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Weak Charge Form Factor Determination at the Electron-Ion Collider

Hooman Davoudiasl, Hongkai Liu, Sonny Mantry, Ethan T. Neil

Abstract

Determining the weak charge form factor, $F_W(Q^2)$, of nuclei over a continuous range of momentum transfers, $0\lesssim Q^2 \lesssim 0.1$ GeV$^2$, is essential for mapping out the distribution of neutrons in nuclei. The neutron density distribution has significant implications for a broad range of areas, including studies of nuclear structure, neutron stars, and physics beyond the Standard Model. Currently, our knowledge of $F_W(Q^2)$ comes primarily from fixed target experiments that measure the parity-violating longitudinal electron spin asymmetry in coherent elastic electron-ion scattering. Fixed target experiments, such as CREX and PREX-1,2, have provided high-precision weak charge form factor extractions for the $^{48}{\rm Ca}$ and $^{208}{\rm Pb}$ nuclei, respectively. However, a major limitation of fixed target experiments is that they each provide data only at a single value of $Q^2$. With the proposed Electron-Ion Collider (EIC) on the horizon, we explore its potential to impact the determination of the weak charge form factor. While it cannot compete with the precision of fixed target experiments, it can provide data over a wide and continuous range of $Q^2$ values, and for a wide variety of nuclei. We show that for integrated luminosities of $\mathcal{L} > $ 200/$A$ fb$^{-1}$, where $A$ denotes the nucleus atomic weight, the EIC can be complementary to fixed target experiments, and can significantly impact constraints from CREX and PREX-1,2 by lifting degeneracies in theoretical models of the neutron density distribution.

Weak Charge Form Factor Determination at the Electron-Ion Collider

Abstract

Determining the weak charge form factor, , of nuclei over a continuous range of momentum transfers, GeV, is essential for mapping out the distribution of neutrons in nuclei. The neutron density distribution has significant implications for a broad range of areas, including studies of nuclear structure, neutron stars, and physics beyond the Standard Model. Currently, our knowledge of comes primarily from fixed target experiments that measure the parity-violating longitudinal electron spin asymmetry in coherent elastic electron-ion scattering. Fixed target experiments, such as CREX and PREX-1,2, have provided high-precision weak charge form factor extractions for the and nuclei, respectively. However, a major limitation of fixed target experiments is that they each provide data only at a single value of . With the proposed Electron-Ion Collider (EIC) on the horizon, we explore its potential to impact the determination of the weak charge form factor. While it cannot compete with the precision of fixed target experiments, it can provide data over a wide and continuous range of values, and for a wide variety of nuclei. We show that for integrated luminosities of 200/ fb, where denotes the nucleus atomic weight, the EIC can be complementary to fixed target experiments, and can significantly impact constraints from CREX and PREX-1,2 by lifting degeneracies in theoretical models of the neutron density distribution.

Paper Structure

This paper contains 14 equations, 5 figures, 2 tables.

Figures (5)

  • Figure 1: The SM prediction for $A_{\rm PV}$ (black), together with the expected statistical (red) and systematic (blue) uncertainties from EIC measurements, shown over the $Q^2$ range from 0.001 GeV$^2$ to $0.1$ GeV$^2$. The corresponding values of pseudorapidity $\eta_e$ or inelasticity $y$ are displayed on the top axis for $E_e = 10$ GeV. The uncertainties from the current PREX-1 and -2 measurements are shown as a cyan triangle and green square, respectively.
  • Figure 2: The 1$\sigma$ limits on $a_{\rm W}$ and $c_{\rm W}$ for $^{48}{\rm Ca}$ (upper panel) and $^{208}{\rm Pb}$ (lower panel). We assume 99% veto efficiency of incoherent events. The CREX results are shown by green in the upper panel. In the lower panel, the PREX-1 and -2 results are shown by cyan and green, respectively. The EIC constraints, assuming $(200,500,1000)$/fb/A integrated luminosity, are shown by dashed (purple,orange,red) contours. The combined results of fixed target experiments and the EIC are shown by the solid contours. The black stars indicate the fiducial values of $a_{\rm W}^*$ and $c_{\rm W}^*$ shown in Table. \ref{['tab:S2pF']}.
  • Figure 3: Constraints on the weak charge form factor in the S2pF model using the 1$\sigma$ allowed region for the $(a_W,c_W)$ parameters shown in Fig. \ref{['fig:ac_99']}, using the CREX+EIC and PREX-1+PREX-2+EIC combined data for $^{48}$Ca (upper panel) and $^{208}$Pb (lower panel), respectively.
  • Figure 4: The 1$\sigma$ limits on $a_{\rm W}$ and $c_{\rm W}$ for $^{132}{\rm Xe}$ (left panel) and $^{40}{\rm Ar}$ (right panel). We assume 99% veto efficiency of incoherent events.
  • Figure 5: Constraints on the weak charge form factor in the S2pF model using the 1$\sigma$ allowed region for the $(a_W,c_W)$ parameters shown in Fig. \ref{['fig:ac_SuM']}, using the 200/A/fb and 1000/A/fb data for $^{132}$Xe (left panel) and $^{40}$Ar (right panel), respectively. The veto efficiency of incoherent events is assumed to be 99%.