Tracing the origin of the gA problem in the Skyrme model

A prominent feature of the first order rotational correction (or the 1/Nc correction) to gA recently found within the framework of the chiral quark soliton model (CQSM) is that the corresponding effect is entirely 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, which is nothing but a path integral formulation of the CQSM, it is shown that a crucial ingredient leading to this novel 1/Nc correction is the correct account of the physical time order of two collective space operators in the quantization of the rotational zero-energy mode. On the other hand, the standard functional bosonization of the same lagrangian turns out to lose this indispensable information on the chronological order of these two operators. Once this information is lost, the generalized time-reversal invariance or the particle conjugation symmetry does not allow this 1/Nc correction to survive, which explains the reason why the gA problem of the Skyrme model arises. On the other hand, within the CQSM the existence of the 1/Nc correction to gA is shown to be nothing incompatible with the particle conjugation symmetry of strong interactions. It is emphasized that the same 1/Nc correction to gA is also obtained by using an ordinary perturbation theory based on the cranking procedure, contrary to a recent claim. We also discuss the recently raised PCAC consistency problem to show that the required 1/Nc correction term in the equation of motion naturally follows from an action principle so that there is no contradiction between the new 1/Nc correction to gA and the PCAC relation. (author)