Model-independent analysis of B → πℓ + ℓ − decays

Abstract

The results obtained by calculating, on the basis of the Standard Model, the branching fractions for the decays B → π + − ( ± = e ± , μ ± ) and the invariant-mass spectrum of dileptons for the process B + → π + + − are presented. The resulting theoretical estimates depend on the choice of model for the B → π transition form factors f + (q 2 ), f 0 (q 2 ), and f T (q 2 ). However, one can get rid of this arbitrariness by employing experimental data or the results of QCD lattice calculations to determine the parameter dependence of the form factors. Data from B-meson factories were used to determine the dependence of the form factor f + (q 2 ) on the transfer momentum squared. Yet another required form factor, f T (q 2 ), was extracted from available lattice data on B → π and B → K transitions with allowance for nearly identical effects of the breakdown of flavor SU (3) F symmetry in the respective form factors. The resulting value of the decay branching fraction, B(B + → π + μ + μ − ) = 1.88 +0.32 −0.21 × 10 −8 , is in good agreement with the results of measurements of the LHCb Collaboration. The branching fraction for the isospin analog of the decay under consideration is B(B 0 → π 0 μ + μ − ) = 0.94 +0.16 −0.11 × 10 −8 . Therefore, this decay can be measured at the Super-B factory under construction.

Annihilation-Type Semileptonic B-Meson Decays

“…Our prediction for the branching fraction of the B ± → π ± µ + µ − decay coincides with the LHCb measurement [22] within large experimental errors. The B + → π + µ + µ − dilepton invariant-mass spectrum was measured by the LHCb collaboration recently [23] and is also in a good agreement with theoretical predictions [18,19] except the first bin q 2 < 1 GeV 2 . This part of the spectrum is sizably enhanced by the long-distance contributions from the two-body B-meson decays like B → π(ρ, ω, φ) and was worked out in [24] which correct our predictions.…”

“…This part of the spectrum is sizably enhanced by the long-distance contributions from the two-body B-meson decays like B → π(ρ, ω, φ) and was worked out in [24] which correct our predictions. The predictions for the B 0 → π 0 + − decay also presented by us [18,19] can be precisely tested at the forthcoming Super-KEKB factory at KEK. There exist more rare Semileptonic and radiative decays of B-mesons which are of the annihilation type and consequently they are not observed at present.…”

“…Within the QCD Factorization approach, the phenomenological analysis of the B ± → π ± + − decays, where is an electron or muon, has been completed [18,19]. These decays are very similar to the exclusive B → (K, K * ) + − decays which have received a lot of theoretical attention in the past and are under intensive experimental and phenomenological analysis at present (see [20,21]).…”

Rare $$B\rightarrow \pi l\bar{l}$$ B → π l l ¯ and $$B\rightarrow \rho l \bar{l}$$ B → ρ l l ¯ decays in the relativistic quark model

“…The rough estimate of the total uncertainty of the form factors within our model is of order of 5 %. In Table 2 we compare the predictions of our model for the weak B → π(ρ) decay form factors at the maximum recoil point q 2 = 0 with other theoretical calculations [16][17][18][19][20][21][22]. The different versions of light-cone sum rules are employed in Refs.…”

“…The authors of Ref. [22] extract the form factors combining available experimental data on semileptonic B → πlν l decays and lattice QCD calculations of the corresponding form factors for the rare B → K transitions within the SU (3)-breaking Ansatz. Comparison of the results presented in this table shows that, although there are some differences between the central values of predictions, in general there is a reasonable agreement between the values of these form factors at zero recoil calculated using significantly different theoretical methods.…”