We study the time-momentum representation of the kernel needed to compute the hadronic vacuum polarization contribution to the muon g-2 in the space-like region at next-to-leading order. For small values of the time, we present analytical series expansions; for large values of the time, we present numerical series expansions which overcome the problems showed by naïve asymptotic expansions. These results are to be employed in lattice QCD determination of the hadronic vacuum polarization contribution to the muon g-2 at next-to-leading order.

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon g-2 Theory Initiative to update the Standard Model prediction.

The recent measurement of the muon g-2 at Fermilab confirms the previous Brookhaven result. The leading hadronic vacuum polarization (HVP) contribution to the muon g-2 represents a crucial ingredient to establish if the Standard Model prediction differs from the experimental value. A recent lattice QCD result by the BMW collaboration shows a tension with the low-energy e+e−→hadrons data which are currently used to determine the HVP contribution. We refer to this tension as the new muon g-2 puzzle. In this Letter we consider the possibility that new physics contributes to the e+e−→hadrons cross-section. This scenario could, in principle, solve the new muon g-2 puzzle. However, we show that this solution is excluded by a number of experimental constraints.

We present simple analytic expressions to compute the hadronic vacuum polarization contribution to the muon g-2 in the space-like region up to next-to-next-to-leading order. These results can be employed in lattice QCD calculations of this contribution as well as in space-like determinations based on scattering data, like that expected from the proposed MUonE experiment at CERN.

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.

A confirmation of the long-standing muon $g$-2 discrepancy requires both experimental and theoretical progress. On the theory side, the hadronic corrections are under close scrutiny, as they induce the leading uncertainty of the Standard Model prediction. Recently, the MUonE experiment has been proposed at CERN to provide a new determination of the leading hadronic contribution to the muon $g$-2 via the measurement of the differential cross section of muon-electron scattering. The precision expected at this experiment raises the question whether possible new-physics (NP) could affect its measurements. We address this issue studying possible NP signals in muon-electron collisions due to heavy or light mediators, depending on whether their mass is higher or lower than ${\cal O} (1{\rm GeV})$. We analyze the former in a model-independent way via an effective field theory approach, whereas for the latter we focus on scenarios with light scalar and vector bosons. Using existing experimental bounds, we show that possible NP effects in muon-electron collisions are expected to lie below MUonE's sensitivity. This result confirms and reinforces the physics case of the MUonE proposal.

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.

Multiple scattering effects of 12 and 20 GeV electrons on 8 and 20 mm thickness carbon targets have been studied with high-resolution silicon microstrip detectors of the UA9 apparatus at the H8 line at CERN. Comparison of the scattering angle between data and GEANT4 simulation shows excellent agreement in the core of the distributions leaving some residual disagreement in the tails.

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, alpha(mu) = (g(mu) - 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(-)-> hadrons cross section, sigma(had)(s), are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, alpha(had,VP)(mu), as well as the five-flavor hadronic contribution to the running QED coupling at the Z-pole, Delta alpha((5))(had)(M-z(2)), which enters natural relations and global EW fits. The EW fit prediction of Delta alpha((5))(had)(M-z(2)) = 0.02722(41) agrees well with Delta alpha((5))(had)(M-z(2)) = 0.02761(11) obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy Delta alpha(mu) = alpha(exp)(mu) - alpha(SM)(mu) than currently expected. Postulating that the Delta alpha(mu) difference may be due to unforeseen missing sigma(had)(s) contributions, implications for M-w, sin(2) theta(lep)(eff) and M-H obtained from global EW fits are investigated. Shifts in sigma(had)(s) needed to bridge Delta alpha(mu) are found to be excluded above root S greater than or similar to 0.7 GeV at the 95% C.L. Moreover, prospects for Delta alpha(mu) originating below that energy are deemed improbable given the required increases in the hadronic cross section. Such hypothetical changes to the hadronic data arc also found to affect other related observables, such as the electron anomaly, alpha(SM)(e), the resealed ratio R-e/mu = (m(mu)/m(e))(2) (alpha(had,LOVP)(e)/alpha(had,LOVP)(mu)), and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

The standard model prediction for muon-electron scattering beyond leading order requires the inclusion of QCD contributions which cannot be computed perturbatively. At next-to- and next-to-next-to-leading order, they arise from one- and two-loop diagrams with hadronic vacuum polarization insertions in the photon propagator. We present their evaluation using the dispersive approach with hadronic e^{+}e^{-} annihilation data and estimate their uncertainty. We find that these corrections are crucial for the analysis of future high-precision muon-electron scattering data, like those of the recently proposed MUonE experiment at CERN.

The Standard Model prediction for muon-electron scattering beyond leading order requires the inclusion of QCD contributions which cannot be computed perturbatively. At next-to- and next-to-next-to-leading order, they arise from one- and two-loop diagrams with hadronic vacuum polarization insertions in the photon propagator. We present their evaluation using the dispersive approach with hadronic $e^+e^-$ annihilation data and estimate their uncertainty. We find that these corrections are crucial for the analysis of future high-precision muon-electron scattering data, like those of the recently proposed MUonE experiment at CERN.

In this talk, we review the recent developments of the next-to-next-to leading order contribution to the mu e-elastic scattering. We focus our discussion on the interference between the two-loop and the Born amplitude. In particular, we discuss the analytic reduction of the two-loop amplitude by means of the integrand reduction methods and the application of the integration-by-parts identities. On top of it, we show preliminary results for the ultraviolet renormalisation of the latter.

We report on the current status of the analytic evaluation of the two-loop corrections to the μescattering in Quantum Electrodynamics, presenting state-of-the art techniques which have been developed to address this challenging task.

Contributions of a spin 0 axion-like particle (ALP) to lepton dipole moments, g-2 and EDMs, are examined. Light-by-light loop effects from a light pseudoscalar ALP are found to be capable of resolving the long-standing muon g-2 discrepancy at the expense of relatively large ALP- gamma gamma couplings. The compatibility of such large couplings with direct experimental constraints and perturbative unitarity bounds is discussed. Future tests of such a scenario are described. For CP violating ALP couplings, the electron EDM is found to probe much smaller, theoretically more easily accommodated ALP interactions for mass and coupling parameters that could also be studied by the SHiP (Search for Hidden Particles) proposal at CERN.

Contributions of a spin 0 axion-like particle (ALP) to lepton dipole moments, g-2 and EDMs, are examined. Barr-Zee and light-by-light loop effects from a light pseudoscalar ALP are found to be capable of resolving the long-standing muon g-2 discrepancy at the expense of relatively large ALP-gammagamma couplings. The compatibility of such large couplings with direct experimental constraints and perturbative unitarity bounds is discussed. Future tests of such a scenario are described. For CP violating ALP couplings, the electron EDM is found to probe much smaller, theoretically more easily accommodated ALP interactions. Future planned improvement in electron EDM searches is advocated as a way to not only significantly constrain ALP parameters but also, to potentially unveil a new source of CP violation which could have far reaching ramifications.

We propose a new method to probe the magnetic and electric dipole moments of the τ lepton using precise measurements of the differential rates of radiative leptonic τ decays at high-luminosity B factories. Possible deviations of these moments from the Standard Model values are analyzed in an effective Lagrangian approach, thus providing model-independent results. Analytic expressions for the relevant non-standard contributions to the differential decay rates are presented. Earlier proposals to probe the τ dipole moments are examined. A detailed feasibility study of our method is performed in the conditions of the Belle and Belle II experiments at the KEKB and Super-KEKB colliders, respectively. This study shows that our approach, applied to the planned full set of Belle II data for radiative leptonic τ decays, has the potential to improve the present experimental bound on the τ anomalous magnetic moment. On the contrary, its foreseen sensitivity is not expected to lower the current experimental limit on the τ electric dipole moment.

We present the differential rates and branching ratios of the radiative decays \( \tau \to l\overline{\nu}\nu \gamma \), with l = e or μ, and \( \mu \to e\overline{\nu}\nu \gamma \) in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass ml of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the ml → 0 limit. Our results agree with the measurements of the branching ratios \( \mathrm{\mathcal{B}}\left(\mu \to e\overline{\nu}\nu \gamma \right) \) and \( \mathrm{\mathcal{B}}\left(\tau \to \mu \overline{\nu}\nu \gamma \right) \) for a minimum photon energy of 10 MeV in the μ and τ rest frames, respectively. Babar’s recent precise measurement of the branching ratio \( \mathrm{\mathcal{B}}\left(\tau \to e\overline{\nu}\nu \gamma \right) \), for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.

Recently, it was shown that insertions of hadronic vacuum polarization at O(alpha^4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g-2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.

We update the constraints on two-Higgs-doublet models (2HDMs) focusing on the parameter space relevant to explain the present muon g −2 anomaly, Δa μ , in four different types of models, type I, II, "lepton specific" (or X) and "flipped" (or Y). We show that the strong constraints provided by the electroweak precision data on the mass of the pseudoscalar Higgs, whose contribution may account for Δa μ , are evaded in regions where the charged scalar is degenerate with the heavy neutral one and the mixing angles α and β satisfy the Standard Model limit β − α ≈ π/2. We combine theoretical constraints from vacuum stability and perturbativity with direct and indirect bounds arising from collider and B physics. Possible future constraints from the electron g −2 are also considered. If the 126 GeV resonance discovered at the LHC is interpreted as the light CP-even Higgs boson of the 2HDM, we find that only models of type X can satisfy all the considered theoretical and experimental constraints.