Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
نویسنده
چکیده
We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pionpion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler–Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell. We find, with current data, that both the pion-pion and pion-nucleon sum rules are satisfied to better than six percent, and we give detailed estimates of the experimental and extrapolation errors in the closure discrepancies. Typeset with PHysMaTEX -evaluation of the axial vector commutator sum rule for pion-pion scattering
منابع مشابه
Estimates for Pion-Photon Transition Distributions
In the scaling regime, amplitudes for backward virtual Compton scattering and hadron annihilation into two photons depend on structure functions that describe the hadron-photon transition at the partonic level. We construct simple analytical models for the vector and axial-vector pion-photon transition distribution amplitudes based on double distributions. Via a sum rule, these models are tuned...
متن کاملHELICITY AND PLANAR AMPLITUDES IN PION-PROTON SCATTERING AT 6.0 GeV/c
In addition to optimal conditions, invariant laws of Lorentz, parity and time reversal are imposed to find the relation between observables (spin rotation parameters) and bilinear combination of helicity amplitudes in pion-proton elastic scattering at 6.0 GeV/c. By normalizing the differential cross-section to unity, the magnitudes of helicity amplitudes and the angle between them are dete...
متن کامل4 Pion form factor and QCD sum rules : case of axial current
We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of axial-vector pion currents. The theoretical predictions for Q 2-dependence of pion form factor are in good agreement with available experimental data. It is shown, that NLO corrections are large in this case and should be taken into account in rigorous theoretical analysis.
متن کامل00 4 Pion form factor and QCD sum rules : case of axial current
We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of axial-vector pion currents. The theoretical predictions for Q 2-dependence of pion form factor are in good agreement with available experimental data. It is shown, that NLO corrections are large in this case and should be taken into account in rigorous theoretical analysis.
متن کاملSpectral density functions and their sum rules in an effective chiral field theory
The validity of Weinberg’s two sum rules for massless QCD, as well as the six additional sum rules introduced into chiral perturbation theory by Gasser and Leutwyler, are investigated for the extended Nambu-Jona-Lasinio chiral model that includes vector and axial vector degrees of freedom. A detailed analysis of the vector, axial vector and coupled pion plus longitudinal axial vector modes is g...
متن کامل