Perturbative corrections to curvature sum rules

Abstract

Two new sum rules were recently discovered by Le Yaouanc et al. by applying the operator product expansion to the nonforward matrix element of a time-ordered product of $b\to c$ currents in the heavy-quark limit of QCD. They lead to the constraints ${\sigma }^2>5{\rho }^2/4$ and ${\sigma }^2>3({\rho }^2{)}^2/5+4{\rho }^2/5$ on the curvature of the $\bar{B}\to D^{(\ast )}$ Isgur-Wise function, both of which imply the absolute lower bound ${\sigma }^2>15/16$ when combined with the Uraltsev bound ${\rho }^2>3/4$ on the slope. This paper calculates order ${\alpha }_s$ corrections to these bounds, increasing the accuracy of the resultant constraints on the physical form factors. The latter may have implications for the determination of $|V_{cb}|$ from exclusive semileptonic $B$ meson decays.

19 pages, 4 figures; minor clarifications, additional figure

References in corpus (22)

• Heavy Quark Symmetry
• Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors
• Precision Corrections to Dispersive Bounds on Form Factors
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• Model-Independent Extraction of |V_{cb}| Using Dispersion Relations
• Two-loop QCD corrections to $b\to c$ transitions at zero recoil
• New Exact Heavy Quark Sum Rules
• Improved Bounds for the Slope and Curvature of $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$ Form Factors
• QCD Sum Rule Analysis of the Subleading Isgur-Wise Form Factor ${\chi }_2(v\cdot v^{\prime })$
• The Subleading Isgur-Wise Form Factor ${\xi }_3(v\cdot v^{\prime })$ and its Implications for the Decays $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$
• Perturbative corrections to zero recoil inclusive $B$ decay sum rules
• Two-loop QCD Corrections to $b\to c$ Transitions at Zero Recoil: Analytical Results
• Measurement of Br(Bbar -> D+l-nubar) and Determination of |Vcb|
• The Subleading Isgur-Wise Form Factor ${\chi }_3(v\cdot v^{\prime })$ to Order ${\alpha }_s$ in QCD Sum Rules
• Lower bounds on the curvature of the Isgur-Wise function
• Semileptonic B and Lambda_b Decays and Local Duality in QCD
• Determination of |Vcb| using the semileptonic decay \bar{B}^0 --> D^{*+}e^-\barν
• Heavy quark symmetry in B -> D(*) ell nu spectra
• 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
• Corrections to the Bjorken and Voloshin sum rules
• Bounding Heavy Meson Form Factors Using Inclusive Sum Rules

Cited by in corpus (10)

• A proposal to solve some puzzles in semileptonic B decays
• On the significance of B-decays to radially excited D
• Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu
• Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0
• 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
• Lagrangian perturbations at order 1/m${}_{\mathbf{Q}}$ and the non-forward amplitude in Heavy Quark Effective Theory
• Isgur-Wise functions and unitary representations of the Lorentz group : the meson case j = 1/2
• Isgur-Wise functions, Bjorken-Uraltsev Sum Rules and their Lorentz group interpretation, In Memoriam Nikolai Uraltsev