$1\mathrm{/}{N}_c$ Rotational Corrections to $g_A$ and Isovector Magnetic Moment of the Nucleon

The $1\mathrm{/}{N}_c$ 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 $\mathrm{\Omega }\sim \frac{1}{N_c}$. We find non-zero $1\mathrm{/}{N}_c$ 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 ${\mu }^{IV}$ in the leading order. The axial constant $g_A$ is well reproduced, whereas the isovector magnetic moment ${\mu }^{IV}$ is still underestimated by 25 %.