Studying the Strangeness $D$-Term in Hall C via Exclusive $φ$ Electroproduction

TL;DR

This proposal advocates a high-luminosity, near-threshold measurement of exclusive φ electroproduction in Hall C to constrain the strangeness D-term $D_s(0)$ via the $ractal{}t$-dependence of $d\sigma/d\lvert t\rvert$. By connecting the cross section to generalized parton distributions and the proton gravitational form factors, the study aims to determine whether $D_s(0)$ is large, small, or sign-opposite to the total $D$-term, with potential implications for the gluon D-term if $D_s(0)$ is small. The experimental plan includes robust background handling, final-state interaction assessments, and a detailed uncertainty budget, supported by replica-based extractions to quantify sensitivity. In addition to the φ measurement, the dataset enables first measurements of η' electroproduction and detailed, multi-differential η and ω production, offering broad insights into GPD modeling and the gluonic structure of hadrons. Overall, the work promises to illuminate the proton’s mechanical structure, constrain the flavor decomposition of the D-term, and guide future global analyses of gravitational form factors.

Abstract

We propose a measurement of exclusive electroproduction of $φ$ mesons near threshold in Hall C. We will measure the |t|-dependence of the exclusive $φ$ electroproduction cross section, which has recently been proposed as an observable sensitive to the strangeness $D$-term. The contribution of strangeness to the total $D$-term is presently unknown, with different arguments favoring $D_s$ being large, being small, or even having opposite sign from the total $D$-term. Our exploratory measurement is designed to distinguish between these hypotheses. If $D_s$ turns out to be small, $φ$ electroproduction can be used to study the gluon $D$-term. In addition, this dataset will allow us to perform measurements of other exclusive meson final states, including the first measurement of $η'$ electroproduction and multi-differential measurements of $η$ and $ω$ electroproduction.

Figures (19)

• Figure 1: Leading order perturbative processes contributing to exclusive $\phi$ electroproduction. Left: Exclusive $\phi$ electroproduction via strange quark exchange. Right: Exclusive $\phi$ electroproduction via two gluon exchange.
• Figure 2: Contour of $|t|$ vs. $W$ with isolines of constant $\xi$ for $Q^2=3.4$ GeV$^2$. The projected Hall C $\phi$ data sit in the green trapezoidal region. To minimize the theoretical uncertainty, the data should be in the region $\xi \gtrsim 0.35$ and $|t|<Q^2/3$.
• Figure 3: Left: World average of $R$ at $Q^{2}$ = 3.4 $\mathrm{GeV}^2$. The CLAS and Cornell datapoints have been scaled according to the model of Ref. CLAS12Phi, which finds a global scaling relation between $R$ and $Q^2$ of $R(Q^{2}\xspace) = 0.4Q^{2}\xspace/m^2_{\phi}$. The KN model values are from Ref. Kim:2020wrd, and the GK model values were provided by the authors of Ref. Goloskokov:2006hr. Right: A selected weighted average of $D_g(0)$. The results are from Refs. Guo:2025jizDuran:2022xagShanahan:2018nnvHackett:2023rif.
• Figure 4: Theoretical predictions for $d\sigma_L/d\lvert t \rvert\xspace$ at $Q^{2}$ = 3.4 $\mathrm{GeV}^2$ and $W=2.25$ GeV with different assumptions for $D_{s}(0)$. In this kinematic range $t_{\mathrm{min}}\approx0.8$$\mathrm{GeV}^2$. The inner error band corresponds to the perturbative scale variation of $Q/2 < \mu < 2Q$, and the outer error band corresponds to the effect of varying $D_g(0)=-2.07$ by $\pm~0.23$ and summing it in quadrature with the scale uncertainty. Therefore, the outer error band represents the total uncertainty on the theory.
• Figure 5: Top Row: Reconstructed kinematics for $\phi$ events using the spectrometer settings shown in Table \ref{['Tab:Settings']}. Bottom Row: Correlations between kinematic variables.