Amplitude analysis of the radiative decay $B^0_s\to K^+K^-\gamma$

TL;DR

This paper reports the first observation of the radiative decay $B^0_s o f'_2(1525)\gamma$, analyzing the resonant structure of the $K^+K^-\gamma$ final state using LHCb data, and measuring the relative branching ratio with high precision.

Contribution

It provides the first observation of the $B^0_s o f'_2(1525)\gamma$ decay and offers detailed amplitude analysis of the resonant structure in radiative $B^0_s$ decays.

Findings

Dominance of the $ ext{phi}(1020)$ resonance in the $K^+K^-$ spectrum.

Measurement of the tensor contribution to the amplitude as approximately 16.8%.

First observation of the $B^0_s o f'_2(1525)\gamma$ decay with a measured relative branching ratio.

Abstract

A search for radiative decay of $B^0_s$ mesons to orbitally excited $K^+K^-$ states is performed using proton proton collisions recorded by the \mbox{LHCb}\xspace experiment, corresponding to an integrated luminosity of 9~fb$^{-1}$. The dikaon spectrum in the mass range $m_{KK}<2400$~{\ensuremath{\,\text{Me\kern -0.1em V\!/}c^2}\xspace} is dominated by the $\phi(1020)$ resonance that accounts for almost 70$\%$ of the decay rate. Considering the possible contributions of $f_2{(1270)}$, $f'_2{(1525)}$ and $f_2{(2010)}$ meson states, the overall tensor contribution to the amplitude is measured to be \begin{equation} {\cal F}_{\{f_2\}}=16.8\pm 0.5\mathrm{~(stat.)}\pm0.7\mathrm{~(syst.)}\%,\nonumber \end{equation} mostly dominated by the $f'_2(1525)$ state. Several statistically equivalent solutions are obtained for the detailed resonant structure depending on whether the smaller amplitudes interfere destructively or constructively with the dominant amplitude. The preferred solution that corresponds to the lowest values of the fit fractions along with constructive interference leads to the relative branching ratio measurement \begin{equation} \frac{{\cal B}(B^0_s\to f'_2\gamma)}{{\cal B}(B^0_s\to\phi\gamma)}= 19.4^{+0.9}_{-0.8}\mathrm{~(stat.)}{}^{+1.4}_{-0.5}\mathrm{~(syst.)}\pm0.5\mathrm{~(\cal{B})}\%\nonumber, \end{equation} where the last uncertainty is due to the ratio of measured branching fractions to the $K^+K^-$ final state. This result represents the first observation of the radiative $B^0_s\to f'_2(1525)\gamma$ decay, which is the second radiative transition observed in the $B^0_s$ sector.