2008/08/31 by A. Le Yaouanc, L. Oliver, J.‐C. Raynal +1 · 11 citations
Mathematics · Physics and Astronomy · #Baryon #Black Holes and Theoretical Physics #Branching fraction #Combinatorics #Electron #Hadron #Lambda #Lepton #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #Semileptonic decay #hep-ph
paper · pdf · doi:10.1103/physrevd.79.014023
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 79(1) (American Physical Society) · 16 pages
arxiv created 2008/12/03 · openalex publication_date 2009/01/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the heavy quark limit of QCD, using the operator product expansion, the formalism of Falk for hadrons of arbitrary spin, and the nonforward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function \ensuremathξ_\ensuremathΛ(w) of the baryon transition \ensuremathΛb\ensuremath→\ensuremathΛc\ensuremathℓ\ensuremathν_\ensuremathℓ, where the light cloud has jP=0+ for both initial and final baryons. We recover the lower bound for the slope \ensuremathρ_\ensuremathΛ2=\ensuremath-\ensuremathξ_\ensuremathΛ^\ensuremath'(1)\ensuremath≥0 obtained by Isgur et al., and we generalize it by demonstrating that the Isgur-Wise function \ensuremathξ_\ensuremathΛ(w) is an alternate series in powers of (w\ensuremath-1), i.e. (\ensuremath-1)n\ensuremathξ_\ensuremathΛ(n)(1)\ensuremath≥0. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, \ensuremathσ_\ensuremathΛ2=\ensuremathξ_\ensuremathΛ^\ensuremath'\ensuremath'(1)\ensuremath≥(3)/(5)[\ensuremathρ_\ensuremathΛ2+(\ensuremathρ_\ensuremathΛ2)2]. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay \ensuremathΛb\ensuremath→\ensuremathΛc\ensuremathℓ\ensuremathν_\ensuremathℓ, that has a large measured branching ratio, of about 5%.