Evidence for the decay mode $X(3872)\rightarrow\psi(2S)\gamma$ in $B^+\rightarrow X(3872)K^+$ decays is found with a significance of 4.4 standard deviations. The analysis is based on a data sample of protonproton collisions, corresponding to an integrated luminosity of 3fb$^{1}$ collected with the LHCb detector, at centreofmass energies of 7 and 8TeV. The ratio of the branching fraction of the $X(3872)\to\psi(2S)\gamma$ decay to that of the $X(3872)\rightarrow J/\psi \gamma$ decay is measured to be $$ \frac{Br(X(3872)\rightarrow\psi(2S)\gamma)}{Br(X(3872)\rightarrow J/\psi\gamma)} = 2.46\pm0.64\pm0.29, %\pm0.06,$$ where the first uncertainty is statistical and the second is systematic. The measured value agrees with expectations for a pure charmonium interpretation of the $X(3872)$ state and a mixture of charmonium and molecular interpretations. However, it does not support a pure $D\bar{D}^{*}$ molecular interpretation of the $X(3872)$state.
a) Distribution of the ${ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \gamma K ^+ }$ invariant mass with fit projection overlaid, restricted to those candidates with ${ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \gamma }$ invariant mass within $\pm 3\sigma$ from the $ X (3872)$ peak position. b) Distribution of the ${ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \gamma }$ invariant mass with fit projection overlaid, restricted to those candidates with ${ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \gamma K ^+ }$ invariant mass within $\pm 3\sigma$ from the $ B ^+ $ peak position. The total fit (thick solid blue) together with the signal (thin solid green) and background components (dashdotted orange for the combinatorial, dashed magenta for the peaking component and long dashed blue for their sum) are shown. 
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a) Distribution of the ${\psi {\mathrm{(2S)}} \gamma K ^+ }$ invariant mass with fit projection overlaid, restricted to those candidates with ${\psi {\mathrm{(2S)}} \gamma }$ invariant mass within $\pm 3\sigma$ from the $ X (3872)$ peak position. % b) Distribution of the ${\psi {\mathrm{(2S)}} \gamma }$ invariant mass with fit projection overlaid, restricted to those candidates with ${\psi {\mathrm{(2S)}} \gamma K ^+ }$ invariant mass within $\pm 3\sigma$ from the $ B ^+ $ peak position. The total fit (thick solid blue) together with the signal (thin solid green) and background components (dashdotted orange for the combinatorial, dashed magenta for the peaking component and long dashed blue for their sum) are shown. 
Fig_2.pdf [113 KiB] HiDef png [318 KiB] Thumbnail [264 KiB] *.C file tex code 

Animated gif made out of all figures. 
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Parameters of the signal functions of the fits to the twodimensional mass distributions of the ${ B ^+ \rightarrow X (3872) K ^+ }$ decays followed by ${ X (3872) \rightarrow \psi \gamma }$. Uncertainties are statistical only. 
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Relative systematic uncertainties on the ratio of branching fractions ($R_{\psi \gamma }$). 
Table_2.pdf [47 KiB] HiDef png [93 KiB] Thumbnail [46 KiB] tex code 
Created on 18 October 2019.