Improved phenomenology of $πN$ transition distribution amplitudes

TL;DR

This work develops a flexible phenomenological model for nucleon-to-pion TDAs, $πN$ TDAs, within the QCD collinear-factorization framework for backward hard exclusive electroproduction. It builds a spectral representation using quadruple distributions, with a two-component Ansatz that respects threshold constraints and includes a forward-limit piece fitted to data, and it employs a hexagon-based orthogonal-polynomial basis to parametrize the forward function. The model, constrained by CLAS unseparated cross sections and incorporating a modified dipole $G(u)$, makes quantitative predictions for backward $ep o e'nπ^+$ and $ep o epπ^0$ cross sections and leading-twist polarization observables at JLab kinematics, exploring sensitivity to nucleon DAs. The results show that the $rac{π^+}{π^0}$ channels provide complementary information on TDAs, and underscore the importance of polarization measurements in testing the TDA framework, with practical implementation in the EpIC Monte Carlo enabling experimental planning and acceptance studies.

Abstract

To study cross sections and polarization asymmetries for the processes $e p \to e n π^+$ and $e p \to e p π^0$ in the backward region, we develop a flexible phenomenological model for nucleon-to-pion transition distribution amplitudes ($πN$ TDAs), which are used in the QCD collinear factorization description of the scattering amplitudes. Our model is based on the two-component factorized Ansatz for the corresponding spectral densities, quadruple distribution. It takes into account the constraints for $πN$ TDAs arising from the threshold pion production theorem and also includes a forward limit contribution that can be fitted to experimental data. We examine the sensitivity of observable predictions to various modelling assumptions.

Figures (4)

• Figure 1: Kinematical quantities and the collinear factorization mechanism for $\gamma^* N \to \pi N$ in the near-backward kinematical regime (large $Q^2$, $s$; fixed $x_B$; $|u| \sim 0$). The lower blob, denoted $\pi N$ TDA, depicts the nucleon-to-pion transition distribution amplitude; the $N$ DA blob depicts the nucleon distribution amplitude; CF denotes the hard subprocess amplitude (coefficient function). Figure is taken from Ref. Pire:2025wbf.
• Figure 2: Orthogonal polynomials on the hexagon, multiplied by the weight function (\ref{['eq:def_weight']}) with $d=1$, $W(\sigma, \rho)\,p_{i}(\sigma,\rho)$, for $i=0,\ldots,5$. Figure is taken from Ref. Pire:2025wbf.
• Figure 3: Sensitivity to the choice of DA parametrization. Selected observables for the exclusive production of (solid lines) $\pi^+$ and (dashed lines) $\pi^0$ mesons in the backward kinematics are: cross sections as a function of $Q^2$ for $W = 2.2~\mathrm{GeV}$ and $-u = 0.5~\mathrm{GeV}^2$; cross sections and asymmetries as a function of $x_B$ for $Q^2 = 2.44~\mathrm{GeV}^2$ and $-u = 0.5~\mathrm{GeV}^2$. The asymmetries are evaluated for the electron beam energy $E_e = 10.6~\mathrm{GeV}$. The CLAS data CLAS:2017rgp are represented by black markers. Figure is taken from Ref. Pire:2025wbf.
• Figure 4: Various model predictions ($d=1,2,3$) for the $Q^2$ and $x_B-$dependences of the cross section (upper row) and for the two leading-twist double spin asymmetries (lower row) for both $\pi^+$ (solid curves) and $\pi^0$ (dashed curves) electroproduction. See Captions of Fig. \ref{['fig:scan_da']} for other details. Figure is taken from Ref. Pire:2025wbf.