2001/02/28 by Hungchong Kim · 1 citation
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.64.014022
published as Phys.Rev. D64 (2001) 014022 · 14 pages including 3 figures. slightly revised. Accepted for publication in Physical Review D
arxiv created 2001/04/02 · openalex publication_date 2001/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the higher order corrections of quark masses to the Gell-Mann--Oakes--Renner (GOR) relation by constructing QCD sum rules exclusively for pseudoscalar mesons from the axial-vector correlation function, i\ensuremath∫d4xe^ip\ensuremath⋅x〈0|T[A_\ensuremathμ(x)A_\ensuremathν(0)]|0〉. To project out the pseudoscalar meson contributions, we apply \ensuremath-p^\ensuremathμp^\ensuremathν/p2 to this correlation function and construct sum rules for the decay constants of pseudoscalar mesons, f_\ensuremathπ,fk, and f_\ensuremathη8. The operator product expansion (OPE) is proportional to quark masses due to PCAC (partial conservation of axial-vector current). To leading order in quark mass, each sum rule reproduces the corresponding GOR relation. For kaon and \ensuremathη8, the deviation from the GOR relation due to higher orders in quark mass is found to be substantial. But the deviation gives better agreement with phenomenology. Our sum rule provides a sensitive relation between fK and ms, which stringently constrains the value for ms. To reproduce the experimental value for fK, ms is found to be 186 MeV at 1 GeV scale. The f_\ensuremathη8 sum rule also supports this finding.