Dressed quarks and the nucleon's axial charge

The nucleon's axial charge, $g_A$, expresses features that are both fundamental to the strong interaction and crucial to its connection with weak-interaction physics. We show that dynamical chiral symmetry breaking (DCSB) suppresses the axial charge of a dressed quark, $g_A^q$, at infrared momenta. Since this effect disappears as chiral symmetry is restored, one may argue that $g_A$ vanishes with the restoration of chiral symmetry because no nucleon bound state survives the associated transition. The suppression of $g_A^q$ is shown to be part of an explanation for a 25$\%$ reduction of $g_A$ from its nonrelativistic quark-model value. Critical, too, however, is the presence of dressed-quark angular momentum within the nucleon. The value of $g_A^q$ depends on the kernels of the gap and Bethe-Salpeter equations. We find that incorporation of essentially nonperturbative effects associated with DCSB into these kernels inflates the value relative to that obtained at leading order in a widely used truncation of QCD's Dyson-Schwinger equations. Such corrections also affect the nucleon's axial radius. In both cases, however, agreement with experiment will require similar improvements to the Faddeev kernel and associated interaction current.

Figure 1

Selected functions in the axial-vector vertex, Eq. (31): rainbow-ladder (RL) result cf. that obtained with DCSB-improved kernels for gap and Bethe-Salpeter equations (DB). Curves, all dimensionless: (solid) $F_1^{\mathrm{DB}}$ and (dashed) $F_1^{\mathrm{RL}}$; (very-long-dashed) $2M_E^{\mathrm{DB}}{F}_3^{\mathrm{DB}}$ and (dot-dashed) $2M_E^{\mathrm{RL}}{F}_3^{\mathrm{RL}}$; and (dot-dash-dash) $(-4M_E^{\mathrm{DB}{}^2}{F}_7^{\mathrm{DB}})$ and (dot-dot-dash) $(-4M_E^{\mathrm{RL}{}^2}{F}_7^{\mathrm{RL}})$. ($M_E^{\mathrm{DB}}=0.36$GeV and $M_E^{\mathrm{RL}}=0.41$.)

Figure 2

The ratio $|g_A^{q\mathrm{DB}}\left(k^2\right)|/|g_A^{q\mathrm{RL}}\left(k^2\right)|$ (solid curve) with the elements defined in association with Eq. (33). The straight line with dotted outliers represents the band $1.064\pm 0.003$.

Figure 3

$P^2$ dependence of the functions appearing in Eq. (33). Curves, all dimensionless: (solid) $F_1^{\mathrm{DB}}(k^2=0;P^2)$ and (dashed) $F_1^{\mathrm{RL}}(k^2=0;P^2)$ and then (long-dashed) $2M_E^{\mathrm{DB}}{F}_3^{\mathrm{DB}}(k^2=0;P^2)$ and (dot-dashed) $2M_E^{\mathrm{RL}}{F}_3^{\mathrm{RL}}(k^2=0;P^2)$. ($M_E^{\mathrm{DB}}=0.36$GeV and $M_E^{\mathrm{RL}}=0.41$.)