a μ , a e and Implications for a Muon EDM

Andreas Crivellin aμ, ae and Implications for a Muon EDM Based on: AC, and M. Hoferichter and P. Schmidt-Wellenburg; arXiv:1807.11484

Outline Introduction: Searching for NP with flavour observables Experimental situation: Lepton Flavour Universality Violation Anomalous magnetic moments • aμ • ae Combined explanations A large muon EDM Conclusions Andreas Crivellin

Muon Anomalous Magnetic Moment • 3σ deviation (order of SM-EW contribution) • Single measurement from BNL • Theory prediction sound but challenging because of hadronic effects. • Soon new experimental results from Fermilab

Electron AMM • 2.5 σ deviation with opposite sign than aμ • AMM usually used to determine α • With now best determination of α from Cs atoms • Compared to the electron AMM measurement • Normalized to the lepton mass

Processes intrinsically connected Dipoles in the EFT Effective Hamiltonian Anomalous magnetic moment Electric Dipole moment Radiative Lepton decays

Explaining the Muon AMM • Light particles or chiral enhancement • Effect of the order of the EW-SM contribution needed enhancement necessary • Light particles • Neutral scalars • Neutral vector (Z’ Dark Photon) • Chiral enhancement: Chiriality flip does not come from the muon mass but rather from an NP mass inside the loop

Light particles and the Muon AMM • By construction real, i.e. no EDMs • Light particles: • Neutral scalars: • Neutral vector (Z’ Dark Photon): • Sime sign in muon and electron AMM • Strong limits from direct searches for dark photons etc..

Chiral enhancement • A priori arbitrary phase • Enhancement by the mass of the fermion in the loop • MSSM: (tan(ß)) • Leptoquarks: mt/mμ • Model with vector like fermions: mΨ/mμ

Z→μμ at future colliders Leptoquarks in aμ • Chirally enhanced effects via top-loops Left-, right- handed muons-topcoupling E. Leskow, A.C., G. D'Ambrosio, D. MüllerarXiv:1612.06858 8

Unavoidable constraints from h→τμ 2HDMs • Chirally enhancement of mτ/mµ AC, D. Müller, C. WiegandarXiv:1903.xxxxx 8

Common explanation of aμ and ae • Muon and electron sector must be decoupled • Opposite sign: no single light mediator • Minimal Flavour Violation: generic flavour structure • Single new particle: 8 orders of magnitude too large several new particles

Models for a common explanation • Most popular models do not work • MSSM • Constrained MFV does not work • With generic A-terms has problem with vacuum stability • With large tan(ß) and flavour violation • 2HDMs & LQs: Problems with μ→eγ • Extra dimensions • Can only explain the muon or the electron AMM because of μ→eγ

Model with new vector-like leptons • Muon and electro sector must be decoupled • Chirally enhanced by vκL,R/mμ

Model with new vector-like leptons • Works for ae but tension with aμ

Modifications to the model • Many realizations possible • Add neutral scalar • Effect in aμ possible without affecting h→μμ • Impose abelian flavour symmetry (e.g. Lμ-Lτ) in order to avoid μ→eγ • More minimal model with one generation of vector-like fermions possible if ae is explained by the SM Higgs and aμ via a new scalar • New scalar could be Lμ-Lτflavon

Improvement of direct limit important Limits on the Muon EDM MFV: Contribution only starts at the 3-loop level Direct limit

Dedicatedexperimentneeded? Future experimental sensitivity Fermilab/J-PARC PSI (frozen spin)

aμ>0 • ae<0 • dμ un-constrained • zero dμ Conclusions • ε'/ε aμ>0 ae>0 • Generic chiral enhance-ment • Lightparticles Andreas Crivellin

a μ , a e and Implications for a Muon EDM