Radiative heavy meson transitions

We evaluate the radiative and hadronic decay rates of the D mesons using the Heavy Quark Effective Theory and the Vector Meson Dominance hypothesis. We also estimate the width of the B electromagnetic transitions and the radiative decays of positive parity J = 0, 1 charmed mesons. e-mail address: [email protected] In this letter we wish to show that the heavy quark and chiral SU(3)L × SU(3)R symmetries of QCD, together with the Vector Meson Dominance (VMD) hypothesis, can be used to relate radiative and semileptonic charmed meson decays. We shall show that, using experimental data on the D → πlνl, D → Klνl and D → Klνl transitions as an input, it is possible to predict the radiative branching ratios D → Dγ, the hadronic rate D → Dπ and therefore the full D width. Moreover, the heavy quark flavour symmetry will provide us with a prediction of the B decay rate. We shall also employ information on the positive parity J = 0, 1 charmed mesons (masses and couplings) from the analysis of semileptonic D decays via axial currents in order to get predictions on the radiative decays of these states as well. The calculation is based on a chiral lagrangian approach to the heavy and light meson interactions incorporating the chiral symmetry and the heavy quark spin flavour symmetry [1, 2]. At the lowest order in the light meson derivatives, the chiral lagrangian can be written as follows: L = L0 + L2 + ... , (1) where L0 contains the light meson matrix Σ and the heavy meson fields H : L0 = f 2 π 8 < ∂Σ∂μΣ † > +i < Hbv DμbaH̄a > +ig < Hbγμγ5AμbaH̄a > , (2) whereas L2 [2] describes the interactions with the light J = 1 mesons: L2 = − f 2 π 2 a < (Vμ − ρμ)2 > + 1 2g V < Fμν(ρ)F (ρ) > + iβ < Hbv μ (Vμ − ρμ)ba H̄a > + β 2f 2 πa < H̄bHaH̄aHb > +iλ < Hbσ Fμν(ρ)baH̄a > . (3) In eqs.(2,3) < . . . > means the trace, fπ = 132MeV and: Dμba = δba∂μ + Vμba = δba∂μ + 1 2 (