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Electroweak Radiative Corrections to Parity-Violating Electron-Nucleus Scattering

Brendan T. Reed, C. J. Horowitz

Abstract

Parity-violating electron-scattering provides a largely model independent way of measuring neutron densities in nuclei that has important implications for the structure of nuclei and neutron stars. In this paper we calculate radiative corrections to the parity-violating asymmetry $A_{\rm pv}$ in electron-nucleus scattering including vertex and vacuum polarization contributions. We find large cancellations between the vertex corrections to the vector and axial-vector vertices. As a result the total radiative correction in 2nd Born approximation is dominated by vacuum polarization and is of order -0.5\%. Coulomb distortions have modest effects on radiative corrections for $^{12}$C and $^{48}$Ca nuclei. For $^{208}$Pb Coulomb distortions reduce the total radiative correction to only about 0.1\%. Therefore, these corrections are not important for the interpretation of the PREX and MREX experiments on $^{208}$Pb and for the CREX experiment on $^{48}$Ca. However, radiative corrections must be carefully included for a precision measurement of the weak charge of $^{12}$C.

Electroweak Radiative Corrections to Parity-Violating Electron-Nucleus Scattering

Abstract

Parity-violating electron-scattering provides a largely model independent way of measuring neutron densities in nuclei that has important implications for the structure of nuclei and neutron stars. In this paper we calculate radiative corrections to the parity-violating asymmetry in electron-nucleus scattering including vertex and vacuum polarization contributions. We find large cancellations between the vertex corrections to the vector and axial-vector vertices. As a result the total radiative correction in 2nd Born approximation is dominated by vacuum polarization and is of order -0.5\%. Coulomb distortions have modest effects on radiative corrections for C and Ca nuclei. For Pb Coulomb distortions reduce the total radiative correction to only about 0.1\%. Therefore, these corrections are not important for the interpretation of the PREX and MREX experiments on Pb and for the CREX experiment on Ca. However, radiative corrections must be carefully included for a precision measurement of the weak charge of C.
Paper Structure (13 sections, 50 equations, 10 figures, 4 tables)

This paper contains 13 sections, 50 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. First and 2nd Born Approximations
  3. Electromagnetic Corrections
  4. Vacuum Polarization
  5. Vertex Correction
  6. Radiative Corrections to Weak Interactions
  7. Axial-vector vertex
  8. Weak Vacuum Polarization
  9. Asymmetry in 2nd Born Approximation
  10. Coulomb distortions
  11. Results
  12. Discussion
  13. Conclusions

Figures (10)

  • Figure 1: Radiative corrections for the electron leg. Individually shown are the electron vertex diagram for vector $\gamma^\mu$ (a) and for axial-vector $\gamma^\mu\gamma^5$ interactions (b) and vacuum polarization diagrams for the photon (c) and $Z^0$ (d).
  • Figure 2: Tee-level diagrams for parity-violating electron-scattering.
  • Figure 3: Parity-violating asymmetry $A_{pv}$ for $^{208}$Pb at 1 GeV versus momentum transfer $Q$ calculated in Born approximation (dashed) and with Coulomb distortions (solid). Neither curve includes radiative corrections.
  • Figure 4: Parity-violating asymmetry $A_{pv}$ for $^{48}$Ca at 2.18 GeV versus momentum transfer $Q$ calculated in Born approximation (heavy black dashed curve) and with Coulomb distortions (heavy black solid curve). Also shown is $A_{pv}$ for $^{12}$C at 150 MeV (thin red curves).
  • Figure 5: Plot of charge (red) and weak (blue) densities in $^{208}$Pb (left) and $^{48}$Ca (right). Vacuum polarization (dotted) and vertex (dashed) corrections are also shown for each density according to \ref{['eq:densities']}. The weak densities are multiplied by -1 to show their effective scale compared to the charge densities.
  • ...and 5 more figures