Lower bounds on the curvature of the Isgur-Wise function

Abstract

Using the OPE, we obtain new sum rules in the heavy quark limit of QCD, in addition to those previously formulated. Key elements in their derivation are the consideration of the non-forward amplitude, plus the systematic use of boundary conditions that ensure that only a finite number of $j^P$ intermediate states (with their tower of radial excitations) contribute. A study of these sum rules shows that it is possible to bound the curvature ${\sigma }^2={\xi }^{\prime \prime }(1)$ of the elastic Isgur-Wise function $\xi (w)$ in terms of its slope ${\rho }^2=-{\xi }^{\prime }(1)$. Besides the bound ${\sigma }^2\ge \frac{5}{4}{\rho }^2$, previously demonstrated, we find the better bound ${\sigma }^2\ge \frac{1}{5}[4{\rho }^2+3({\rho }^2{)}^2]$. We show that the quadratic term $\frac{3}{5}({\rho }^2{)}^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. At the lowest possible value for the slope ${\rho }^2=\frac{3}{4}$, both bounds imply the same bound for the curvature, ${\sigma }^2\ge \frac{15}{16}$. We point out that these results are consistent with the dispersive bounds, and, furthermore, that they strongly reduce the allowed region by the latter for $\xi (w)$.

39 pages, 2 figures

References in corpus (2)

• Bounds on the derivatives of the Isgur-Wise function from sum rules in the heavy quark limit of QCD
• Sum rules in the heavy quark limit of QCD

Cited by in corpus (27)

• Semileptonic Decays of Heavy Lambda Baryons in a Quark Model
• New analysis of semileptonic B decays in the relativistic quark model
• Measurement of the shape of the ${\Lambda }_b^0\to {\Lambda }_c^{+}{\mu }^{-}\overline{\nu }$ differential decay rate
• 'Bs --> Ds l nu' near zero recoil in and beyond the Standard Model
• $\bar{B}\to D\tau {\bar{\nu }}_{\tau }$ vs. $\bar{B}\to D\mu {\bar{\nu }}_{\mu }$
• The decays $\bar{B}\to D^{\ast \ast }\pi$ and the Isgur-Wise functions ${\tau }_{1/2}(w)$, ${\tau }_{3/2}(w)$
• Measurements of the B to D* Form Factors Using the Decay B0 --> D* e nu_e
• On the significance of B-decays to radially excited D
• Isgur-Wise function in a QCD potential model with coulombic potential as perturbation
• Isgur-Wise function and a new approach to Potential Model
• Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu
• Perturbative corrections to curvature sum rules
• Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0
• Finite mass corrections for B -> D(*), D** \ell νdecays in the Bakamjian-Thomas relativistic quark model
• Bounds on the derivatives of the Isgur-Wise function with a non-relativistic light quark
• B => D(*) transitions in a quark model
• Semileptonic decay of $B_c$ meson into $c\bar{c}$ states in a QCD potential model
• Subleading form factors at order 1/m_Q in terms of leading quantities using the non-forward amplitude in HQET
• Explicit form of the Isgur-Wise function in the BPS limit
• Sum rules of Bjorken-Uraltsev type in the Bakamjian-Thomas relativistic quark model
• Bounds on the slope and curvature of Isgur-Wise function in a QCD inspired quark model
• New results on the baryon decay Lambda_b -> Lambda_c ell nu in Heavy Quark Effective Theory
• Isgur-Wise functions and unitary representations of the Lorentz group : the meson case j = 1/2
• Lagrangian perturbations at order 1/m${}_{\mathbf{Q}}$ and the non-forward amplitude in Heavy Quark Effective Theory
• Unexpected pattern of transitions to radial excitations by heavy quark current
• Memorial Contribution about Kolya Uraltsev's Talk at 2012 Workshop $B\to D\ast \ast$
• Isgur-Wise functions, Bjorken-Uraltsev Sum Rules and their Lorentz group interpretation, In Memoriam Nikolai Uraltsev