On the impact of meson mixing on $B_s\to\phi ee$ angular observables at low $q^2$

Decays based on the $b\to s\gamma$ transition are expected to yield left-handed photons in the Standard Model, but could be particularly sensitive to New Physics contributions modifying the short-distance Wilson coefficients $\mathcal{C}_7$ and $\mathcal{C}_{7'}$ defined in the low-energy Effective Field Theory. These coefficients can be determined by combining observables of several modes, among which $B_s\to\phi ee$ at low $q^2$, in a kinematic range where the photon-pole is dominant. We investigate the impact of $B_s-\bar{B}_s$ mixing on the angular observables available for this mode, which induces a time-dependent modulation governed by interference terms between mixing and decay that are sensitive to the moduli and phases of $\mathcal{C}_7$ and $\mathcal{C}_{7'}$. These interference terms can be extracted through a time-dependent analysis but they also affect time-integrated observables. In particular, we show that the asymmetries $A_T^{(2)}$ and $A_T^{(\text{Im});CP}$ receive terms of potentially similar size from mixing-independent and mixing-induced terms, and we discuss how the constraints coming from the angular analysis of $B_s\to\phi ee$ at low $q^2$ should be interpreted in the presence of mixing.