Spin-dependent ${\mu \to e}$ Conversion on Light Nuclei

TL;DR

This paper analyzes the potential to detect and distinguish spin-dependent contributions to muon-to-electron conversion on light nuclei, which could reveal new physics operators beyond the spin-independent effects.

Contribution

It introduces a geometric method to compare different nuclear targets for identifying spin-dependent operator coefficients in muon-to-electron conversion.

Findings

Comparing rates on isotopes with and without spin can detect SD coefficients larger than SI ones.

Distinguishing axial, tensor, and pseudoscalar operators requires nuclear matrix element calculations.

Using nuclei with odd protons vs odd neutrons can differentiate quark flavor operators.

Abstract

The experimental sensitivity to $\mu \to e$ conversion will improve by four or more orders of magnitude in coming years, making it interesting to consider the "spin-dependent" (SD) contribution to the rate. This process does not benefit from the atomic-number-squared enhancement of the spin-independent (SI) contribution, but probes different operators. We give details of our recent estimate of the spin dependent rate, expressed as a function of operator coefficients at the experimental scale, and explore the prospects for distinguishing coefficients by using different targets. For this purpose, a geometric representation of different targets as vectors in coefficient space is introduced. It is found that comparing the rate on isotopes with and without spin could allow to detect spin dependent coefficients that are at least a factor of few larger than the spin independent ones. Distinguishing among the axial, tensor and pseudoscalar operators that induce the SD rate would require calculating the nuclear matrix elements for the second two. Comparing the SD rate on nuclei with an odd proton vs odd neutron could allow to distinguish operators involving $u$ quarks from those involving $d$ quarks; this is interesting because the distinction is difficult to make for SI operators.