https://www.zora.uzh.ch/id/eprint/191493/1/1-s2.0-S0370157320302556-main.pdf

The anomalous magnetic moment of the muon in the Standard Model

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, ${a}_{\ensuremath{\mu}}=({g}_{\ensuremath{\mu}}\ensuremath{-}2)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ cross section, ${\ensuremath{\sigma}}_{\text{had}}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, ${a}_{\ensuremath{\mu}}^{\text{had},\mathrm{VP}}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})$, which enters natural relations and global EW fits. The EW fit prediction of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})=0.02722(41)$ agrees well with $\mathrm{\ensuremath{\Delta}}{\ensuremath{\alpha}}_{\text{had}}^{(5)}({M}_{Z}^{2})=0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}={a}_{\ensuremath{\mu}}^{\mathrm{exp}}\ensuremath{-}{a}_{\ensuremath{\mu}}^{\mathrm{SM}}$ than currently expected. Postulating that the $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ difference may be due to unforeseen missing ${\ensuremath{\sigma}}_{\text{had}}(s)$ contributions, implications for ${M}_{W}$, ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{\mathrm{eff}}^{\mathrm{lep}}$ and ${M}_{H}$ obtained from global EW fits are investigated. Shifts in ${\ensuremath{\sigma}}_{\text{had}}(s)$ needed to bridge $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ are found to be excluded above $\sqrt{s}\ensuremath{\gtrsim}0.7\text{ }\text{ }\mathrm{GeV}$ at the 95% C.L. Moreover, prospects for $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ originating below that energy are deemed improbable given the required increases in the hadronic cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, ${a}_{e}^{\text{SM}}$, the rescaled ratio ${R}_{e/\ensuremath{\mu}}=\phantom{\rule{0ex}{0ex}}({m}_{\ensuremath{\mu}}/{m}_{e}{)}^{2}({a}_{e}^{\text{had},\mathrm{LO}\text{ }\mathrm{VP}}/{a}_{\ensuremath{\mu}}^{\text{had},\mathrm{LO}\text{ }\mathrm{VP}})$, and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

Muon g − 2 and Δ α connection

Constraints on the two-pion contribution to hadronic vacuum polarization

The Fermilab Muon g −2 experiment recently reported its first measurement of the anomalous magnetic moment $$ {a}_{\mu}^{\mathrm{FNAL}} $$
 , which is in full agreement with the previous BNL measurement and pushes the world average deviation $$ \Delta {a}_{\mu}^{2021} $$
 from the Standard Model to a significance of 4.2σ. Here we provide an extensive survey of its impact on beyond the Standard Model physics. We use state-of-the-art calculations and a sophisticated set of tools to make predictions for aμ, dark matter and LHC searches in a wide range of simple models with up to three new fields, that represent some of the few ways that large ∆aμ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large ∆aμ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the aμ result can only be explained by rather small masses and/or large couplings and enhanced chirality flips, which can lead to conflicts with limits from LHC and dark matter experiments. Our results show that the new measurement excludes a large number of models and provides crucial constraints on others. Two-Higgs doublet and leptoquark models provide viable explanations of aμ only in specific versions and in specific parameter ranges. Among all models with up to three fields, only models with chirality enhancements can accommodate aμ and dark matter simultaneously. The MSSM can simultaneously explain aμ and dark matter for Bino-like LSP in several coannihilation regions. Allowing under abundance of the dark matter relic density, the Higgsino- and particularly Wino-like LSP scenarios become promising explanations of the aμ result.

/pdf/new-physics-explanations-of-am-in-light-of-the-fnal-muon-g-2-1jm5y615bn.pdf

New physics explanations of aμ in light of the FNAL muon g − 2 measurement

We point out that heavy new physics contributions in leptonic dipole moments and high-energy cross sections of lepton pairs into Higgs bosons and photons are connected model-independently. In particular, we demonstrate that a muon collider, running at center-of-mass energies of several TeV, can provide a unique test of new physics in the muon $g\ensuremath{-}2$ through the study of high-energy processes such as ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}h\ensuremath{\gamma}$. This high-energy test would be of the utmost importance to shed light on the longstanding muon $g\ensuremath{-}2$ anomaly as it is not affected by the hadronic and experimental uncertainties entering the current low-energy determination of the muon $g\ensuremath{-}2$. Furthermore, we show that the current bound on the muon electric dipole moment can be improved by three orders of magnitude, down to $\mathrm{few}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}\text{ }\text{ }e\text{ }\mathrm{cm}$.

Probing the muon g − 2 anomaly with the Higgs boson at a muon collider

We review the current status of the theory predictions for elastic $\mu$-$e$ scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment.

/pdf/theory-for-muon-electron-scattering-10ppm-a-report-of-the-3sf391t4sb.pdf

Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative

We review the current status of the theory predictions for elastic μ-e scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment

/pdf/theory-for-muon-electron-scattering-10-ppm-t8s90fpa1q.pdf

Theory for muon-electron scattering @ 10 ppm

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively. Dimensional regularization is employed to evaluate the loop integrals. Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme. The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four. The structure of the residual infrared divergences of the virtual amplitude is in agreement with the prediction of the Soft Collinear Effective Theory. Our analytic results are an essential ingredient for the computation of the scattering cross section for massive fermion-pair production in massless fermion-pair annihilation, i.e. $f^- f^+ \to F^- F^+$, and crossing related processes such as the elastic scattering $f F \to f F$, with up to Next-to-Next to Leading Order accuracy.

J. Ronca

Papers

Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative

Theory for muon-electron scattering @ 10 ppm

The two-loop four-fermion scattering amplitude in QED