The SU(3) Nambu-Jona-Lasinio soliton in the collective quantization formulation

Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model. I. Phenomenological predictions

“…This is in contrast to some authors' claim that the imaginary action should not be regularized [23], [35]. The ground of their assertion is that the imaginary part of the Euclidean action is ultraviolet finite and that the introduction of regularization would destroy conservation laws of some fundamental quantities like the baryon number and/or the quark numbers.…”

“…It is a straightforward generalization of the SU(2) model [22], [23], except for one important new feature, i.e. the existence of SU(3) symmetry breaking term due to the sizably large mass difference ∆m s between the strange and nonstrange quarks.…”

Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model. II. Theoretical formalism

“…(67), the antisymmetric term O (1) [A,B] does not appear from the first. A favorable aspect of this symmetrization procedure is that it does not cause an internal inconsistency of the SU(3) CQSM, which was first pointed out by Prasza lowicz et al [23] Unfortunately, however, it also eliminates the phenomenologically-welcome first-order rotational correction to g (3) A , the sprout of which is contained in the first term of (67). As repeatedly emphasized, the presence of this novel 1/N c correction itself is nothing incompatible with any symmetry of strong interaction.…”

“…with U γ 5 (x) = exp[iγ 5 λ a π a (x)/f π ] being the basic lagrangian of the CQSM with three flavors [2], [3]. Here, the mass difference ∆m s between the strange quark and nonstrange quarks is introduced with use of the projection operator…”

“…Different choice of ordering would in general define different quantum theory. It was shown, however, that the existence of this new O(Ω 1 ) contribution is a natural consequence of a physically reasonable choice of operator ordering that keeps the time-order of the relevant operators and that this O(Ω 1 ) contribution to g (3) A is nothing incompatible with any symmetry of strong interactions including the G-parity symmetry [19]- [21]. We also recall the fact that this time-order-keeping quantization procedure is nothing extraordinary in that it gives the same answer as the so-called cranking approach familiar in the nuclear many-body theory [20].…”