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 $9~\text{fb}^{-1}$ at centre-of-mass energies of $7$, $8$, and $13~\text{TeV}$.

The analysis is performed in the very low dielectron invariant mass-squared region between

$0.0009~\text{GeV}^2/c^4 \quad \text{and} \quad 0.2615~\text{GeV}^2/c^4.$

The longitudinal polarisation fraction of the $\phi$ meson is measured to be less than $11.5\%$ at $90\%$ confidence level. The \texttt{AReCPT} 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, $A^{(2)}_T$ and $A_{\text{ImCPT}}$, which are sensitive to the virtual photon polarisation, are found to be

$A^{(2)}_T = -0.045 \pm 0.235 \pm 0.014 \quad \text{and} \quad A_{\text{ImCPT}} = 0.002 \pm 0.247 \pm 0.016,$

respectively. The results are consistent with Standard Model predictions.