{pi}- and K-meson Bethe-Salpeter amplitudes
{pi}- and K-meson Bethe-Salpeter amplitudes
复制标题
DOI：
10.1103/physrevc.56.3369
复制
发表时间：
1997-08
影响因子：
3.1
通讯作者：
P. Maris;C. Roberts
中科院分区：
文献类型：
--
作者：
P. Maris;C. Roberts
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 groupmore » 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}« less
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 groupmore » 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}« less