Sum rules for radiative and strong decays of heavy mesons.

We derive two model-independent sum rules relating the transition matrix elements for radiative and strong decays of excited heavy mesons to properties of the lowest-lying heavy mesons. The sum rule for the radiative decays is an analog of the Cabibbo-Radicati sum rule and expresses the sum of the radiative widths in terms of the isovector charge radius of the ground state heavy meson. Using model-dependent estimates and heavy hadron chiral perturbation theory calculations, we show that this sum rule is close to saturation with states of excitation energies less than 1 GeV. An analog of the AdlerWeisberger sum rule gives an useful sum rule for the pionic widths of heavy excited mesons, which is used to set a model-independent upper bound on the coupling of the P-wave heavy mesons. Typeset using REVTEX 1 We present in this paper two model-independent sum rules for the photon and pion couplings to the light constituents in a heavy meson. They relate properties of the ground state such as charge radius, magnetic moment and axial coupling to matrix elements which govern the radiative and strong transitions between excited heavy meson states and the ground state. The latter parameters can be in principle extracted from experiment and in fact, a few of them have been already determined in this way. The sum rules themselves are not new, they are direct analogs of the Cabibbo-Radicati (CR) [1] and respectively Adler-Weisberger (AW) [2,3] sum rules, familiar from current algebra. However, in this new context they turn out to be considerably more predictive than in their original application, due to additional constraints on the quantum numbers of the available final states. Moreover, when considered in the large-Nc limit, the form of the sum rules simplifies further due to the suppression of the continuum contribution. The CR sum rule reduces in this limit to a constituent-quark sum rule familiar from nonrelativistic quantum mechanics, connecting the charge radius of the ground state to a sum over electric dipole matrix elements between excited states and the ground state [4]. These sum rules are of interest from a phenomenological point of view, as they can be used to place constraints on the photon and pion couplings of low-lying heavy mesons to excited ones. As a sample application, we derive model-independent upper bounds on the pionic decay widths of the charmed p-wave heavy mesons with the quantum numbers of the light degrees of freedom sl l = 1/2 . The Cabibbo-Radicati sum rule can be derived (we follow here the derivation given in [5–7]) by considering the forward scattering amplitude of isovector photons of energy ω and helicity λ on a target B