Coulomb corrections in rare decays of neutral $B$ mesons with $ll^+ll^-$-pair in final state

We present a systematic analysis of Coulomb corrections for leptonic ($B^0_{d,s}\to \ell^+\ell^-$), semileptonic ($B^0_{d,s}\to h^0,\ell^+\ell^-$, $B^0_{d,s}\to V^0\ell^+\ell^-$) and radiative leptonic ($B^0_{d,s}\to γ\ell^+\ell^-$) decays of neutral $B$-mesons. The relativization of the Coulomb factor was performed by comparing the Gamow-Sommerfeld-Sakharov factor, the exact relativistic approach of Crater-Alstine-Sazdjian applied by us to scalar systems, and well-known one-loop QED calculations. Coulomb corrections are calculated for differential, angular, and double-differential distributions, as well as for partial decay widths. For the $B_s^0 \to μ^+μ^-$ channel, Coulomb corrections improve the prediction of the partial width to $δ= |\mathcal{B}^{(exp)} - \mathcal{B}^{(theory)}|/\mathcal{B}^{(exp)} = 2%$. This improvement brings the prediction closer to the LHCb/CMS experimental results within the current experimental (11%) and theoretical (5% lattice QCD) errors. In the decays $B^0\to K^0μ^+μ^-$ and $B^0 \to K^{0*}μ^+μ^-$, Coulomb effects also reduce the discrepancies between theoretical predictions and experimental data (to less than $δ= 1%$ and from $δ= 11%$ to $δ= 4%$ respectively). Finally, for the decays involving $τ$-leptons, the Coulomb correction $\mathcal{K} = \mathcal{B}^{(Coulomb)}/ \mathcal{B}^{(free)}$ reaches 4%. While currently smaller than the dominant form-factor uncertainties and experimental errors, the Coulomb correction represents a non-negligible systematic effect. It should be accounted for in the high-precision era of $B$-physics, where such effects may become significant for the interpretation of potential New Physics signals.

💡 Research Summary

The paper presents a comprehensive study of Coulomb corrections in rare neutral‑B‑meson decays that produce a charged lepton pair in the final state. The authors consider three classes of processes: purely leptonic decays (B⁰_{d,s} → ℓ⁺ℓ⁻), semileptonic decays with a neutral pseudoscalar meson (B⁰_{d,s} → h⁰ℓ⁺ℓ⁻), semileptonic decays with a neutral vector meson (B⁰_{d,s} → V⁰ℓ⁺ℓ⁻), and radiative leptonic decays (B⁰_{d,s} → γℓ⁺ℓ⁻). The central goal is to quantify how the electromagnetic interaction between the two oppositely charged leptons modifies decay rates, differential distributions, and angular observables, and to assess whether these effects can alleviate the long‑standing tensions between Standard Model (SM) predictions and LHCb/CMS/Belle‑II measurements.

Methodological comparison
Three independent ways of computing the Coulomb “K‑factor” are examined. (i) The non‑relativistic Gamow‑Sommerfeld‑Sakharov (GSS) factor K(v)=2π α/v /