{"paper":{"title":"Sum rules in the heavy quark limit of QCD and Isgur-Wise functions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. Le Yaouanc, F. Jugeau, J.-C. Raynal, L. Oliver","submitted_at":"2004-12-10T16:03:32Z","abstract_excerpt":"Using the OPE, we formulate new sum rules in the heavy quark limit of QCD. These sum rules imply that the elastic Isgur-Wise function $\\xi (w)$ is an alternate series in powers of $(w-1)$. Moreover, one gets that the $n$-th derivative of $\\xi (w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute lower bound for the $n$-th derivative $(-1)^n \\xi^{(n)}(1) \\geq {(2n+1)!! \\over 2^{2n}}$. Moreover, for the curvature we find $\\xi ''(1) \\geq {1 \\over 5} [4 \\rho^2 + 3(\\rho^2)^2]$ where $\\rho^2 = - \\xi '(1)$. We show that the quadratic term ${3 \\over 5} (\\rho^2)^2$ has a transparent phys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0412144","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}