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.