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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Z α 2 correction to superallowed beta decays in effective field theory and implications for | V u d |

Superallowed ( 0 + → 0 + ) beta decays currently provide the most precise extraction of quark mixing in the Standard Model. Their interpretation as a measurement of | V u d | relies on a reliable first-principles computation of QED radiative corrections expressed as a series in Z α and α . In this work, we provide the first model-independent result for two-loop, O ( Z α 2 ) , long-distance radiative corrections where the nuclei are treated as heavy pointlike particles. We use renormalization group analysis to obtain new results at O ( Z α 3 ) for the coefficient of double logarithms in the ratio of the maximal beta energy to the inverse nuclear size, E m / R - 1 . We use the Kinoshita-Lee-Nauenberg theorem to obtain new results at O ( Z 2 α 3 ) for the coefficient of logarithms in the ratio of maximal beta energy to the electron mass, log ( 2 E m / m ) . We identify a structure-dependent, and, therefore, short-distance, contribution to the traditional Z α 2 correction that should be revisited. We provide the first comprehensive update to the long-distance corrections in almost 40 years and comment on the impact of our findings for extractions of | V u d | . We find that shifts in the long-distance corrections are 2.5 × larger than past estimates of their uncertainty, 1.5 × 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.

Cao, Zehua [Kentucky U.] (ORCID:0009000354256423)↗
DOE OSTI2022

Towards a direct measurement of the quantum-vacuum Lagrangian coupling coefficients using two counterpropagating super-intense laser pulses

In this paper we will show that photon–photon collision experiments using extreme lasers can provide measurable effects giving fundamental information about the essence of QED, its Lagrangian. A possible scenario with two counterpropagating ultra-intense lasers for an experiment to detect scattering between optical photons is analyzed. We discuss the importance of the pulse widths and waists, the best scenario for overlapping the beams and signal detection, as well as ways to distinguish the signal from the noise. This would need a high-precision measurement, with control of temporal jitter and noise. We conclude that such experiment is barely feasible at 10 23 W cm -2 and very promising at 10 24 W cm -2

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Probing New Hadronic Forces with Heavy Exotic Atoms

We explore the potential of precision spectroscopy of heavy exotic atoms where electrons are substituted by negative hadrons to detect new force carriers with hadronic couplings. The selected transitions are unaffected by nuclear contact terms, thus enabling highly accurate calculations using bound-state QED, provided that the nuclear polarization is under control. Alternatively, we demonstrate that the dipole polarizability, a fundamental property of nuclei, can be extracted from the spectroscopy of exotic atoms in a novel way by combining two transitions while maintaining high sensitivity to new physics. Based on existing data, we extracted world-leading bounds on mediator masses ranging from 0.1 to 10 MeV for two benchmark models and show that forthcoming experiments could enhance the sensitivity to new physics by 2 orders of magnitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Radiative corrections: from medium to high energy experiments

Abstract Radiative corrections are crucial for modern high-precision physics experiments, and are an area of active research in the experimental and theoretical community. Here we provide an overview of the state of the field of radiative corrections with a focus on several topics: lepton–proton scattering, QED corrections in deep-inelastic scattering, and in radiative light-hadron decays. Particular emphasis is placed on the two-photon exchange, believed to be responsible for the proton form-factor discrepancy, and associated Monte-Carlo codes. We encourage the community to continue developing theoretical techniques to treat radiative corrections, and perform experimental tests of these corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Advances for QCD and the standard model: color-confining light-front holography and the principle of maximum conformality

Here, I review how the application of superconformal quantum mechanics and light-front holography leads to new insights into the physics of color confinement, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. Spontaneous chiral symmetry breaking is automatically fulfilled by supersymmetric Light-Front QCD. The light-front holographic approach (HLFQCD) also predicts the behavior of the QCD running coupling and other observables from the nonperturbative color-confining domain to the perturbative domain. One can determine the QCD running coupling to high precision from the data of just a single experiment over the entire perturbative regime by using the Principle of Maximum Conformality (PMC). The PMC, which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order Standard Model predictions, consistent with the principles of the renormalization group. I also briefly review a novel feature of hadronic physics predicted by QCD: intrinsic heavy quarks.

Brodsky, Stanley J. [SLAC National Accelerator Lab↗
DOE OSTI2023

High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μ r and thus determining the correct values of the QCD running coupling α s (μ r ) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μ r $\in$ [Q/2, 2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist’s choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the N c → 0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC ∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e + e - annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC ∞ applied to the thrust distribution investigating both the QCD conformal window and the QED N c → 0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC ∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC ∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities R e+e- , R$_Τ$ and Γ (H→$b\bar{b}$) up to the four-loop accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

QED radiative corrections to neutrino-nucleon elastic scattering

Neutrino oscillation experiments at accelerator energies aim to establish CP violation in the neutrino sector by measuring the energy-dependent rate of $\nu_e$ appearance and $\nu_\mu$ disappearance in a $\nu_\mu$ beam. Extracting the correct oscillation rate demands control over QED radiative corrections at the percent level. Focusing on the critical charged-current neutrino-nucleon scattering process, we show that the cross section factorizes into two pieces. The first piece depends on hadron structure but is universal for $\nu_e$ and $\nu_\mu$, and hence constrained by high-statistics $\nu_\mu$ data. The second piece is nonuniversal and suffers large logarithm enhancements, but is computed to high precision using renormalization group improved perturbation theory. Our results provide a missing ingredient for the robust interpretation of current NOvA and T2K experiments, and can be applied to future experiments such as DUNE and HyperK.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

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 limit of small electron mass and large electron energy. Numerical enhancements from the infrared region are resummed using renormalization group methods. Power corrections, cancellation of singularities in the small-mass expansion, renormalization scheme dependence, and bound-state effects are also discussed. These results provide the most precise determination of long-distance radiative corrections to neutron beta decay and impact the determination of |𝑉 𝑢⁢𝑑 | from the measured neutron lifetime and thus set a target for uncertainty reductions in the experimental and short-distance inputs.

Beta decay↗
NASA NTRS2007

Asymptotic Energies and QED Shifts for Rydberg States of Helium

This paper reviews progress that has been made in obtaining essentially exact solutions to the nonrelativistic three-body problem for helium by a combination of variational and asymptotic expansion methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. As an example, the results are applied to the calculation of isotope shifts for the short-lived 'halo' nucleus He-6 relative to He-4 in order to determine the nuclear charge radius of He-6 from high precision spectroscopic measurements carried out at the Argonne National Laboratory. The results demonstrate that the high precision that is now available from atomic theory is creating new opportunities to create novel measurement tools, and helium, along with hydrogen, can be regarded as a fundamental atomic system whose spectrum is well understood for all practical purposes.

Drake, G.W.F.↗
DOE OSTI2023

Beam dynamics corrections in the measurement of the anomalous precession frequency at the Muon $g-2$ experiment at Fermilab

The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, a μ , updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the e + e - → π + π - cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a^{SM}_{μ}$ = 116 592 033 (62) x $10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1–6 of E989 at Fermilab, one finds $a^{exp}_{μ} -a^{SM}_{μ}= 38 (63)$ x $10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Probing strong-field QED in beam-plasma collisions

Ongoing progress in laser and accelerator technology opens new possibilities in high-field science, notably to investigate the largely unexplored strong-field quantum electrodynamics (SFQED) regime where electron-positron pairs can be created directly from light-matter or even light-vacuum interactions. Laserless strategies such as beam-beam collisions have also been proposed to access the nonperturbative limit of SFQED. Here we report on a concept to probe SFQED by harnessing the interaction between a high-charge, ultrarelativistic electron beam and a solid conducting target. When impinging onto the target surface, the beam self fields are reflected, partly or fully, depending on the beam shape; in the rest frame of the beam electrons, these fields can exceed the Schwinger field, thus triggering SFQED effects such as quantum nonlinear inverse Compton scattering and nonlinear Breit-Wheeler electron-positron pair creation. Through reduced modeling and kinetic numerical simulations, we show that this single-beam setup can achieve interaction conditions similar to those envisioned in beam-beam collisions, but in a simpler and more controllable way owing to the automatic overlap of the beam and driving fields. This scheme thus eases the way to precision studies of SFQED and is also a promising milestone towards laserless studies of nonperturbative SFQED.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A precise electron EDM constraint on CP-odd heavy-quark Yukawas

CP-odd Higgs couplings to bottom and charm quarks arise in many extensions of the standard model and are of potential interest for electroweak baryogenesis. These couplings induce a contribution to the electron EDM. The experimental limit on the latter then leads to a strong bound on the CP-odd Higgs couplings. We point out that this bound receives large QCD corrections, even though it arises from a leptonic observable. We calculate the contribution of CP-odd Higgs couplings to the bottom and charm quarks in renormalisation-group improved perturbation theory at next-to-leading order in the strong interaction, thereby reducing the uncertainty to a few percent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Detailed comparison of renormalization scale-setting procedures based on the principle of maximum conformality

The Principle of Maximum Conformality (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC ∞ ). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities R e+e– , R τ , and $Γ(H→b\bar{b}$) up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling α s (Q) by the recursive use of the renormalization group equation, whose argument Q represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Dark moments for the Standard Model?

If dark matter (DM) interacts with the Standard Model (SM) via the kinetic mixing (KM) portal, it necessitates the existence of portal matter (PM) particles which carry both dark and SM quantum numbers that will appear in vacuum polarization-like loop graphs. In addition to the familiar ~ eϵQ strength, QED-like interaction for the dark photon (DP), in some setups different loop graphs of these PM states can also induce other coupling structures for the SM fermions that may come to dominate in at least some regions of parameter space regions and which can take the form of ‘dark’ moments, e.g., magnetic dipole-type interactions in the IR, associated with a large mass scale, Λ. In this paper, motivated by a simple toy model, we perform a phenomenological investigation of a possible loop-induced dark magnetic dipole moment for SM fermions, in particular, for the electron. We show that at the phenomenological level such a scenario can not only be made compatible with existing experimental constraints for a significant range of correlated values for Λ and the dark U(1) D gauge coupling, g D , but can also lead to quantitatively different signatures once the DP is discovered. In this setup, assuming complex scalar DM to satisfy CMB constraints, parameter space regions where the DP decays invisibly are found to be somewhat preferred if PM mass limits from direct searches at the LHC and our toy model setup are all taken seriously. High precision searches for, or measurements of, the e + e - → γ + DP process at Belle II are shown to provide some of the strongest future constraints on this scenario.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Intrinsic nonlocality of spin- and polarization-resolved probabilities in strong-field quantum electrodynamics

Spin and polarization are central to precision tests of fundamental physics and for interpreting radiation from astrophysical sources and ultraintense laser-matter experiments. Here, focusing on the fundamental process of nonlinear Compton scattering, we demonstrate that a key assumption underlying current strong-field quantum electrodynamics models, i.e., that emission can be treated as an instantaneous random event sampled from a local differential rate, is inconsistent once emission angles, electron spin, and/or photon polarization are resolved. Namely, even in strictly constant and uniform fields , the resulting fully differential distribution is sign indefinite, yielding negative inferred probabilities. The physical reason is that the photon emission probability builds up over a finite length of the electron trajectory, the formation region, during which the electron direction changes by roughly the same small angle that defines the radiation cone. Therefore, we put forward a new method where we integrate over this formation region analytically to obtain a physically consistent electron spin and photon polarization model. We show that the implementation of our model is compatible with existing Monte Carlo and particle-in-cell workflows. Simulations of a GeV-class electron-laser collision accessible at current petawatt facilities and of emission in a pulsarlike magnetic field are shown to reveal spin and polarization patterns that differ even qualitatively from state-of-the-art local models. In particular, our new model predicts substantial angle-dependent circular photon polarization where the well-known collinear-emission approach yields none, and a pronounced helicity bias in the recoiling electrons absent from current predictions. These findings have direct implications for upcoming strong-field QED experiments and for interpreting polarized radiation from extreme astrophysical environments.

astrophysical electromagnetic fields↗