The Nucleon Wave Function in Light-Front Dynamics

Abstract

The general spin structure of the relativistic nucleon wave function in the 3qmodel is found. It contains 16 spin components, in contrast to 8 ones known previously, since in a many-body system the parity conservation does not reduce the number of the components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results. * e-mail: karmanov@sci.lebedev.ru known long ago [16] that in a many-body system the parity conservation does not reduce the number of the spin components. Hence, for the nucleon we get 2×2×2×2 = 16. This opportunity is absent in any two-body system and in the nonrelativistic three-body one. Technically, the extra components can be constructed since the particle four-momenta in any off-energy-shell relativistic amplitude, in particular, in the wave function, are not related by the conservation law: for the minus-projections k − = k 0 − k z the sum of the quark momenta k 1,2,3 and the nucleon momentum p are not equal to each other: (k 1 + k 2 + k 3 ) − = p − . Hence, we have in our disposal 4 four-vectors and can construct the pseudoscalar C ps = e µνργ k 1µ k 2ν k 3ρ p γ . Due to that, in addition to "old" eight components given in [8], we construct another eight spin structures with "wrong" P-parity (the pseudoscalar structures) and then "correct" them by multiplying by C ps . However, this way to find the spin components is not obligatory. One can construct an equivalent set of sixteen components such that only a few of them (less than eight) contain the factor C ps . These extra components (relative to the paper [8]) are necessary in order to represent even symmetric S-wave spin structure (initially given in c.m.-system) in arbitrary system of reference in terms of the Dirac matrices sandwiched with the spinors. In other language this corresponds to multiplying the center-of-mass wave function by the Melosh rotation matrices. If we will omit these extra components and come back to the c.m.-system, we would not reproduce our initial S-wave but again will find some extra components. In general case one should start with the wave function containing all sixteen components in any system of reference. They are forming the full basis. Their total number does not depends, of course, on the representation. Their relative magnitude is determined by dynamics.Secondly, we will represent the nucleon wave function in the 3q model in the explicitly covariant form. This will allow one to use in calculations the standard Dirac-matrices algebra and the trace techniques. In particular, we will see that there is no any need to introduce explicitly any Melosh rotation matr...