$1/N_c$ Rotational Corrections to $g_A$ and Isovector Magnetic Moment of the Nucleon

Abstract

The $1/N_c$ rotational corrections to the axial vector constant and the isovector magnetic moment of the nucleon are studied in the Nambu -- Jona-Lasinio model. We follow a semiclassical quantization procedure in terms of path integrals in which we can include perturbatively corrections in powers of angular velocity $\hat{I}\text{c◯}\sim \frac{1}{N_c}$. We find non-zero $1/N_c$ order corrections from both the valence and the Dirac sea quarks. These corrections are large enough to resolve the long-standing problem of a strong underestimation of both $g_A$ and $\hat{I}{¼}^{IV}$ in the leading order. The axial constant $g_A$ is well reproduced, whereas the isovector magnetic moment $\hat{I}{¼}^{IV}$ is still underestimated by 25 \%.

(Revtex), 10 pages (3 figures available on request), report RUB-TPII-53/93