Damped oscillation regular structures from the deuteron "effective" electromagnetic form factor data

TL;DR

The paper addresses whether damped oscillation regular structures (DORS) exist in the deuteron’s effective electromagnetic form factor data. It constructs a Unitary and Analytic (U&A) representation for the deuteron form factors $G_C(t)$, $G_M(t)$, $G_Q(t)$ on a four-sheeted Riemann surface, normalizes them at $t=0$, and connects them to spacelike observables $A(t)$, $B(t)$ and $T_{20}(t)$, while enabling analytic continuation to the timelike region to predict $\sigma_{tot}(e^+e^- \to D\bar D)(s)$. By fitting spacelike data and extrapolating timelike behavior, the authors generate artificial deuteron data and compare a three-parameter empirical TGR fit with the U&A-based description. They find that DORS emerge under the empirical TGR parametrization but vanish when the U&A framework is used, implying that the oscillations are artefacts of purely empirical fitting rather than intrinsic hadronic structure. The results advocate for analyticity- and unitarity-grounded approaches to hadron EM structure, providing reliable predictions for timelike processes and clarifying the interpretation of oscillatory features in form-factor data.

Abstract

The deuteron ``D'' is the simplest nucleus with the spin S=1, therefore its electromagnetic structure is completely described by three different, the charge $G_C(t)$, magnetic $G_M(t)$ and quadrupole $G_Q(t)$ form factors, where $t=-q^2$ is the momentum transfer squared of the electrons or the deuterons in the elastic scattering of electrons on deuterons. All three deuteron form factors are theoretically related to the functions $A(t)$, $B(t)$ and $T_{20}(t)$ to be numerically evaluated with errors, whereby $A(t)$ and $B(t)$ in a measurement of the differential cross section of elastic scattering of unpolarized electrons on unpolarized deuterons, and $T_{20}$ in measurements of the elastic scattering of the longitudinally polarized electrons, respectively also on polarized deuteron target. The obtained data are utilized to fix parameters of the deuteron electromagnetic form factors to be constructed in the form of the Unitary and Analytic model. Afterwards these form factors are analytically continued into the time-like region, with the aim to predict artificial behavior of the total cross section $σ_{tot}(e^+e^- \to D \bar D)(s)$. By means of the latter artificial data with errors on the deuteron ``effective'' electromagnetic form factor are produced theoretically. Finally, such data render a possibility to investigate the deuteron damped oscillation regular structures.

Figures (9)

• Figure 1: Complex s-plane with square root braqnch points $s_0$ and $s_{inl}$ left and conformally mapped four sheeted Riemnn surface into one plane with unit disc right).
• Figure 2: Existing experimental data on A(t) left and B(t) right in space-like region.
• Figure 3: The data on $T_{20}(t)$ in the space-like region left and predicted behavior of $\sigma_{tot}(e^+e^- \to D\bar{D})(s)$ right.
• Figure 4: Predicted behavior of the deuteron "effective" EM FF $G^{eff}_D(s)$ by means of the expression (\ref{['efff']}) and $\sigma_{tot}(e^+e^- \to D\bar{D})$ presented in FIG. 3 right.
• Figure 5: By means of the nucleon U$\&$A model predicted curve of the "effective" proton EM FF and its comparison with existing experimental data with errors.