Parity violation in Møller scattering within low-energy effective field theory

TL;DR

The paper tackles the parity-violating left-right asymmetry $A_{LR}$ in Møller scattering at low energy, aiming for percent-level theoretical precision for the MOLLER experiment by employing a low-energy effective field theory (LEFT). It builds a framework with dimension-5 and dimension-6 LEFT operators, matching at the electroweak scale and running down to the soft scale to resum large logarithms via Wilson coefficients $C_i(μ_s)$, while incorporating fixed-order QED corrections up to NNLO and hadronic vacuum-polarization effects. The full differential predictions are implemented in the McMule Monte Carlo, enabling realistic comparisons with experimental cuts and including real radiation. The study demonstrates that leading-log resummation is essential and that potential next-to-leading-log corrections can be at the percent level, motivating further two-loop matching and refined hadronic treatments to fully exploit MOLLER's precision program.

Abstract

We include electroweak effects in Moller scattering at low energies in an effective field theory approach and compute the left-right parity-violating asymmetry. The calculation using low-energy effective field theory provides a solid framework to integrate out heavy particles with masses of the order of the electroweak scale, allowing the resummation of all large logarithms between the electroweak scale and the scale, where QCD perturbation theory breaks down. The NLO electroweak corrections with leading logarithmic resummation, combined with QED corrections at NNLO and hadronic effects are implemented into the Monte Carlo framework McMule. Thus, we obtain a fully differential description and present results adapted to the MOLLER experiment. The potential impact of large logarithms at the next-to-leading logarithmic level is investigated.

Figures (6)

• Figure 1: Representative diagrams for the amplitude \ref{['AmpMoller']}. The top line are LO, NLO, and NNLO QED diagrams. The bottom line shows LO and NLO diagrams with a single insertion of a higher-dimensional operator. The required real amplitudes are indicated by additional (grey) external photons.
• Figure 2: The virtual part of $A^{\text{exp}}_{LR}$ for Møller scattering at $\sqrt{s}=2\,\text{GeV}$ at LO (light colours) and NLO (dark colours) in RGE-improved perturbation theory at LL (solid lines) and NLL (dotted lines) accuracy for different values of $\mu_s$ from the EW scale down to $\sqrt{s}$. For $\mu_s=2\,\text{GeV}$, threshold corrections are properly taken into account in LEFT by integrating out the $b$ quark at its mass threshold, up to one-loop order and dimension six.
• Figure 3: $A_{LR}$ for the MOLLER experiment, as a function of $\theta$ defined in \ref{['eq:CoMtheta']} in the centre-of-mass frame at LO and NLO in RGE-improved perturbation theory, for three choices of $\mu_s$. Solid and dotted lines correspond to \ref{['ALRfull']} and \ref{['ALRexp']} respectively. The bottom panel shows the impact of real corrections for the expanded version of $A_{LR}$.
• Figure 4: Same as Figure \ref{['fig:mollercm']} but with modified angular cuts $10^\circ \le \theta_{3,4} \le 170^\circ$.
• Figure 5: $A_{LR}$ for the MOLLER experiment, as a function of $\tilde{\theta}_s$ in the laboratory frame at LO and NLO in RGE-improved perturbation theory, for three choices of $\mu_s$. Solid and dotted lines correspond to \ref{['ALRfull']} and \ref{['ALRexp']} respectively. The hard cuts around $\tilde{\theta}_c=9.64\,\rm{mrad}$ and $\tilde{\theta}_c=18.58\,\rm{mrad}$ are a consequence of $2\to2$ kinematics and \ref{['cutsThetaCoM']}. The bottom panel shows the impact of real correction for the expanded version of $A_{LR}$ for $\tilde{\theta}_s > \tilde{\theta}_c$. For $\tilde{\theta}_s < \tilde{\theta}_c$, the expanded version \ref{['ALRexp']} is not defined.