Asymptotic Freedom and Bose Quark Dynamics

Abstract

Recently the quantum chromo-dynamics (QCD) based on the confined-color Fermi quark model seems to be widely accepted, giving many interesting results. One of the most attractive points of the QCD is that it shows the asymptotic free (AF) property!) which is believed to give a theoretical background for the success of the parton model. However, it should also be noted that we have not yet any direct and/ or firm evidence for existence of the color freedom. The theoretical bases for calculating the decay rate r(1[°-->2y) and the Drell ratio R, which are supposed to be the evidences, seem to us not so persuasive as usually believed. Moreover, the notion of confined-color makes us lose one of the most important reasons for introduction of the color freedom, since the usual spin-statistics connection is needed only for particles which can be free. On the other hand there has been another stream of unified models of hadrons, to be called the Bose quark model,2).3) where the usual spin-statistics connection of hadrons is consistently supposed with the symmetric Bose-like behavior of constituent quarks without the color freedom. Here it may be worth-while noting an interesting fact 4 ) that the empirical rule, ILlII=1/2 (SU(3) 8dominance), for non-Ieptonic weak interactions naturally follows from assuming Bose statistics for quarks appeared in the usual current x current form of weak interaction. In this short note we shall point out another interesting point from this line of approaches, that an inner dynamics (to be called the Bose Quark dynamics (BQD)) for the system of quarks quantized with Bose statistics and of an Abelian gauge field (flavorsinglet gluon without the color) becomes asymptotically free. As is well known, an Abelian gauge theory with normal quantization like the QED is not asymptotically free. An essential ingredient to get the AF in our BQD is that for the abnormal case of half integer spin connected with symmetrical Bose statistics a relativistically covariant quantized field theory is possible, introducing an indefinite metric, as was shown by Pauli ) thirty years ago; and in this case the Feynman rule for calculating scattering amplitudes becomes completely identical to that in the normal case except that in the former no minus-sign factor is needed for quark loops where it is in the latter.