Sum rules for radiative and strong decays of heavy mesons

Abstract

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 REVT E X 1

Four-fermion heavy quark operators and light current amplitudes in heavy flavor hadrons

“…At q 2 = 0 this sum rule is just the familiar Adler-Weisberger sum rule and the amplitudes G n are related to pion couplings between the ground and excited states. The explicit form of these sum rules for heavy mesons and baryons can be found in [14,17]. Therefore, we expect the type of bounds (46,48) to hold also for the axial current expectation values as well.…”

“…The valence formfactors are expected to decrease for non-zero q 2 . For the isovector formfactor the slope at q 2 = 0 (related to the corresponding charge radius) can be estimated in terms of experimentally observable quantities by an analogue of the Cabibbo-Radicati sum rule for heavy hadrons [14]:…”

Predictions fors-wave andp-wave heavy baryons from sum rules and the constituent quark model: Strong interactions

“…Experience with the lowest order χP T results shows that this is very likely the case. 5 A similar reasoning applied to pion-heavy meson scattering gives the inequality h 2 + (S-wave, I=1/2 continuum) ≤ 0.368 (with the notations of [17]). In this case however we can invoke large-N c arguments to argue that the continuum is suppressed.…”

“…have been discussed in [14][15][16][17][18] for the heavy meson case). One possible derivation, which will prove most convenient in the following, is based on the use of the forward (spin-averaged) matrix element of the retarded commutator 3…”

“…We will restrict ourselves to the study of the continuum contributions to the sum rule on a 3 baryon (4.9). Even without an explicit calculation it can be argued, as in the heavy meson case [17], that the continuum contribution must be positive since there are more states containing one heavy quark with isospin 1/2 than 3/2. Our explicit calculations will confirm this conjecture, at least for the low-energy region where we can compute the continuum contribution.…”