Spin-flavor structure of chiral-odd generalized parton distributions in the large-$N_c$ limit

We study the spin-flavor structure of the nucleon's chiral-odd generalized parton distributions (transversity GPDs) in the large-$N_c$ limit of QCD. In contrast to the chiral-even case, only three combinations of the four chiral-odd GPDs are nonzero in the leading order of the $1/N_c$ expansion: ${\overline{E}}_T=E_T+2{\tilde{H}}_T,H_T$, and ${\tilde{E}}_T$. The degeneracy is explained by the absence of spin-orbit interactions correlating the transverse momentum transfer with the transverse quark spin. It can also be deduced from the natural $N_c$ scaling of the quark-nucleon helicity amplitudes associated with the GPDs. In the GPD ${\overline{E}}_T$ the flavor-singlet component $u+d$ is leading in the $1/N_c$ expansion, while in $H_T$ and ${\tilde{E}}_T$ it is the flavor-nonsinglet components $u-d$. The large-$N_c$ relations are consistent with the spin-flavor structure extracted from hard exclusive ${\pi }^0$ and $\eta$ electroproduction data, if it is assumed that the processes are mediated by twist-3 amplitudes involving the chiral-odd GPDs and the chiral-odd pseudoscalar meson distribution amplitudes.

Figure 1

Representation of GPDs in the region $\xi <x<1$ as nucleon-quark helicity amplitudes. In the nucleon and quark states (denoted as $N,q$) the second label denotes the fraction of the light-cone plus momentum $P^{+}$ carried by the particle, and the third label denotes the light-cone helicity.