2002/10/31 by A. Le Yaouanc, L. Oliver, J. -C. Raynal +1 · 23 citations
Physics and Astronomy · #Bounded function #Function (biology) #High-Energy Particle Collisions Research #Limit (mathematics) #Operator product expansion #Particle physics theoretical and experimental studies #QCD sum rules #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Sum rule in quantum mechanics #hep-ph
paper · pdf · doi:10.1016/s0370-2693(03)00180-1
published in Physics Letters B 557(3-4), 207-212 (Elsevier BV) · 9 pages, Latex
arxiv created 2002/11/06 · openalex publication_date 2003/03/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Using the OPE and the trace formalism, we have obtained a number of sum rules in the heavy quark limit of QCD that include the sum over all excited states for any value jP of the light cloud. We show that these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w-1). Moreover, we obtain sum rules involving the derivatives of the elastic Isgur-Wise function ξ(w) at zero recoil, that imply that the n-th derivative can be bounded by the (n-1)-th one. For the curvature σ2 = ξ''(1), this proves the already proposed bound σ2 ≥ 5 \over 4 ρ2. Moreover, we obtain the absolute bound for the n-th derivative (-1)n ξ(n)(1) ≥ (2n+1)!! \over 22n, that generalizes the results ρ2 ≥ 3 \over 4 and σ2 ≥ 15 \over 16.