Hadron Electromagnetic and Weak Form Factors in the Minimal Boosted SU(6) Scheme of the Relativistic Quark Model

Abstract

In this paper, we present a relativistically invariant formulation of the hadron electromagnetic and semilcptonic weak vertex function in the minimal boosted SU (6) model, that is, in the SU (6) 1r®O (3, 1) based on the relativistic quark model. The various form factors obtained from this model are compared with those given by the 11(12)®0(3, 1) model. It is also shown that existing experiments can be fairly well reproduced by the SU (Ci) ,' I®O (3, 1) rather than by the U (12) ®0 (3, 1). § l. IntroductionRecently Ishida, JVIatsuda and Namiki haYe presented a ne\V formulation for relativistic generalization of the SU(6) scheme, called SU(G) Jr, to formulate the spinor part of the hadron ~wave functions. 1 l The SU (6) Jr scheme was originally introduced by Fujimura, Kobayashi and Namiki"J in an intuitive way of formulating the relativistic wa\·e functions different from the U (12) scheme. One of the important results of the SU(6),1r(290(3, 1) model is that \YC can obtain electromagnetic form factors of the dipole type for nucleon and of the simple pole type for pion in good agreement \vith existing experimental results. Such q'-dependenccs of the form factors essentially come from the o\·erlapping integral o£ the inner orbital wave functions describing the Lorentz contraction effect as a dynamical result of the relativistic harmonic oscillator model with Takabayashi's subsidiary condition. 3 l In order to obtain the \Nhole scheme of form factors, however, we must formulate the spinor-unitary spinor part of the hadron wcn·e :functions and details of the current Ycrtex function, and examine the other multiplicative :factors of the form factors coming from them. The first attempt given by Fujimura, Kobayashi and Namiki is not so satisfactory as to the relati,-istic covariance and the gauge invanance. Feynman, Kisslinger and Ravndal proposed a method to give the relati,·istic covariant and gauge invariant current in the framework of U (12) (290 (3, 1) . 1 ) Along the same line o£ thought, BlagojeYic and Lalm·ic obtained the current Yertex function obeying the relativistic covariance and the gauge innuiance in the case of SU(6) ,,£(290( 3, 1) . 5 l It seems to us that the mathematical structure of