Constraints on the photon polarisation in $b\to s\gamma$ transitions using $B_s^0\to \phi e^{+}{e}^{-}$ decays

An angular analysis of the $B_s^0\to \phi e^{+}{e}^{-}$ decay is performed using the proton-proton collision dataset collected between 2011 and 2018 by the LHCb experiment, corresponding to an integrated luminosity of $9{\mathrm{f}\mathrm{b}}^{-1}$ at centre-of-mass energies of 7, 8 and $13\mathrm{T}\mathrm{e}\mathrm{V}$. The analysis is performed in the very low dielectron invariant mass-squared region between $0.0009$ and $0.2615{\mathrm{G}\mathrm{e}\mathrm{V}}^2\text{\hspace{0.17em}⁣}\mathrm{/}{c}^4$. The longitudinal polarisation fraction of the $\phi$ meson is measured to be less than $11.5\mathrm{\%}$ at $90\mathrm{\%}$ confidence level. The $A_{\mathrm{T}}^{\mathcal{R}eC\text{\hspace{0.17em}⁣}P}$ observable, which is related to the lepton forward-backward asymmetry, is measured to be $0.116\pm 0.155\pm 0.006$, where the first uncertainty is statistical and the second systematic. The transverse asymmetries, $A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathcal{I}mC\text{\hspace{0.17em}⁣}P}$, which are sensitive to the virtual photon polarisation, are found to be $-0.045\pm 0.235\pm 0.014$ and $0.002\pm 0.247\pm 0.016$, respectively. The results are consistent with Standard Model predictions.