Leptonic constant from B meson radiative decay

We propose a method to determine the leptonic decay constant fB∗ in the infinite heavy quark mass limit from the analysis of the radiative decay mode B− → lν̄lγ. The method relies on HQET symmetries and on experimental data from D∗0 → Dγ. E-mail address: [email protected] The measurement of fB and fB∗ , the leptonic decay constants of the B and B ∗ mesons, defined by the matrix elements: < 0|b̄γμγ5q|B(p) >= ipμfB (1) < 0|b̄γμq|B(p, ǫ) >= mB∗fB∗ǫμ , (2) represents one of the main goals of the current and future experimental investigations in the heavy quark physics. The reason can be found in the prime role played by fB in the hadronic systems containing one heavy quark. To give an example, f 2 B appears in the formula relating the mass difference between the B-meson mass eigenstates to |Vtd| in the box diagram computation of the B − B̄ mixing; therefore, the size of the unitarity triangle and the analysis of possible CP violations in the B systems crucially depend on the value of this hadronic parameter. As a second example of the relevance of the leptonic B constant, we can consider the Heavy Quark Effective Theory applied to the physical world of the heavy hadrons. In the limit mb → ∞, fB and fB∗ scale according to the relation fB = fB∗ = F̂ √ mB . (3) The parameter F̂ , independent (modulo logarithmic corrections) of the heavy quark mass, represents a low-energy parameter related to the non-perturbative dynamics of light quark and gluon degrees of freedom, and plays a role analogous to fπ in chiral theories for light hadrons. On the theoretical side, much effort has been devoted to the calculation of fB = F̂ √ mB by non-perturbative methods such as lattice QCD [1] and QCD sum rules [2]; for example, a QCD sum rules analysis in the infinite heavy quark mass limit provides us with the value: F̂ = 0.25− 0.45 GeV 3 2 . (4) (depending on the inclusion of αs corrections). On the experimental side, the most natural process to measure fB would be the purely leptonic decay mode B− → lν̄l, whose decay width is given by: Γ(B → lν̄l) = GF 8π |Vub|f 2 B (