“Spin-dependent” $$\varvec{\mu \rightarrow e}$$ μ → e conversion on light nuclei

Abstract

The experimental sensitivity to μ → e conversion will improve by four or more orders of magnitude in coming years, making it interesting to consider the "spindependent" (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. Then we explore the prospects for distinguishing coefficients or models by using different targets, both in an EFT perspective, where a geometric representation of different targets as vectors in coefficient space is introduced, and also in three leptoquark models. It is found that comparing the rate on isotopes with and without spin could allow one 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 one to distinguish operators involving u quarks from those involving d quarks; this is interesting because the distinction is difficult to make for SI operators.

Low-energy lepton physics in the MRSSM: (g − 2)μ, μ→eγ and μ→e conversion

“…We remark that in parallel to model specific studies there has been significant recent progress on model-independent effective field theoretical (EFT) approaches to CLFV: loop corrections to µ → eγ have been evaluated in an EFT with dimension-6 operators [39,40]; higher-order corrections to µ → eγ, µ → eee and µ → e from running below the weak scale have been evaluated [41][42][43] and disentanglement of different Wilson coefficients by experimental observables has been studied [44,45].…”

Lepton-flavour-violating gluonic operators: constraints from the LHC and low energy experiments

“…However spin-dependent µ-e conversion may become an interesting probe in the future as it has been pointed out in Refs. [54,55]. The future COMET [56] and Mu2e [57] experiments may probe a relevant region of parameter space for the parity-violating dimension-8 gluon operators which induce a spin-dependent pseudo-scalar coupling to nucleons.…”

Selecting μ → e conversion targets to distinguish lepton flavour-changing operators

“…It is well-known, since the study of Kitano, Koike and Okada (KKO) [16], that different target nuclei have different relative sensitivity to the various operator coefficients. In Section 5, using the notion of targets as vectors in the space of operator coefficients introduced in Reference [11], we explore which current experimental bounds can give independent constraints on operator coefficients, given the current theoretical uncertainties. Section 6 discusses the prospects of future experiments, Section 7 compares the number of operator coefficients to the number of constraints that could be obtained from µ → e conversion, µ → eēe and µ → eγ, and Section 8 is the summary.…”

“…The estimate for S Au p is based on the Odd Group Model of [24], assuming J=1/2. The estimated form factors S I (m µ )/S I (0) for Titanium and Lead are an extrapolation from [11], discussed in the Appendix.…”