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The traditional Fermi function (long-distance radiative contribution) ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge $Z$ and/or small electron velocity $\beta$. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold.
We provide the corrected calculation of the (g − 2) μ in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F 1 (q 2 ) and F 2 (q 2 ) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 10 5 −10 10 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.
In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.
In this work, we examine the implications of electroweak corrections beyond leading order for processes of special interest in the Higgs sector. We especially explore the role of these corrections given the introduction of an explicit parton distribution function (PDF) for the photon in the proton, an object which emerges necessarily in global PDF fits which include QED effects (i.e., ‘QCD+QED PDFs’). We concentrate on several representative cases, including total Higgs-production cross sections through gluon fusion, gg → H, vector-boson fusion (VBFH), and associated production, pp → V H; we also examine differential distributions, taking a representative Higgs-strahlung process, pp → W + H. We find that the recently developed LUX formalism for the photon PDF significantly stabilizes the PDF dependence of both QED-PDF and electroweak corrections in the Higgs sector, while leaving overall ~ 3–4% cross-section-level variations, depending on the chosen QCD+QED PDF. We illustrate this QCD+QED PDF dependence by exploring predictions based upon recent analyses of the CTEQ-TEA, MSHT, and NNPDF analysis groups, fitted either at NNLO or approximate N3LO in QCD.
We present a fully analytic computation of the complete electron and photon structure functions, or QED lepton parton distribution functions (PDFs) up to two-loop order. Our computation is performed using modern techniques of reduction to Master Integrals and solving them with the differential equation method. We obtain explicit expressions for the electron-in-electron, positron-in-electron, photon-in-electron, electron-in-photon, and photon-in-photon distributions at next-to-next-to-leading order (NNLO). Cross-checks against one-loop results, existing two-loop calculations, and a recent soft-collinear effective theory (SCET) analysis of the electron structure functions are presented.
We compute $\mathcal{O}\left({\alpha}^2Z\right)$ radiative corrections to superallowed β decays with a heavy-particle effective field theory that systematically describes the interactions of low-energy ultrasoft photons with nuclei. We calculate two-loop virtual and one-loop real-virtual amplitudes by reducing the Feynman integrals to a set of master integrals, which we solve analytically using a variety of techniques. These techniques can be applied to other phenomenologically interesting observables. The ultrasoft corrections can then be combined with contributions arising from the exchange of potential photons to obtain the complete $\mathcal{O}\left({\alpha}^2Z\right)$ correction to the decay rate, with resummation of large logarithms of the electron energy times the nuclear radius. We find that $\mathcal{O}\left({\alpha}^2Z\right)$ ultrasoft loops induce a relative correction to the decay rate that ranges from 0.7 ∙ 10 −3 in the decay of 10 C to 3.6 ∙ 10 −3 in the decay of 54 Co, and will thus impact the extraction of V ud at the permille level. We show that the inclusion of these corrections reduces the residual renormalization scale dependence of the decay rate to a negligible level, making missing ultrasoft perturbative corrections a subdominant source of theoretical uncertainty.
The measurement of the anomalous electron magnetic moment g – 2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this “cavity shift” must subtract the electron’s divergent self-field, and thus require knowledge of the exact Green’s function for the cavity’s electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.
In this work, we complete our CT18qed study with the neutron’s photon parton distribution function (PDF), which is essential for the nucleus scattering phenomenology. Two methods, CT18lux and CT18qed, based on the LUXqed formalism and the DGLAP evolution, respectively, to determine the neutron’s photon PDF have been presented. Various low-Q 2 non-perturbative variations have been carefully examined, which are treated as additional uncertainties on top of those induced by quark and gluon PDFs. The impacts of the momentum sum rule as well as isospin symmetry violation have been explored and turned out to be negligible. A detailed comparison with other neutron’s photon PDF sets has been performed, which shows a great improvement in the precision and a reasonable uncertainty estimation. Finally, two phenomenological implications are demonstrated with photon-initiated processes: neutrino-nucleus W-boson production, which is important for the near-future TeV–PeV neutrino observations, and the axion-like particle production at a high-energy muon beam-dump experiment.
We introduce a useful framework for high-precision studies of the neutron beta decay by merging the current algebra description and the fixed-order effective field theory calculation of the electroweak radiative corrections to the neutron axial form factor. We discuss the advantages of this hybrid method and show that it only requires a minimal amount of lattice QCD inputs to achieve a 10 –4 theory accuracy for the Standard Model prediction of the neutron lifetime and the axial-to-vector coupling ratio λ, both important to the search for physics beyond the Standard Model.
We investigate contributions to the anomalous magnetic moments of charged leptons in the neutrino-extended Standard Model Effective Field Theory (νSMEFT). We discuss how νSMEFT operators can contribute to a lepton’s magnetic moment at one- and two-loop order. We show that only one operator can account for existing electronic and muonic discrepancies, assuming new physics appears above 1 TeV. In particular, we find that a right-handed charged current in combination with minimal sterile-active mixing can explain the discrepancy for sterile neutrino masses of $\mathcal{O}$(100) GeV while avoiding direct and indirect constraints. We discuss how searches for sterile neutrino production at the (HL-)LHC, measurements of h → μ + μ - and searches for h → e + e - , neutrinoless double beta decay experiments, and improved unitarity tests of the CKM matrix can further probe the relevant parameter space.
Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e - → π + π - channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e - → 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e- → 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives for the total 3π contribution to the anomalous magnetic moment of the muon, of which ${a}^{FSR}_\mu [3\pi]$ = 0.51(1) x 10 -10 and ${a}^{\rho - \omega}_\mu [3\pi]$ = -2.68(70) x 10 -10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e + e - → 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782.70(3) MeV, M Φ = 1019.21(2) MeV, Γ ω = 8.71(3) MeV, and Γ Φ = 4.27(1) MeV.
We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in |V us | and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.
Fundamental quantum electrodynamical (QED) processes, such as spontaneous emission and electron-photon scattering, encompass phenomena that underlie much of modern science and technology. Conventionally, calculations in QED and other field theories treat incoming particles as single-momentum states, omitting the possibility that coherent superposition states, i.e., shaped wavepackets, can alter fundamental scattering processes. Here, we show that free electron waveshaping can be used to design interferences between two or more pathways in a QED process, enabling precise control over the rate of that process. As an example, we show that free electron waveshaping modifies both spatial and spectral characteristics of bremsstrahlung emission, leading for instance to enhancements in directionality and monochromaticity. The ability to tailor general QED processes opens up additional avenues of control in phenomena ranging from optical excitation (e.g., plasmon and phonon emission) in electron microscopy to free electron lasing in the quantum regime.
Protons and neutrons, i.e. nucleons, are the basic building blocks of the matter in the visible universe. The strong force binds the nucleons to form nuclei. The electromagnetic force forms the atoms by binding the electrons with the nuclei. The electromagnetic interaction is well understood by Quantum Electrodynamics (QED), which shows the most precise predictability amongst all the theories in physics. In QED, charges interact with each other by exchanging photons. The Quantum Chromodynamics (QCD) describes the strong interaction. Its degrees of freedom are quarks and gluons, the fundamental constituents of the nucleons. The quarks interact with each other by exchanging gluons. However, unlike QED, the gluons interact amongst themselves. This feature of self bindings of the gluons confines the quarks and gluons in the nucleons/hadrons, never to be seen as free. In order to study some of the features of QCD, such as confinement or the structure of the nucleon, one usually needs to rely on experiments. Electromagnetic probes, governed by the well-understood QED, are excellent tools to probe the nucleon. In general, different scales, e.g. electron beam energies, probe different regions of the nucleon. At low energy, of the order of a few GeV, the electron probes the nucleon in the valence quark region. As its energy increases, the electron probes the sea quark and gluon regions. The study of the nucleon structure in all these regions is needed to fully understand QCD. Form factors and parton distribution functions measured from elastic scattering and deep inelastic scattering of leptons off nucleons have provided a partial view of the internal structure of the nucleon. In the mid-1990s, Generalized Parton Distributions (GPDs) were developed. These new objects are a generalization of the form factors and parton distribution functions, but contain richer information on the nucleon internal structure. GPDs are accessible experimentally by deep exclusive reactions. Deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP) are some examples. The first dedicated DVCS/DVMP experiment took place in 2004 in Hall A at The Thomas Jefferson National Accelerator Facility, i.e. Jefferson Lab, in Virginia, U.S.A. A new DVCS/DVMP experiment, after the beam energy upgrade of Jefferson Lab, was carried out in Hall A in a wider kinematic range. Its data were taken from 2014 to 2016. In Hall C at Jefferson Lab, the next DVCS/DVMP experiment will take place. The Hall C experiment will further exploit the kinematic range with higher precision. A Neutral Particle Spectrometer (NPS) is in development to measure DVCS/DVMP events under high background conditions. Jefferson Lab will provide the highest precision data in the valence quark region for various exclusive reactions. The Electron-Ion Collider (EIC) is a future experimental facility currently planned to start operations around 2030 in the U.S.A. Its high energy and high luminosity will probe the sea quark and gluon regions providing answers to the outstanding questions of QCD, in particular in the region where matter is dominated by gluons. First of all, this document describes the data analysis and results of the Hall A neutral pion electroproduction off the proton, from the data taken in 2014-2016. Later, some of the developments towards the construction of the electromagnetic calorimeter of the NPS for the upcoming DVCS/DVMP experiment in Hall C are presented. Finally, one of the candidate materials for the EIC calorimeter, a glass scintillator, will be briefly introduced. I have participated to all these projects, in collaboration with many colleagues. I present in this thesis my contributions to each of these projects. My contributions to the neutral pion data analysis were focused on background subtractions on the calorimeter, acceptance calculations, and the estimation of the systematic uncertainty associated to the event selection cuts. Some necessary information on calibrations of the detectors and data analysis methods are also described. In the NPS project, I performed background dose calculations and energy and position resolution studies of the calorimeter, all using Monte Carlo simulations, with realistic geometries of the experimental apparatus. Characterization of the crystals of the calorimeter was also done. Additionally, I measured the radiation hardness of some glass scintillator in its early stage of development. In order to have a future reference when the glass calorimeter prototype will be tested, I simulated the energy resolution of the prototype.
The Muon Campus at Fermilab provides world class accelerator infrastructure supporting the next generation intensity frontier experiments. The anti-proton source from the Tevatron era was converted to the present day Muon Campus at the end of the collider program in 2011. Currently, the Muon Campus delivers highly polarized muon beams to the Muon g-2 experiment and in a few years, it will provide muon beams to the Mu2e experiment. The Muon g-2 experiment is a high precision test of the standard model; it is precise enough to measure QED, Weak, and QCD Standard Model contributions.The Muon g-2 experiment looks for a significant deviation from the Standard Model whereas the Mu2e experiment looks for rare processes using high intensity muon beams. The Muon g-2 experiment has measured the anomalous magnetic moment of muons to an unprecedented 460 ppb precision with Run 1 data. The experiment has completed 5 runs, accumulating 19$\times$ Brookhaven E821 data set. The Mu2e experiment has completed the construction phase and first beam to the Diagnostic Absorber was run on April 14, 2022. Installation and commissioning of the Mu2e experiment will begin in 2023 and beam commissioning and physics run is currently planned for 2026.
Abstract Motivated by precision computations of neutrino decoupling at MeV temperatures, we show how QED corrections to the thermal neutrino interaction rate can be related to the electron-positron spectral function as well as an effective$$\overline{\nu }\nu \gamma $$vertex. The spectral function is needed both in a timelike and in a spacelike domain, and for both of its physical polarization states (transverse and longitudinal with respect to spatial momentum). Incorporating an NLO evaluation of this spectral function, an estimate of the$$\overline{\nu }\nu \gamma $$vertex, and HTL resummation of scatterings mediated by soft Bose-enhancedt-channel photons, we compute the interaction rate as a function of the neutrino momentum and flavour. Effects on the – (0. . .2)% level are found, noticeably smaller than a previous estimate of a related quantity.
Analogous to the well-known proton charge radius puzzle, a similar puzzle exists for the deuteron charge radius, r d . There are discrepancies observed in the results of r d , measured from electron-deuteron (e - d) scattering experiments, as well as from atomic spectroscopy. In order to help resolve the charge radius puzzle of the deuteron, the PRad collaboration at Jefferson Lab has proposed an experiment for measuring r d , named DRad. This experiment is designed to measure the unpolarized elastic e - d scattering cross section in a low-Q 2 region. To extract the cross section with a high precision, having reliable knowledge of QED radiative corrections is important. Here, in this paper, we present complete numerical calculations of the lowest-order radiative corrections in e - d scattering for the DRad kinematics. The calculations have been performed within a covariant formalism and beyond the ultra-relativistic approximation ($m^2_e$ $\ll$ Q 2 ). Besides, we present a systematic uncertainty on r d arising from higher-order radiative corrections, estimated based on our cross-section results.
The fabrication of large segmented optics requires a polishing process that can correct the figure of a surface to within a short distance from its edges-typically, a few millimeters. The work here is to develop QED's Magnetorheological Finishing (MRF) precision polishing process to minimize residual edge effects.