TRACING THE ORIGIN OF THE G(A) PROBLEM IN THE SKYRME MODEL

A prominent feature of the first order rotational correction (or the 1 /N-c correction) to g(A) recently found within the framework of the ch iral quark soliton model (CQSM) is that the corresponding effect is en tirely missing in the Skyrme model. We attempt to reveal the origin of this crucial observation through a comparison of two approaches based on the lagrangian of the chiral quark model. In the first approach, w hich is nothing but a path integral formulation of the CQSM, it is sho wn that a crucial ingredient leading to this novel 1/N-c correction is the correct account of the physical time order of two collective spac e operators in the quantization of the rotational zero-energy mode. On the other hand, the standard functional bosonization of the same lagr angian turns out to lose this indispensable information on the chronol ogical order of these two operators. Once this information is lost, th e generalized time-reversal invariance or the particle conjugation sym metry does not allow this 1/N-c correction to survive, which explains the reason why the g(A) problem of the Skyrme model arises. On the oth er hand, within the CQSM the existence of the 1/N-c correction to g(A) is shown to be nothing incompatible with the particle conjugation sym metry of strong interactions. It is emphasized that the same 1/N-c cor rection to g(A) is also obtained by using an ordinary perturbation the ory based on the cranking procedure, contrary to a recent claim. We al so discuss the recently raised PCAC consistency problem to show that t he required 1/N-c correction term in the equation of motion naturally follows from an action principle so that there is no contradiction bet ween the new 1/N-c correction to g(A) and the PCAC relation.