Impact of NNLO QED corrections on lepton-proton scattering at MUSE

We present the complete next-to-next-to-leading order (NNLO) pure pointlike QED corrections to lepton-proton scattering, including three-photon-exchange contributions, and investigate their impact in the case of the MUSE experiment. These corrections are computed with no approximation regarding the energy of the emitted photons and taking into account lepton-mass effects. We contrast the NNLO QED corrections to known next-to-leading order corrections, where we include the elastic two-photon exchange (TPE) through a simple hadronic model calculation with a dipole ansatz for the proton electromagnetic form factors. We show that, in the low-momentum-transfer region accessed by the MUSE experiment, the improvement due to more sophisticated treatments of the TPE, including inelastic TPE, is of similar if not smaller size than some of the NNLO QED corrections. Hence, the latter have to be included in a precision determination of the low-energy proton structure from scattering data, in particular for electron-proton scattering. For muon-proton scattering, the NNLO QED corrections are considerably smaller.

Measurement of the axial vector form factor from antineutrino-proton scattering

Scattering of high energy particles from nucleons probes their structure, as was done in the experiments that established the non-zero size of the proton using electron beams¹. The use of charged leptons as scattering probes enables measuring the distribution of electric charges, which is encoded in the vector form factors of the nucleon². Scattering weakly interacting neutrinos gives the opportunity to measure both vector and axial vector form factors of the nucleon, providing an additional, complementary probe of their structure. The nucleon transition axial form factor, F_A, can be measured from neutrino scattering from free nucleons, ν_μn → μ^-p and [Formula: see text], as a function of the negative four-momentum transfer squared (Q²). Up to now, F_A(Q²) has been extracted from the bound nucleons in neutrino-deuterium scattering^3-9, which requires uncertain nuclear corrections¹⁰. Here we report the first high-statistics measurement, to our knowledge, of the [Formula: see text] cross-section from the hydrogen atom, using the plastic scintillator target of the MINERvA¹¹ experiment, extracting F_A from free proton targets and measuring the nucleon axial charge radius, r_A, to be 0.73 ± 0.17 fm. The antineutrino-hydrogen scattering presented here can access the axial form factor without the need for nuclear theory corrections, and enables direct comparisons with the increasingly precise lattice quantum chromodynamics computations^12-15. Finally, the tools developed for this analysis and the result presented are substantial advancements in our capabilities to understand the nucleon structure in the weak sector, and also help the current and future neutrino oscillation experiments^16-20 to better constrain neutrino interaction models.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2 γ -exchange) corrections to the S-levels in muonic ( μ D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic 2 γ -exchange contribution in μ D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2 γ -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2 γ -exchange contributions in μ D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the μ D Lamb shift, the 2 S - 1 S transition in D, and the 2 S - 1 S hydrogen-deuterium isotope shift, with the respective 2 γ -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

QED radiative corrections for accelerator neutrinos

Neutrino oscillation experiments at accelerator energies aim to establish charge-parity violation in the neutrino sector by measuring the energy-dependent rate of ν_e appearance and ν_μ disappearance in a ν_μ beam. These experiments can precisely measure ν_μ cross sections at near detectors, but ν_e cross sections are poorly constrained and require theoretical inputs. In particular, quantum electrodynamics radiative corrections are different for electrons and muons. These corrections are proportional to the small quantum electrodynamics coupling α ≈ 1/137; however, the large separation of scales between the neutrino energy and the proton mass (~GeV), and the electron mass and soft-photon detection thresholds (~MeV) introduces large logarithms in the perturbative expansion. The resulting flavor differences exceed the percent-level experimental precision and depend on nonperturbative hadronic structure. We establish a factorization theorem for exclusive charged-current (anti)neutrino scattering cross sections representing them as a product of two factors. The first factor is flavor universal; it depends on hadronic and nuclear structure and can be constrained by high-statistics ν_μ data. The second factor is non-universal and contains logarithmic enhancements, but can be calculated exactly in perturbation theory. For charged-current elastic scattering, we demonstrate the cancellation of uncertainties in the predicted ratio of ν_e and ν_μ cross sections. We point out the potential impact of non-collinear energetic photons and the distortion of the visible lepton spectra, and provide precise predictions for inclusive observables.

Simultaneous Measurement of Proton and Lepton Kinematics in Quasielasticlike ν_{μ}-Hydrocarbon Interactions from 2 to 20 GeV

Neutrino charged-current quasielastic-like scattering, a reaction category extensively used in neutrino oscillation measurements, probes nuclear effects that govern neutrino-nucleus interactions. This Letter reports the first measurement of the triple-differential cross section for ν_{μ} quasielastic-like reactions using the hydrocarbon medium of the MINERvA detector exposed to a wideband beam spanning 2≤E_{ν}≤20  GeV. The measurement maps the correlations among transverse and longitudinal muon momenta and summed proton kinetic energies, and compares them to predictions from a state-of-art simulation. Discrepancies are observed that likely reflect shortfalls with modeling of pion and nucleon intranuclear scattering and/or spectator nucleon ejection from struck nuclei. The separate determination of leptonic and hadronic variables can inform experimental approaches to neutrino-energy estimation.