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Radiative E1 decays of X(3872)

Radiative E1 decay widths of $\rm X(3872)$ are calculated through the relativistic Salpeter method, with the assumption that $\rm X(3872)$ is the $χ_{c1}$(2P) state, which is the radial excited state of $χ_{c1}$(1P). We firstly calculated the E1 decay width of $χ_{c1}$(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 $χ_{c1}$(2P). Results are: $Γ({\rm X(3872)}\rightarrow γ\sl J/ψ)=33.0$ keV, $Γ({\rm X(3872)}\rightarrow γψ(2S))=146$ keV and $Γ({\rm X(3872)}\rightarrow γψ(3770))=7.09$ keV. The ratio ${{\rm Br(X(3872)}\rightarrowγψ(2{\rm S}))}/{{\rm Br(X(3872)}\rightarrow γ{\sl J}/ψ)}=4.4$ 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: $Γ(χ_{b1}(1\rm P))\rightarrow γΥ(1\rm S))=30.0$ keV, $Γ(χ_{b1}(2\rm P))\rightarrow γΥ(1\rm S))=5.65$ keV and $Γ(χ_{b1}(2\rm P))\rightarrow γΥ(2S))=15.8$ keV, and the full widths: $Γ(χ_{b1}(1\rm P))\sim 85.7$ keV, $Γ(χ_{b1}(2\rm P))\sim 66.5$ keV.