Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ($\gamma \gamma$) and a massive pair of leptons (${\ell }^{+}{\ell }^{-}$) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction $x$ dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs.

Figure 1

Diphoton mesoproduction process [Eq. (3)] in the SDHEP frame. The DY dilepton process [Eq. (2)] is obtained by simply replacing the two final-state photons with leptons.

Figure 2

Kernels $K^a$ for the special $x$ integrals of GPDs $F$ and $\tilde{F}$, respectively, shown for $\xi =0.2$ and two values of $c\equiv \cos \theta$. Negative $c$ values can be seen from the symmetry $K^a(x,\xi ,-c)=K^a(-x,\xi ,c)$. The solid and dashed lines refer to the real and imaginary parts, respectively.

Figure 3

Transition GPD models for $H_{pn}^{[u\overline{d}]}$ and ${\tilde{H}}_{pn}^{[u\overline{d}]}$ at $(t,\xi )=(-0.2{\mathrm{GeV}}^2,0.2)$. The GPD $H_3$ is obtained from $H_0$ by adding a shadow $D$-term.

Figure 4

Same as Fig. 3, but for the transition GPDs $E_{pn}^{[u\overline{d}]}$ and ${\tilde{E}}_{pn}^{[u\overline{d}]}$.

Figure 5

Special integrals ${\overline{I}}^{\pm }$ for the GPDs $H_{pn}^{[u\overline{d}]+}$ and ${\tilde{H}}_{pn}^{[u\overline{d}]+}$ evaluated at $(t,\xi )=(-0.2{\mathrm{GeV}}^2,0.2)$ for different GPD models labeled by the subscripts 0–3. The solid and dashed lines refer to the real and imaginary parts, respectively. The shadow $D$-term in $H_{pn,3}^{[u\overline{d}]+}$ does not contribute to the imaginary part, so the corresponding curve coincides with the dashed black line and is not shown.

Figure 6

Same as Fig. 5, but for the GPD $E_{pn}^{[u\overline{d}]+}$ and ${\tilde{E}}_{pn}^{[u\overline{d}]+}$.

Figure 7

Unpolarized $q_T$ distributions and SSAs at $E_{\pi }=20\mathrm{GeV}$ and $(t,\xi )=(-0.2{\mathrm{GeV}}^2,0.2)$ evaluated for different GPD models obtained by varying $H$ and $\tilde{H}$. Left panel: ${\pi }^{-}p$ reaction. Right panel: ${\pi }^{+}n$ reaction.

Figure 8

Same as Fig. 7, but for $E_{\pi }=100\mathrm{GeV}$. The vertical scales of the upper panels are logarithmic.

Figure 9

Unpolarized $q_T$ distributions and SSAs for the DY dilepton process. The vertical scales of the upper panels are logarithmic.