The polarization of photons produced in radiative $B^{0}_{s}$ decays is studied for the first time. The data are recorded by the LHCb experiment in $pp$ collisions corresponding to an integrated luminosity of 3fb$^{-1}$ at center-of-mass energies of $7$ and $8$TeV. A time-dependent analysis of the $B^{0}_{s} to phi gamma$ decay rate is conducted to determine the parameter ${mathcal{A}}^Delta$, which is related to the ratio of right- over left-handed photon polarization amplitudes in $b to s gamma$ transitions. A value of ${mathcal{A}}^Delta=-0.98^{,+0.46,+0.23}_{,-0.52,-0.20}$ is measured. This result is consistent with the Standard Model prediction within two standard deviations.
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