We present theoretical predictions for μ → e conversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities,   <math> <msub> <mover> <mi>v</mi> <mo>→</mo> </mover> <mi>N</mi> </msub> </math>  $$ {\overrightarrow{v}}_N $$  and   <math> <msub> <mover> <mi>v</mi> <mo>→</mo> </mover> <mi>μ</mi> </msub> </math>  $$ {\overrightarrow{v}}_{\mu } $$ , with   <math> <mfenced> <msub> <mover> <mi>v</mi> <mo>→</mo> </mover> <mi>N</mi> </msub> </mfenced> </math>  $$ \left|{\overrightarrow{v}}_N\right| $$  &gt;   <math> <mfenced> <msub> <mover> <mi>v</mi> <mo>→</mo> </mover> <mi>μ</mi> </msub> </mfenced> </math>  $$ \left|{\overrightarrow{v}}_{\mu}\right| $$ . To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scale μ ≈ 2 GeV WET is formulated in terms of u, d, s quarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested in μ → e conversion.

United States

Wick Haxton

Kenneth McElvain

Tony Menzo

Evan Rule

Jure Zupan

Effective theory tower for μ → e conversion

The search for charged-lepton flavor violation in muon capture on nuclei is a powerful probe of heavy new physics. A smoking gun signal for <math><mi>μ</mi><mo>→</mo><mi>e</mi></math> conversion is a monochromatic electron with energy almost equal to the muon mass. We show that light new physics can mimic this signature and that it can also lead to electrons above the <math><mi>μ</mi><mo>→</mo><mi>e</mi></math> signal peak. A concrete example of such light new physics is <math><msup><mi>μ</mi><mo>−</mo></msup></math>-nucleon annihilation into a light dark sector, which can produce an energetic <math><msup><mi>e</mi><mo>−</mo></msup></math> as well as <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> by-products. Due to the size of the muon mass, the exotic muon capture process can be kinematically allowed, while the otherwise stringent constraints, e.g., from proton decay, are kinematically forbidden. We also discuss other relevant constraints, including those from the stability of nuclei and muon capture in the interior of neutron stars.

Patrick J. Fox

Matheus Hostert

Maxim Pospelov

Muon-induced baryon number violation

We study the exotic muon decays with five charged tracks in the final state. First, we investigate the Standard Model rate for μ + → 3e + 2e  −  2ν (  <math> <mi>B</mi> </math>  $$ \mathcal{B} $$  = 4.0 × 10 −10) and find that the Mu3e experiment should have tens to hundreds of signal events per 1015 μ + decays, depending on the signal selection strategy. We then turn to a neutrinoless μ + → 3e + 2e  −  decay that may arise in new-physics models with lepton-flavor-violating effective operators involving a dark Higgs h  d . Following its production in μ + → e + h  d  decays, the dark Higgs can undergo a decay cascade to two e + e  −  pairs through two dark photons, h  d  → γ  d  γ  d  → 2(e + e  − ). We show that a μ + → 3e + 2e  −  search at the Mu3e experiment, with potential sensitivity to the branching ratio at the   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10 −12) level or below, can explore new regions of parameter space and new physics scales as high as Λ ∼ 1015 GeV.

Canada

New physics in multi-electron muon decays

We introduce a new unbinned two sample test statistic sensitive to CP violation utilizing the optimal transport plan associated with the Wasserstein (earth mover’s) distance. The efficacy of the test statistic is shown via two examples of CP asymmetric distributions with varying sample sizes: the Dalitz distributions of B 0 → K + π  −  π 0 and of D 0 → π + π  −  π 0 decays. The windowed version of the Wasserstein distance test statistic is shown to have comparable sensitivity to CP violation as the commonly used energy test statistic, but also retains information about the localized distributions of CP asymmetry over the Dalitz plot. For large statistic datasets we introduce two modified Wasserstein distance based test statistics — the binned and the sliced Wasserstein distance statistics, which show comparable sensitivity to CP violation, but improved computing time and memory scalings. Finally, general extensions and applications of the introduced statistics are discussed.

United Kingdom

Adam Davis

Ahmed Youssef

Earth mover’s distance as a measure of CP violation

We investigate the phenomenological implications of the recent W mass measurement by the CDF collaboration, which exhibits tension with the standard model (SM) electroweak fit. Performing the fit to the electroweak observables within the SM effective field theory, we find that the new physics that contributes either to the determination of the electroweak vacuum expectation value, or to the oblique parameters, can improve the agreement with data. The best description is obtained from a fit where flavor universality is not required in the new physics operators, with 2 to 3 σ indications for several nonzero Wilson coefficients. We point out that top partners with order TeV masses could lead to the observed shift in the W mass.