{pi}- and K-meson Bethe-Salpeter amplitudes
- Physics Division, Building 203, Argonne National Laboratory, Argonne, Illinois 60439-4843 (United States)
Independent of assumptions about the form of the quark-quark scattering kernel K, we derive the explicit relation between the flavor-nonsinglet pseudoscalar-meson Bethe-Salpeter amplitude {Gamma}{sub H} and the dressed-quark propagator in the chiral limit. In addition to a term proportional to {gamma}{sub 5}, {Gamma}{sub H} necessarily contains qualitatively and quantitatively important terms proportional to {gamma}{sub 5}{gamma}{center_dot}P and {gamma}{sub 5}{gamma}{center_dot}kk{center_dot}P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by {Gamma}{sub H}, whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues, with the Gell-Mann{endash}Oakes{endash}Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behavior of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behavior of the chiral limit quark mass function, and is characteristic of the QCD renormalization group. The rainbow-ladder {ital Ansatz} for K, with a simple model for the dressed-quark-quark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalization group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction. {copyright} {ital 1997} {ital The American Physical Society}
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 550623
- Journal Information:
- Physical Review, C, Journal Name: Physical Review, C Journal Issue: 6 Vol. 56; ISSN PRVCAN; ISSN 0556-2813
- Country of Publication:
- United States
- Language:
- English
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