QCD sum rules for the pseudoscalar decay constants: To constrain the strange quark mass
We study the higher order corrections of quark masses to the Gell-Mann{endash}Oakes{endash}Renner (GOR) relation by constructing QCD sum rules exclusively for pseudoscalar mesons from the axial-vector correlation function, i{integral}d{sup 4}xe{sup ip{dot x}}{l_angle}0{vert_bar}T[A{sub {mu}}(x)A{sub {nu}}(0)]{vert_bar}0{r_angle}. To project out the pseudoscalar meson contributions, we apply {minus}p{sup {mu}}p{sup {nu}}/p{sup 2} to this correlation function and construct sum rules for the decay constants of pseudoscalar mesons, f{sub {pi}},f{sub k}, and f{sub {eta}{sub 8}}. 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 {eta}{sub 8}, 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 f{sub K} and m{sub s}, which stringently constrains the value for m{sub s}. To reproduce the experimental value for f{sub K}, m{sub s} is found to be 186 MeV at 1 GeV scale. The f{sub {eta}{sub 8}} sum rule also supports this finding.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40204468
- Journal Information:
- Physical Review D, Vol. 64, Issue 1; Other Information: DOI: 10.1103/PhysRevD.64.014022; Othernumber: PRVDAQ000064000001014022000001; 036113PRD; PBD: 1 Jul 2001; ISSN 0556-2821
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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