamma}({\rm X(3872)}\rightarrow \gamma \sl J/\psi)=33.0$ keV, ${\Gamma}({\rm X(3872)}\rightarrow \gamma \psi(2S))=146$ keV and ${\Gamma}({\rm X(3872)}\rightarrow \gamma \psi(3770))=7.09$ keV. The ratio ${{\rm Br(X(3872)}\rightarrow\gamma\psi(2{\rm S}))}/{{\rm Br(X(3872)}\rightarrow \gamma {\sl J}/\psi)}=4.4$ agrees with experimental data by BaBar, but larger than the new up-bound reported by Belle recently. With the same method, we also predict the decay widths: ${\Gamma}(\chi_{b1}(1\rm P))\rightarrow \gamma \Upsilon(1\rm S))=30.0$ keV, ${\Gamma}(\chi_{b1}(2\rm P))\rightarrow \gamma \Upsilon(1\rm S))=5.65$ keV and ${\Gamma}(\chi_{b1}(2\rm P))\rightarrow \gamma \Upsilon(2S))=15.8$ keV, and the full widths: ${\Gamma}(\chi_{b1}(1\rm P))\sim 85.7$ keV, ${\Gamma}(\chi_{b1}(2\rm P))\sim 66.5$ keV.