Completeness and complementarity for μ → eγ, μ → $$ e\overline{e}e $$ and μA → eA
Sacha Davidson
Abstract
A bstract Lepton Flavour Violation (LFV) is New Physics that must occur, but is stringently constrained by experiments searching for μ ↔ e flavour change, such as μ → eγ , μ → $$ e\overline{e}e $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>e</mml:mi> <mml:mover> <mml:mi>e</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>e</mml:mi> </mml:math> or μ → e conversion. However, in an Effective Field Theory(EFT) parametrisation, there are many more μ ↔ e operators than restrictive constraints, so determining operator coefficients from data is a remote dream. It is nonetheless interesting to learn about New Physics from data, so this manuscript introduces “observable-vectors” in the space of operator coefficients, which identify at any scale the combination of coefficients probed by the observable. These vectors have an overlap ≳ 10 − 3 with most of the coefficients, and are used to study whether μ → eγ , μ → $$ e\overline{e}e $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>e</mml:mi> <mml:mover> <mml:mi>e</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>e</mml:mi> </mml:math> and μ → e conversion give complementary information about New Physics. The appendix gives updated sensitivities of these processes, (and a subset of τ → ℓ decays), to operator coefficients at the weak scale in the SMEFT and in the EFT below m W .