Reach and complementarity of $$\mu \rightarrow e$$ searches

Abstract

In Effective Field Theory, we describe $$\mu \leftrightarrow e$$ μ ↔ e flavour changing transitions using an operator basis motivated by experimental observables. This implies that $$\mu \rightarrow e_L \gamma $$ μ → e L γ , $$\mu \rightarrow e_L \bar{e} e$$ μ → e L e ¯ e and $$\mu \rightarrow e_L$$ μ → e L conversion on nuclei probe a six-dimensional subspace, where we derive constraints on the New Physics scale from past and future experiments, illustrating the complementarity of the processes in an intuitive way.

Theory introduction to Lepton Flavour Violation

“…Theory Introduction to Lepton Flavour Violation [24]. A bottom-up calculation translates the experimental data at low energy into a combination of operator coefficients at the heavy physics scale, and it identifies the region of coefficient space where models should sit [25].…”

Charge Lepton Flavor Violation in muons: theory overview

“…[2]). A new parametrisation proposal [3], relying on projections onto a space spanned by the most relevant operators for muon cLFV transitions, ì 𝐶 = {𝐶 𝐷 , 𝐶 𝑆 , 𝐶 𝑉 𝑅 , 𝐶 𝑉 𝐿 , 𝐶 N-light , 𝐶 N-heavy } (see [3] for a detailed description), allowed to infer the sensitivity to NP scales of data (current bounds and future sensitivities) stemming from searches for radiative and 3-body decays, and conversion in nuclei. As can be seen from the left panel of Fig.…”

“…1, current bounds from MEG on 𝜇 → 𝑒𝛾 and from SINDRUM on neutrinoless conversion in Gold nuclei allow to draw limits on the scale of cLFV new physics up to O (10 3 TeV), respectively for the cases of dipole or 4-fermion dominated NP contributions (𝜃 𝐷 → 0, 𝜋 or 𝜃 𝐷 → 𝜋/2). In the future, and for both regimes, the expected sensitivity of searches for 𝜇 − 𝑒 conversion in Aluminium by both COMET and Mu2e should allow probing scales Λ NP ∼ 10 4 TeV (or even 10 5 TeV for an advanced muon facility) [3]. 5 orders of magnitude different from the other coefficients, we also plot the reach in a parametrization similar to that introduced in [19] by defining a variable…”

“…On the left, sensitivity to the NP scale of different cLFV muon transitions, as a function of the "dipole" dominance parameter 𝜃 𝐷 : radiative decays (blue), three-body decays (black) and neutrinoless conversion in nuclei (red); solid (dotted) lines denote current bounds (future experimental sensitivity); from [3]. On the right, complementarity of the information for distinct nuclei (𝑍) regarding the NP at the source of 𝜇 − 𝑒 conversion, with respect to that of Aluminium targets; from [4].…”