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Probing the Core of Nuclear Structure through the $πN$ Scattering at an Electron-Positron Collider

Wei Wang, Ji Xu, Ya-Teng Zhang, Xiao-Rong Zhou

Abstract

Short-range correlation pairs (SRCs) -- core of nuclear structure, composed of highly off-shell nucleons -- are mostly studied via electron-nucleon scattering, leaving a gap in meson-based probes. We propose probing SRC off-shell nucleons via quasielastic $π^+$-bound proton scattering ($π^+ p \to π^+ p$) at electron-positron colliders, of which the beryllium-based ($^{9}$Be) beam pipe of the BESIII experiment operating at BEPCII, addresses a key gap and enables meson-beam investigations of SRCs. We point out that off-shellness of SRC nucleons yields measurable signatures: accumulated missing energy ($\sim0.1$\,GeV), shifted proton effective mass (0.7-0.8\,GeV), and cross-section differences from free scattering or with only Fermi motion. As an estimate, we find that BESIII's high luminosity and $π^+$ yield support $\sim10^4$ scattering events, while STCF ($50\times$ higher luminosity) will greatly enhance this number. This first meson-beam SRC study at an electron-positron collider fills $^{9}$Be research gaps and advances understanding of nuclear structure core and nonperturbative QCD.

Probing the Core of Nuclear Structure through the $πN$ Scattering at an Electron-Positron Collider

Abstract

Short-range correlation pairs (SRCs) -- core of nuclear structure, composed of highly off-shell nucleons -- are mostly studied via electron-nucleon scattering, leaving a gap in meson-based probes. We propose probing SRC off-shell nucleons via quasielastic -bound proton scattering () at electron-positron colliders, of which the beryllium-based (Be) beam pipe of the BESIII experiment operating at BEPCII, addresses a key gap and enables meson-beam investigations of SRCs. We point out that off-shellness of SRC nucleons yields measurable signatures: accumulated missing energy (\,GeV), shifted proton effective mass (0.7-0.8\,GeV), and cross-section differences from free scattering or with only Fermi motion. As an estimate, we find that BESIII's high luminosity and yield support scattering events, while STCF ( higher luminosity) will greatly enhance this number. This first meson-beam SRC study at an electron-positron collider fills Be research gaps and advances understanding of nuclear structure core and nonperturbative QCD.

Paper Structure

This paper contains 3 sections, 14 equations, 4 figures, 1 table.

Table of Contents

  1. Appendix A: The Fermi momentum of beryllium and the distribution of $E_\textrm{miss}$
  2. Appendix B: Determination on $\sigma_{\textrm{free}}(\sqrt{s})$
  3. Appendix C: Momentum distributions of protons in beryllium

Figures (4)

  • Figure 1: A pion is produced in electron-positron collision and subsequently strikes the beam pipe. Below is a schematic diagram of the scattering between the pion and a proton within the atomic nucleus of the beam pipe.
  • Figure 2: The initial proton's missing energy $E_{\textrm{miss}}$ (red solid line) and effective mass $m_{N,\textrm{eff}}$ (blue solid line) as functions of its momentum. These two curves are represented by the legends corresponding to their respective colors.
  • Figure 3: Predictions on the cross section of $\pi^+ p$ scattering. The black line represents the experimental data for free $\pi^+ p$ elastic scattering. The blue line shows the result obtained by SRC dominance model. The red line shows the result considering only Fermi motion in Eq. (\ref{['modelbySargsianpure']}). The upper-right subplot depicts the behavior of the cross section at the $\Delta(1232)$ resonant state, illustrating that the nuclear correction reduces its magnitude.
  • Figure 4: The data on cross section for $\pi^+ p$ scattering as a function of $\sqrt{s}$, with the fitting result represented by the red solid line.