πe3Form Factorf-Near the Mass Shell

Abstract

The generalized Ward-Takahashi identity (gWTI) in the pion sector for broken isotopic symmetry is derived and used for the modelindependent calculation of the longitudinal form factor − of the 3 vector vertex. The on-shell − is found to be proportional to the mass difference of the pions and the difference between the vector isospin = 1 and scalar isospin = 2 pion radii. A numerical estimate of the form factor yields a value two times higher than the previous estimate from the quark model. Off-shell form factors are known to be ambiguous because of the gauge dependence and the freedom in the parameterization of the fields. The nearmass-shell − appears to be an exception, allowing for experimental verification of the consequences of the gWTI. We calculate the near-mass-shell − using the gWTI and dispersion techniques. The results are discussed in the context of the conservation of vector current (CVC) hypothesis.

Longitudinal vector form factors in weak decays of nuclei

“…F ++ 3 (p ′2 , p 2 , q 2 ) is in general different from zero, but in the limit of exact isotopic symmetry its contribution to physical amplitudes can vanish because of the factor p ′2 − p 2 . Similar properties hold for the longitudinal vector form factor of the pion β decay [5].…”