In pursuit of new physics with B_s,d ⁰ → ℓ ⁺ ℓ ⁻

Leptonic rare decays of B_s,d ⁰ mesons offer a powerful tool to search for physics beyond the Standard Model. The B_s ⁰ → μ⁺μ⁻ decay has been observed at the Large Hadron Collider and the first measurement of the effective lifetime of this channel was presented, in accordance with the Standard Model. On the other hand, B_s ⁰ → τ⁺τ⁻ and B_s ⁰ → e⁺e⁻ have received considerably less attention: while LHCb has recently reported a first upper limit of 6.8 × 10⁻³ (95% C.L.) for the B_s ⁰ → τ⁺τ⁻ branching ratio, the upper bound 2.8 × 10⁻⁷ (90% C.L.) for the branching ratio of B_s ⁰ → e⁺e⁻ was reported by CDF back in 2009. We discuss the current status of the interpretation of the measurement of B_s ⁰ → μ⁺μ⁻, and explore the space for New-Physics effects in the other B_s,d ⁰ → ℓ⁺ℓ⁻ decays in a scenario assuming flavour-universal Wilson coefficients of the relevant four-fermion operators. While the New-Physics effects are then strongly suppressed by the ratio m_μ/m_τ of the lepton masses in B_s ⁰ → τ⁺τ⁻, they are hugely enhanced by m_μ/m_e in B_s ⁰ → e⁺e⁻ and may result in a B_s ⁰ → e⁺e⁻ branching ratio as large as about 5 times the one of B_s ⁰ → μ⁺μ⁻, which is about a factor of 20 below the CDF bound; a similar feature arises in B_d ⁰ → e⁺e⁻. Consequently, it would be most interesting to search for the B_s,d ⁰ → e⁺e⁻ channels at the LHC and Belle II, which may result in an unambiguous signal for physics beyond the Standard Model.