Abstract
We present a systematic analysis of Coulomb corrections for the interaction of charged leptons in the final state in lepton and semilepton decays of neutral \(B\) -mesons. The calculation is performed within the Furry picture. For scalar systems, a comparison is made between the nonrelativistic Gamow–Sommerfeld–Sakharov approximation, the exact relativistic method of Crater–Alstine–Sazdjian, and the Furry approach. Based on this comparison, an assumption is made about the applicability of the Furry method for calculating Coulomb corrections in the considered \(B\) -meson decays. The corrections are applied to the analysis of lepton ( \(B^{0}_{d,s}\to\ell^{+}\ell^{-}\) ) and semilepton ( \(B^{0}_{d,s}\to h^{0}\,\ell^{+}\ell^{-}\) , \(B^{0}_{d,s}\to V^{0}\ell^{+}\ell^{-}\) ) channels. Differential, angular, and for the first time double differential distributions, along with partial decay widths, are calculated. For the \(B_{s}^{0}\to\mu^{+}\mu^{-}\) channel, Coulomb corrections improve the prediction of the partial width by 2 \(\%\) , improving the agreement with the LHCb/CMS experimental results within the current experimental (11 \(\%\) ) and theoretical (5 \(\%\) lattice QM) errors. In the decays \(B^{0}\to K^{0}\mu^{+}\mu^{-}\) and \(B^{0}\to K^{*0}\mu^{+}\mu^{-}\) , Coulomb effects also reduce the discrepancies between theoretical predictions and experimental data (to less than \(1\%\) and from 11 to 4 \(\%\) , respectively). Finally, for the decays \(B^{0}_{d,s}\to\{h^{0},V^{0}\}\,\tau^{+}\tau^{-}\) , the Coulomb correction reaches 7 \(\%\) , which is comparable to the uncertainties of the non-perturbative contributions of the strong interaction. The latter result suggests that the Coulomb correction may become significant in the search for new physics in rare \(B\) -meson decays, especially those involving \(\tau\) -leptons in the final states.
