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Deeply virtual $φ$-meson production near threshold

Yoshitaka Hatta, Henry T. Klest, Kornelija Passek-K., Jakob Schoenleber

TL;DR

The paper develops a perturbative QCD framework for φ-meson electroproduction near threshold using generalized parton distributions and a conformal partial wave approach. By applying a threshold approximation that retains only the j=1 CP moment, the authors show that near-threshold DVMP amplitudes are largely governed by gluon and strangeness gravitational form factors, and they test this at NLO with realistic GPD models. They quantify the accuracy of the approximation (10–20% errors, better for ξ ≳ 0.4–0.6) and demonstrate strong sensitivity of the longitudinal cross section to D_g and D_s. Realistic event generator studies for EIC and SoLID indicate that near-threshold φ production can be measured, enabling constraints on gravitational form factors and offering a path toward a global analysis of nucleon structure from GPDs to GFFs.

Abstract

We discuss exclusive $φ$-meson electroproduction off the proton near threshold within the GPD factorization framework. We propose the `threshold approximation' in which only the leading term of the conformal partial wave expansion of the meson production amplitudes is kept in both the quark and gluon exchange channels. We test the validity of this approximation to next-to-leading order in QCD and demonstrate the strong sensitivity of the cross section to the gluon and strangeness gravitational form factors. We also perform realistic event generator simulations both for Jefferson Lab and EIC kinematics and demonstrate the capabilities of future facilities for measuring near-threshold $φ$ electroproduction.

Deeply virtual $φ$-meson production near threshold

TL;DR

The paper develops a perturbative QCD framework for φ-meson electroproduction near threshold using generalized parton distributions and a conformal partial wave approach. By applying a threshold approximation that retains only the j=1 CP moment, the authors show that near-threshold DVMP amplitudes are largely governed by gluon and strangeness gravitational form factors, and they test this at NLO with realistic GPD models. They quantify the accuracy of the approximation (10–20% errors, better for ξ ≳ 0.4–0.6) and demonstrate strong sensitivity of the longitudinal cross section to D_g and D_s. Realistic event generator studies for EIC and SoLID indicate that near-threshold φ production can be measured, enabling constraints on gravitational form factors and offering a path toward a global analysis of nucleon structure from GPDs to GFFs.

Abstract

We discuss exclusive -meson electroproduction off the proton near threshold within the GPD factorization framework. We propose the `threshold approximation' in which only the leading term of the conformal partial wave expansion of the meson production amplitudes is kept in both the quark and gluon exchange channels. We test the validity of this approximation to next-to-leading order in QCD and demonstrate the strong sensitivity of the cross section to the gluon and strangeness gravitational form factors. We also perform realistic event generator simulations both for Jefferson Lab and EIC kinematics and demonstrate the capabilities of future facilities for measuring near-threshold electroproduction.
Paper Structure (13 sections, 62 equations, 15 figures, 1 table)

This paper contains 13 sections, 62 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Kinematics
  3. GPD factorization
  4. General consideration
  5. Conformal partial wave expansion
  6. Threshold approximation
  7. Accuracy of the threshold approximation
  8. Numerical analysis
  9. Experimental Projections for the EIC and JLab
  10. EIC
  11. SoLID
  12. Other experimental opportunities
  13. Conclusion

Figures (15)

  • Figure 1: Contour plots of $\xi$ in the $(W,|t|)$ plane at $Q^2=6$ GeV$^2$ (left) and $Q^2=10$ GeV$^2$ (right). The horizontal line is at $|t|=\frac{Q^2}{3}$.
  • Figure 2: Representative NLO diagrams for the three terms in (\ref{['hxi']}) and (\ref{['exi']}). Left: $s$-quark exchange. Middle: 'pure singlet' exchange. Right: gluon exchange.
  • Figure 3: GK model for $H^{u,d,s,g}(x,\xi,t=0,\mu^2)$ at $\xi = 0.5$ and $\mu=2$ GeV with PDF parameters fitted to the PDF sets Alekhin:2017kpjAlekhin:2018pai.
  • Figure 4: Relative error for the amplitude $\mathcal{H}$ from truncating the conformal partial wave expansion after the first term. We plot the $\xi$ dependence at $t = 0$. Plotted quantities are defined in \ref{['eq: R defs']}. The subscript denotes whether the leading order (LO) or next-to-leading order (NLO) coefficient function has been used. We have set $\kappa=1$ and $Q = \mu = 2\,\text{GeV}$ corresponding to $\alpha_s = 0.34$ (from (\ref{['alphas']})).
  • Figure 5: The real (left) and imaginary (right) parts of $\mathcal{H}$ at $\mu=2$ GeV separated into the $s$-quark, pure-singlet and gluon contributions. Results for both LO and NLO predictions are also shown.
  • ...and 10 more figures