New Heavy Quark Limit Sum Rules involving Isgur-Wise Functions and Decay Constants

Abstract

We consider the dominant $c\bar{c}$ contribution to $\Delta \Gamma$ for the $B_s^0$-${\bar{B}}_s^0$ system in the heavy quark limit for both $b$ and $c$ quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron decay, we impose duality between the parton model calculation of $\Delta \Gamma$ and its estimation by a sum over heavy mesons. Varying the mass ratio $m_c/m_b$ and assuming factorization and saturation by narrow resonances $(N_c\to \infty$), we obtain new sum rules that involve the Isgur-Wise functions ${\xi }^{(n)}(w)$ and ${\tau }_{1/2}^{(n)}(w)$ and the decay constants $f^{(n)}$, $f_{1/2}^{(n)}$ ($n$ stands for any radial excitation). Alternatively, we deduce the sum rules with another method free of the factorization hypothesis, from the saturation of the expectation value of a product of two currents by heavy hadrons and by the corresponding free quarks. The sum rules read $\sum _n\frac{f^{(n)}}{f^{(0)}}{\xi }^{(n)}(w)=2\sum _n\frac{f_{1/2}^{(n)}}{f^{(0)}}{\tau }_{1/2}^{(n)}(w)=1$, valid for all $w$. Moreover, we obtain, in the heavy quark limit, $f_{3/2}^{(n)}=0$. As a consequence, unlike the BIW sum rule, the slope of the elastic function $\xi (w)$ is related to radial excitations alone. These are generalizations, rigorous for QCD in the heavy quark limit, of results that have an easy understanding in the non-relativistic quark model.

15 pages

References in corpus (3)

• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays
• Factorization versus Duality in Nonleptonic decays, a Quark Model Approach

Cited by in corpus (26)

• The Physics of the B Factories
• Covariant Light-Front Approach for s-wave and p-wave Mesons: Its Application to Decay Constants and Form Factors
• Dynamics and Decay of Heavy-Light Hadrons
• Decay constants and form factors of s-wave and p-wave mesons in the covariant light-front quark model
• Constituent quark model description of charmonium phenomenology
• Quantitative Predictions for $B$ semileptonic decays into $D,D^{\ast }$ and the orbitally excited $D^{\ast \ast }$ in quark models à la Bakamjian-Thomas
• B0(t) -> DPP time-dependent Dalitz plots, CP-violating angles 2beta, 2beta+gamma, and discrete ambiguities
• Hadronic B Decays Involving Even Parity Charmed Mesons
• How to understand the underlying structures of $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$
• The decays $\bar{B}\to D^{\ast \ast }\pi$ and the Isgur-Wise functions ${\tau }_{1/2}(w)$, ${\tau }_{3/2}(w)$
• Production of P-wave Charmed Mesons in Hadronic B Decays
• Lattice calculation of the Isgur-Wise functions tau_{1/2} and tau_{3/2} with dynamical quarks
• Nonleptonic Weak Decays of B to D_s and D mesons
• Nonleptonic $B\to D^{(\ast )}{D}_{sJ}^{(\ast )}$ decays and the nature of the orbitally excited charmed-strange mesons
• Semileptonic and leptonic $B$ decays, circa 2016
• Decay constants in the heavy quark limit in models à la Bakamjian and Thomas
• Slope of the Isgur-Wise function in the heavy mass limit of quark models à la Bakamjian-Thomas
• Progress on semi-leptonic $B_{(s)}$ decays
• Study of the decays B->D_s1(2536)+ anti-D(*)
• On P-wave meson decay constants in the heavy quark limit of QCD
• Status of $|V_{cb}|$ and $|V_{ub}|$ CKM matrix elements
• Semileptonic $B\to D^{\ast \ast }$ decays in Lattice QCD : a feasibility study and first results
• Finite mass corrections for B -> D(*), D** \ell νdecays in the Bakamjian-Thomas relativistic quark model
• The role of $D^{\star \star }$ in $B^{-}\to D_s^{+}{K}^{-}{\pi }^{-}$
• Study of light-cone distribution amplitudes for p-wave heavy mesons
• Parity-even and Parity-odd Mesons in Covariant Light-front Approach