arXiv subjects

Richard J. Hill

Publications and source records attributed to Richard J. Hill.

At least 19 recordsLinked to original sources

arXiv2026

Nucleon axial-vector form factor and radius from radiatively-corrected antineutrino scattering data

The nucleon axial-vector form factor, $G_A$, is critical to determine the electroweak interactions of leptons with nucleons. Important examples of processes influenced by $G_A$ are elastic (anti)neutrino-nucleon scattering and muon capture by the proton. Sparse experimental data results in a large uncertainty on the momentum dependence of $G_A$ and has motivated the consideration of new experimental probes and first-principles lattice quantum chromodynamics (QCD) evaluations. The comparison of new and precise theoretical predictions for $G_A$ with future experimental data necessitates the application of radiative corrections to experimentally-observable processes. We apply these corrections in the extraction of $G_A$ and the associated axial-vector radius from the recent MINERvA antineutrino-hydrogen data, compare the effects from radiative corrections to other uncertainties in neutrino scattering experiments, and discuss the comparison of lattice QCD evaluations to experimental measurements.

hep-ph↗

arXiv2025

The $Zα^2$ correction to superallowed beta decays in effective field theory and implications for $|V_{ud}|$

Superallowed ($0^+\rightarrow0^+$) beta decays currently provide the most precise extraction of quark mixing in the Standard Model. Their interpretation as a measurement of $|V_{ud}|$ relies on a reliable first-principles computation of QED radiative corrections expressed as a series in $Zα$ and $α$. In this work, we provide the first model-independent result for two-loop, $O(Zα^2)$, long-distance radiative corrections where the nuclei are treated as heavy point-like particles. We use renormalization group analysis to obtain new results at $O(Zα^3)$ for the coefficient of double-logarithms in the ratio of the maximal beta energy to the inverse nuclear size, $\Em/R^{-1}$. We use the Kinoshita-Lee-Nauenberg theorem to obtain new results at $O(Z^2α^3)$ for the coefficient of logarithms in the ratio of maximal beta energy to the electron mass, $\log(2\Em/\me)$. We identify a structure-dependent, and therefore short-distance, contribution to the traditional $Zα^2$ correction that should be revisited.. We provide the first comprehensive update to the long-distance corrections in almost forty years and comment on the impact of our findings for extractions of $|V_{ud}|$. We find that shifts in the long-distance corrections are $2.5\times$ larger than past estimates of their uncertainty, $1.5\times$ larger than the statistical uncertainty from the combined fit of superallowed decays, and about $1/2$ the size of estimated systematic error, which stems dominantly from nuclear structure effects.

hep-ph↗

arXiv2025

Factorization and resummation of QED radiative corrections for neutron beta decay

Details of the two-loop analysis of long-distance QED radiative corrections to neutron beta decay are presented. Explicit expressions are given for hard, jet, and soft functions appearing in the factorization formula that describes the small mass/large energy limit. Power corrections, cancellation of singularities in the small mass expansion, renormalization scheme dependence, and bound state effects are discussed. The results impact the determination of $|V_{ud}|$ from the measured neutron lifetime.

hep-ph↗

arXiv2024

Searching for new physics at $μ\rightarrow e$ facilities with $μ^+$ and $π^+$ decays at rest

We investigate the ability of $μ\rightarrow e$ facilities, Mu2e and COMET, to probe, or discover, new physics with their detector validation datasets. The validation of the detector response may be performed using a dedicated run with $μ^+$, collecting data below the Michel edge, $E_e\lesssim 52$ MeV; an alternative strategy using $π^+\rightarrow e^+ ν_e$ may also be considered. We focus primarily on a search for a monoenergetic $e^+$ produced via two-body decays $μ^+ \rightarrow e^+ X$ or $π^+\rightarrow e^+X$, with $X$ a light new physics particle. Mu2e can potentially explore new parameter space beyond present astrophysical and laboratory constraints for a set of well motivated models including: axion like particles with flavor violating couplings ($μ^+ \rightarrow e^+ a$), massive $Z'$ bosons ($μ^+ \rightarrow Z' e^+$), and heavy neutral leptons ($π^+\rightarrow e^+N$). The projected sensitivities presented herein can be achieved in a matter of days.

hep-ph↗

arXiv2024

All orders factorization and the Coulomb problem

In the limit of large nuclear charge, $Z\gg 1$, or small lepton velocity, $β\ll 1$, Coulomb corrections to nuclear beta decay and related processes are enhanced as $Zα/β$ and become large or even non-perturbative (with $α$ the QED fine structure constant). We provide a constructive demonstration of factorization to all orders in perturbation theory for these processes and compute the all-orders hard and soft functions appearing in the factorization formula. We clarify the relationship between effective field theory amplitudes and historical treatments of beta decay in terms of a Fermi function.

hep-ph↗

arXiv2024

Renormalization of beta decay at three loops and beyond

The anomalous dimension for heavy-heavy-light effective theory operators describing nuclear beta decay is computed through three-loop order in the static limit. The result at order $Z^2α^3$ corrects a previous result in the literature. An all-orders symmetry is shown to relate the anomalous dimensions at leading and subleading powers of $Z$ at a given order of $α$. The first unknown coefficient for the anomalous dimension now appears at $O(Z^2α^4)$.

hep-ph↗

arXiv2024

Field Theory of the Fermi Function

The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $β$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and $π$-enhancements with renormalization group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.

hep-ph↗

arXiv2024

Constraints on new physics with (anti)neutrino-nucleon scattering data

New physics contributions to the (anti)neutrino-nucleon elastic scattering process can be constrained by precision measurements, with controlled Standard Model uncertainties. In a large class of new physics models, interactions involving charged leptons of different flavor can be related, and the large muon flavor component of accelerator neutrino beams can mitigate the lepton mass suppression that occurs in other low-energy measurements. We employ the recent high-statistics measurement of the cross section for $\barν_μp \to μ^+ n$ scattering on the hydrogen atom by MINERvA to place new confidence intervals on tensor and scalar neutrino-nucleon interactions: $\mathfrak{Re} C_T = -1^{+14}_{-13} \times 10^{-4}$, $|\mathfrak{Im} C_T| \le 1.3 \times 10^{-3}$, and $|\mathfrak{Im} C_S| = 45^{+13}_{-19} \times 10^{-3}$. These results represent a reduction in uncertainty by a factor of $2.1$, $3.1$, and $1.2$, respectively, compared to existing constraints from precision beta decay.

hep-ph↗

arXiv2024

Invariant amplitudes, unpolarized cross sections, and polarization asymmetries in (anti)neutrino-nucleon elastic scattering

At leading order in weak and electromagnetic couplings, cross sections for (anti)neutrino-nucleon elastic scattering are determined by four nucleon form factors that depend on the momentum transfer $Q^2$. Including radiative corrections in the Standard Model and potential new physics contributions beyond the Standard Model, eight invariant amplitudes are possible, depending on both $Q^2$ and the (anti)neutrino energy $E_ν$. We review the definition of these amplitudes and use them to compute both unpolarized and polarized observables including radiative corrections. We show that unpolarized accelerator neutrino cross-section measurements can probe new physics parameter space within the constraints inferred from precision beta decay measurements.

hep-ph↗

arXiv2024

Nucleon axial-vector form factor and radius from future neutrino experiments

Precision measurements of antineutrino elastic scattering on hydrogen from future neutrino experiments offer a unique opportunity to access the low-energy structure of protons and neutrons. We discuss the determination of the nucleon axial-vector form factor and radius from antineutrino interactions on hydrogen that can be collected at the future Long-Baseline Neutrino Facility, and study the sources of theoretical and experimental uncertainties. The projected accuracy would improve existing measurements by $1$ order of magnitude and be competitive with contemporary lattice-QCD determinations, potentially helping to resolve the corresponding tension with measurements from (anti)neutrino elastic scattering on deuterium. We find that the current knowledge of the nucleon vector form factors could be one of the dominant sources of uncertainty. We also evaluate the constraints that can be simultaneously obtained on the absolute $\bar ν_μ$ flux normalization.

hep-ph↗

arXiv2023

General Heavy WIMP Nucleon Elastic Scattering

Heavy WIMP (weakly-interacting-massive-particle) effective field theory is used to compute the WIMP-nucleon scattering rate for general heavy electroweak multiplets through order $m_W/M$, where $m_W$ and $M$ denote the electroweak and WIMP mass scales. The lightest neutral component of such an electroweak multiplet is a candidate dark matter particle, either elementary or composite. Existing computations for certain representations of electroweak $\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ reveal a cancellation of amplitudes from different effective operators at leading and subleading orders in $1/M$, yielding small cross sections that are below current dark matter direct detection experimental sensitivities. We extend those computations and consider all low-spin (spin-0, spin-1/2, spin-1, spin-3/2) heavy electroweak multiplets with arbitrary $\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ representations and provide benchmark cross section results for dark matter direct detection experiments. For most self-conjugate TeV WIMPs with isospin $\le 3$, the cross sections are below current experimental limits but within reach of next-generation experiments. An exception is the case of pure electroweak doublet, where WIMPs are hidden below the neutrino floor.

hep-ph↗

arXiv2023

Radiative corrections to inverse muon decay for accelerator neutrinos

Inverse muon decay ($ν_μe^- \to ν_e μ^-$) is a promising tool to constrain neutrino fluxes with energies $E_ν \ge 10.9~\mathrm{GeV}$. Radiative corrections introduce percent-level distortions to energy spectra of outgoing muons and depend on experimental details. In this paper, we calculate radiative corrections to the scattering processes $ν_μe^- \to ν_e μ^-$ and $\barν_e e^- \to \barν_μμ^-$. We present the muon energy spectrum for both channels, double-differential distributions in muon energy and muon scattering angle and in photon energy and photon scattering angle, and the photon energy spectrum for the dominant $ν_μe^- \to ν_e μ^-$ process. Our results clarify and extend the region of applicability of previous results in the literature for the double differential distribution in muon energy and photon energy, and in the muon energy spectrum with a radiated photon above a threshold energy. We provide analytic expressions for single, double and triple differential cross sections, and discuss how radiative corrections modify experimentally interesting observable distributions.

hep-ph↗

arXiv2022

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 $α\approx 1/137$; however, the large separation of scales between the neutrino energy and the proton mass ($\sim{\rm GeV}$), and the electron mass and soft-photon detection thresholds ($\sim{\rm MeV}$) 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.

hep-ph↗

arXiv2022

Neutrino Scattering Measurements on Hydrogen and Deuterium: A Snowmass White Paper

Neutrino interaction uncertainties are a limiting factor in current and next-generation experiments probing the fundamental physics of neutrinos, a unique window on physics beyond the Standard Model. Neutrino-nucleon scattering amplitudes are an important part of the neutrino interaction program. However, since all modern neutrino detectors are composed primarily of heavy nuclei, knowledge of elementary neutrino-nucleon amplitudes relies heavily on experiments performed in the 1970s and 1980s, whose statistical and systematic precision are insufficient for current needs. In this white paper, we outline the motivation for attempting measurements on hydrogen and deuterium that would improve this knowledge, and we discuss options for making these measurements either with the DUNE near detector or with a dedicated facility.

hep-ex↗

arXiv2022

Bubble Chamber Detectors with Light Nuclear Targets: A Snowmass 2021 White Paper

Neutrino cross sections are a critical ingredient in experiments that depend on neutrino scattering to reconstruct event kinematics and infer neutrino characteristics, like NOvA and T2K. An opportunity exists to reduce the 5-10% broad uncertainty on neutrino cross sections by producing more measurements of neutrino scattering from light nuclear targets at the relevant energies. Bubble chambers with light nuclear targets would be ideal for these measurements but the most recent device designed for use with an accelerator neutrino source is at least fifty years old. A new bubble chamber with light nuclear targets could be designed by observing how the technology has progressed for use in dark matter experiments and producing smaller modular devices that use more efficient cooling systems. A smaller modular device could also be designed for deployment to all functioning neutrino beams, but an investigation of the proper operating characteristics is necessary to adapt newer detectors to the structure of contemporary neutrino beams.

physics.ins-det↗

arXiv2022

Physics Opportunities for the Fermilab Booster Replacement

This white paper presents opportunities afforded by the Fermilab Booster Replacement and its various options. Its goal is to inform the design process of the Booster Replacement about the accelerator needs of the various options, allowing the design to be versatile and enable, or leave the door open to, as many options as possible. The physics themes covered by the paper include searches for dark sectors and new opportunities with muons.

hep-ph↗

arXiv2021

The high energy spectrum of internal positrons from radiative muon capture on nuclei

The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons ($μ^-\rightarrow e^+$) as a signal of lepton number violation. A key background for this search is radiative muon capture where either: 1) a real photon converts to an $e^+ e^-$ pair "externally" in surrounding material, or 2) a virtual photon mediates the production of an $e^+e^-$ pair "internally". If the $e^+$ has an energy approaching the signal region then it can serve as an irreducible background. In this work we describe how the near end-point internal positron spectrum can be related to the real photon spectrum from the same nucleus, which encodes all non-trivial nuclear physics.

hep-ph↗

arXiv2020

Parameterization and applications of the low-$Q^2$ nucleon vector form factors

We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers $\lesssim$ few GeV$^2$. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrino-nucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic (CCQE) cross section differs by 3-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, $[r_M^p, r_M^n] = [ 0.739(41)(23), 0.776(53)(28)]$ fm and $[r_Z^p, r_Z^n] = [ 1.0227(94)(51), -0.0445(14)(3)]$ fm; the Friar radius of nucleons, $[(r^p_F)^3, (r^n_F)^3] = [2.246(58)(2), 0.0093(6)(1)]$ fm$^3$; the electric curvatures, $[\langle r^4 \rangle^p_E, \langle r^4 \rangle^n_E ] = [1.08(28)(5), -0.33(24)(3)]$ fm$^4$; and bounds on the magnetic curvatures, $[ \langle r^4 \rangle^p_M, \langle r^4 \rangle^n_M ] = [ -2.0(1.7)(0.8), -2.3(2.1)(1.1)]$ fm$^4$. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.

hep-ph↗