Decay constants in the heavy quark limit in models à la Bakamjian and Thomas

Abstract

In quark models à la Bakamjian and Thomas, that yield covariance and Isgur-Wise scaling of form factors in the heavy quark limit, we compute the decay constants $f^{(n)}$ and $f_{1/2}^{(n)}$ of S-wave and P-wave mesons composed of heavy and light quarks. Heavy quark limit scaling $\sqrt{M}f=Cst$ is obtained, and it is shown that this class of models satisfies the sum rules involving decay constants and Isgur-Wise functions recently formulated by us in the heavy quark limit of QCD. Moreover, the model also satisfies the selection rules of the type $f_{3/2}^{(n)}=0$ that must hold in this limit. We discuss different Ansätze for the dynamics of the mass operator at rest. For non-relativistic kinetic energies $\frac{p^2}{2m}$ the decay constants are finite even if the potential $V(r)$ has a Coulomb part. For the relativistic form $\sqrt{p^2+m^2}$, the S-wave decay constants diverge if there is a Coulomb singularity. Using phenomenological models of the spectrum with relativistic kinetic energy and regularized short distance part (Godfrey-Isgur model or Richardson potential of Colangelo et al.), that yield ${\rho }^2\simeq 1$ for the elastic Isgur-Wise function, we compute the decay constants in the heavy quark limit, and obtain $f_B\simeq$ 300 MeV, of the same order although slightly smaller than in the static limit of lattice QCD. We find the decay constants of $D^{\ast \ast }$ with $j=1/2$ of the same order of magnitude. The convergence of the heavy quark limit sum rules is also studied.

21 pages, 2 figures, LaTeX2e, amsbsy (from the AMS-LaTeX package), epsf

References in corpus (2)

• Quantitative Predictions for $B$ semileptonic decays into $D,D^{\ast }$ and the orbitally excited $D^{\ast \ast }$ in quark models à la Bakamjian-Thomas
• Slope of the Isgur-Wise function in the heavy mass limit of quark models à la Bakamjian-Thomas

Cited by in corpus (12)

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• The decays $\bar{B}\to D^{\ast \ast }\pi$ and the Isgur-Wise functions ${\tau }_{1/2}(w)$, ${\tau }_{3/2}(w)$
• Soft Photon Problem in Leptonic B-decays
• Uraltsev Sum Rule in Bakamjian-Thomas Quark Models
• Spatial distributions in static heavy-light mesons: a comparison of quark models with lattice QCD
• Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons
• On P-wave meson decay constants in the heavy quark limit of QCD
• Finite mass corrections for B -> D(*), D** \ell νdecays in the Bakamjian-Thomas relativistic quark model
• Subleading form factors at order 1/m_Q in terms of leading quantities using the non-forward amplitude in HQET
• Static and dynamic properties of hadronic systems with heavy quarks b and c