Higher-order QED Research Articles

QED effects in inclusive semi-leptonic B decays

We analyse in detail the QED corrections to the total decay width and the moments of the electron energy spectrum of the inclusive semi-leptonic B → Xceν decay. Our calculation includes short-distance electroweak corrections, the complete \U0001d4aa(α) partonic terms and leading-logarithmic QED effects up to OΛQCD3/mb3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\Lambda}_{\ extrm{QCD}}^3/{m}_b^3\\right) $$\\end{document}. A comprehensive numerical comparison of our results against those obtained with the Monte Carlo (MC) tool PHOTOS is presented. While the comparison indicates good overall agreement, our computation contains QED effects not included in PHOTOS and should therefore better describe photon radiation to B → Xceν as measured by the B-factories. Our calculations represent the first steps in the construction of a fully differential higher-order QED MC generator for inclusive semi-leptonic B decays.

Exploring the higher-order QED effects on the differential distributions of vacuum pair production in relativistic heavy-ion collisions

Extensive studies have been conducted in the past few decades to investigate potential signatures of higher-order QED effects in high-energy electromagnetic scattering processes. In our previous work, we have identified evidence of higher-order corrections in the total cross-section for the vacuum pair production in relativistic heavy-ion collisions. However, the presence of higher-order QED corrections cannot be unambiguously proven solely based on total cross-section measurements due to substantial experimental and theoretical uncertainties. The objective of this paper is to explore the sensitivity of specific differential observables in the vacuum pair production to higher-order QED effects in high-energy heavy-ion collisions. These investigations will provide guidance in determining the presence or absence of higher-order QED processes by conducting precise measurements in future experiments.

QED calculations of energy levels of heliumlike ions with 5≤Z≤30

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$ is presented for the ground and $n=2$ excited states of heliumlike ions. After subtracting the first terms of the $Z\ensuremath{\alpha}$ expansion from the all-order results, we identify the higher-order QED effects of order $m{\ensuremath{\alpha}}^{7}$ and higher. Combining the higher-order remainder with the results complete through order $m{\ensuremath{\alpha}}^{6}$ from Yerokhin and Pachucki [Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and nonmixing $n=2$ states of heliumlike ions with $Z=5\text{--}30$. For the mixing $2\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ and $2\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z>10$.

Universal structure of radiative QED amplitudes at one loop

We present two novel results about the universal structure of radiative QED amplitudes in the soft and in the collinear limit. On the one hand, we extend the well-known Low-Burnett-Kroll theorem to the one-loop level and give the explicit relation between the radiative and non-radiative amplitude at subleading power in the soft limit. On the other hand, we consider a factorisation formula at leading power in the limit where the emitted photon becomes collinear to a light fermion and provide the corresponding one-loop splitting function. In addition to being interesting in their own right these findings are particularly relevant in the context of fully-differential higher-order QED calculations. One of the main challenges in this regard is the numerical stability of radiative contributions in the soft and collinear regions. The results presented here allow for a stabilisation of real­virtual amplitudes in these delicate phase-space regions by switching to the corresponding approximation without the need of explicit computations.

Leading-order relativistic corrections to the g factor of H2+

Relativistic corrections of order ${\ensuremath{\alpha}}^{2}$ to the $g$ factor of ${\mathrm{H}}_{2}^{+}$ are calculated with a high accuracy of nine significant digits for a wide range of rovibrational states. The precision of previous calculations [R. A. Hegstrom, Phys. Rev. A 19, 17 (1979) is improved by about five orders of magnitude by performing nonadiabatic variational calculations and by including recoil corrections. These results allow for nondestructive identification of the internal state through the measurement of spin-flip transition frequencies, which is a crucial requirement for proposed spectroscopy experiments on ${\mathrm{H}}_{2}^{+}$ and its antimatter counterpart ${\overline{\mathrm{H}}}_{2}{}^{\ensuremath{-}}$ in Penning traps [E. G. Myers, Phys. Rev. A 98, 010101(R) (2018)]. Further, they pave the way towards precision calculations of the $g$ factor through the calculation of higher-order QED corrections and hence to an alternative precision route to obtaining the proton-electron mass ratio.

Polarization transfer in $$\varvec{e}^+p \rightarrow e^+ \varvec{p}$$ scattering using the Super BigBite Spectrometer

The effects of multi-photon-exchange and other higher-order QED corrections on elastic electron-proton scattering have been a subject of high experimental and theoretical interest since the polarization transfer measurements of the proton electromagnetic form factor ratio \(G_E^p/G_M^p\) at large momentum transfer \(Q^2\) conclusively established the strong decrease of this ratio with \(Q^2\) for \(Q^2 \gtrsim 1\) \(\hbox {GeV}^2\). This result is incompatible with previous extractions of this quantity from cross section measurements using the Rosenbluth Separation technique. Much experimental attention has been focused on extracting the two-photon exchange (TPE) effect through the unpolarized \(e^+p/e^-p\) cross section ratio, but polarization transfer in polarized elastic scattering can also reveal evidence of hard two-photon exchange. Furthermore, it has a different sensitivity to the generalized TPE form factors, meaning that measurements provide new information that cannot be gleaned from unpolarized scattering alone. Both \(\epsilon \)-dependence of polarization transfer at fixed \(Q^2\), and deviations between electron-proton and positron-proton scattering are key signatures of hard TPE. A polarized positron beam at Jefferson Lab would present a unique opportunity to make the first measurement of positron polarization transfer, and comparison with electron-scattering data would place valuable constraints on hard TPE. Here, we propose a measurement program in Hall A that combines the Super BigBite Spectrometer for measuring recoil proton polarization, with a non-magnetic calorimetric detector for triggering on elastically scattered positrons. Though the reduced beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of TPE.

Measurements of dileptons and photon pairs from two-photon scattering in ultra-peripheral and hadronic Pb+Pb collisions with the ATLAS detector

In ultra-relativistic heavy-ion collisions, one expects copious rates of γ + γ processes through the interaction of the large electromagnetic fields of the nuclei, which can produce new particles (e.g. leptons) or even lead to light-by-light scattering via loop diagrams. The latter process is a notable prediction of QED and was only recently observed by ATLAS using the full 2018 dataset of Pb+Pb collisions at LHC. In ultra-peripheral collisions (UPCs), characterized by the large impact parameter between the nuclei, the outgoing leptons and photons are produced exclusively, and exhibit a strong back-to-back momentum correlation, with long tails induced by higher-order QED effects. This work presents measurements of dilepton production and light-by-light scattering performed by the ATLAS collaboration. The angular correlations as well as differential production cross sections in UPCs are measured and compared to theoretical models, including final state QED radiation. Muon pairs produced by the same two-photon scattering process in hadronic Pb+Pb collisions also potentially provide a sensitive probe of the quark gluon plasma. First measurements by ATLAS and STAR of dileptons produced via two-photon scattering in non-ultra-peripheral (non-UPC) nucleus-nucleus collisions showed an unexpected centrality-dependent broadening of the angular correlation between the two leptons and/or of the two-lepton pT distribution. ATLAS has recently measured dimuons produced via two-photon scattering in non-UPC Pb+Pb collisions at sNN=5.02TeV using data collected during the 2015 & 2018 runs at LHC, corresponding to an integrated luminosity of 1.9 nb−1. This data set represents a factor of 4 increase in statistics over the 2015 data set used for the first ATLAS measurement. The increased statistics allow new features to be observed in the data, as well as differential studies of the dependence of the pair-distribution on the transverse-momentum and pseudorapidity of the two muons. The results of the new measurement and the possible physics implications will be discussed.

Resummation of QED radiative corrections in a strong constant crossed field

By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $g=\alpha\chi^{2/3}$, where the dynamical quantum parameter $\chi=e\sqrt{-(Fp)^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $g\gg1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.

Two-photon atomic level widths at finite temperatures

The thermal two-photon level broadening of the excited energy levels in the hydrogen and H-like helium is evaluated via the imaginary part of thermal two-loop self-energy correction for bound electron. All the derivations are presented in the framework of rigorous quantum electrodynamic theory at finite temperatures and are applicable for the H-like ions. On this basis, we found a contribution to the level broadening induced by the blackbody radiation which is fundamentally different from the usual line broadening caused by the stimulated two-photon decay and the Raman scattering of thermal photons. Numerical calculations of the two-loop thermal correction to the two-photon width for the $2s$ state in hydrogen and singly ionized helium atoms show that the effect could significantly exceed the higher-order relativistic and radiative QED corrections commonly included in the calculations. In addition, the thermal two-loop self-energy correction significantly exceeds the "ordinary" stimulated one-photon depopulation rate at the relevant laboratory temperatures. In this work, detailed analysis and the corresponding comparison of the effect with the existing laboratory measurements in H-like ions are carried out.

QED at NNLO with McMule

McMule is a framework for fully differential higher-order QED calculations of scattering and decay processes involving leptons. It keeps finite lepton masses, which regularises collinear singularities. Soft singularities are treated with dimensional regularisation and using FKS^\ellℓ subtraction. We describe the implementation of the framework in Fortran 95, list the processes that are currently implemented, and give instructions on how to run the code. In addition, we present new phenomenological results for muon-electron scattering and lepton-proton scattering, including the dominant NNLO corrections. While the applications presented focus on MUonE, MUSE, and P2, the code can be used for a large number of planned and running experiments.

Approximating higher-order nonlinear QED processes with first-order building blocks

Higher-order tree-level processes in strong laser fields, i.e., cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e., nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particle-in-cell codes. However, the locally-constant-field (LCF) approximation and these particle-in-cell codes cannot be used when the intensity is only moderately high, which is a regime that is experimentally relevant. We have shown that one can still use a sequence of first-order processes to estimate higher orders at moderate intensities provided the field is sufficiently long. An important aspect of our new ``gluing'' approach is the role of the spin and polarization of intermediate particles, which is more nontrivial compared to the LCF regime.

Radiative corrections to elastic-electron proton scattering and uncertainty in proton charge radius

Higher-order QED radiative corrections to elastic electron-proton scattering are discussed. It is shown that they are relevant for high-precision experiments on proton form factor measurements. Analytic result are obtained for next-to-leading second order corrections to the electron line. Light pair corrections are taken into account. The role of the hadronic contribution to vacuum polarization is discussed. Numerical results are given for the conditions of the experiment on proton form factors performed by A1 Collaboration. Preliminary results are also shown for the set-up with reconstruction of momentum transfer from the recoil proton momentum.

Wavelength-dispersive spectroscopy in the hard x-ray regime of a heavy highly-charged ion: the 1s Lamb shift in hydrogen-like gold

Accurate spectroscopy of highly-charged high-Z ions in a storage ring is demonstrated to be feasible by the use of specially adapted crystal optics. The method has been applied for the measurement of the 1s Lamb shift in hydrogen-like gold (Au+78) in a storage ring through spectroscopy of the Lyman x-rays. This measurement represents the first result obtained for a high-Z element using high-resolution wavelength-dispersive spectroscopy in the hard x-ray regime, paving the way for sensitivity to higher-order QED effects.

Charge asymmetry in elastic scattering of massive leptons on protons

The charge asymmetry due to higher-order QED corrections in elastic lepton-proton scattering is estimated without employing the ultrarelativistic approximation. Our calculation is performed by generalizing the soft-photon approximation approach suggested by Tsai. Corresponding loop integrals that take a form of Passarino-Veltman scalar three-point functions are calculated analytically without neglecting the mass of the lepton. Our results provide model-independent charge asymmetry predictions for scattering of unpolarized and massive leptons on proton targets. These predictions can be used in corresponding experiments to determine the contribution coming from model-dependent hard two-photon exchange processes.

Higher-order theories from the minimal length

We show that the introduction of a minimal length in the context of noncommutative space–time gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a generalization of the standard electromagnetism and general relativity by applying a consistent procedure that modifies the original Maxwell and Einstein–Hilbert actions. In order to set a bound on the minimal length, we compare the deviations from the inverse-square law with the potentials obtained in the higher-order theories and discuss the validity of the results. The introduction of a quantum bound for the minimal length parameter [Formula: see text] in the higher-order QED allows us to lower the actual limits on the parameters of higher-derivative gravity by almost half of their order of magnitude.

Spatial characterization of the internal gas target at the ESR for the FOCAL experiment

The FOCAL experiment involves a highly accurate twin crystal spectrometer, designed for the measurement of the ground state Lamb shift of stored highly charged ions, like hydrogen-like Au78+, via spectroscopy in the hard-x-ray regime with an accuracy down to the few-eV level where higher-order QED contributions become accessible. For this level of accuracy all geometrical parameters including the position of the x-ray source are of crucial importance. In this conference proceeding we present our efforts to characterize the internal gas target at the experiment storage ring at GSI Darmstadt where in 2012 the FOCAL experiment was conducted.

Pseudo-observables in Higgs decays

We define a set of pseudo-observables characterizing the properties of Higgs decays in generic extensions of the Standard Model with no new particles below the Higgs mass. The pseudo-observables can be determined from experimental data, providing a systematic generalization of the "kappa-framework" so far adopted by the LHC experiments. The pseudo-observables are defined from on-shell decay amplitudes, allow for a systematic inclusion of higher-order QED and QCD corrections, and can be computed in any Effective Field Theory (EFT) approach to Higgs physics. We analyze the reduction of the number of independent pseudo-observables following from the hypotheses of lepton-universality, CP invariance, custodial symmetry, and linearly realized electroweak symmetry breaking. We outline the importance of kinematical studies of $h\to 4\ell$ decays for the extraction of such parameters and present their predictions in the linear EFT framework.

Relativistic M-subshell radiationless transition probabilities and energies for Zn, Cd and Hg

Theoretical calculations of radiationless transition probabilities and energies for M-subshell vacancies in Zn, Cd, and Hg are tabulated using the Dirac–Fock method. Transition probabilities between an initial vacancy state and a final two-vacancies state are presented for each initial and final atomic angular momentum quantum number. Calculations were performed in the single configuration approach with the Breit interaction, self-energy and (Uehling) vacuum polarization corrections included in the self-consistent method. Higher-order retardation corrections and QED effects were also included as perturbations.

RADIATIVE PRODUCTION OF LIGHTEST NEUTRALINOS IN e+e-COLLISIONS IN SUPERSYMMETRIC GRAND UNIFIED MODELS

We study the production of the lightest neutralinos in the radiative process [Formula: see text] in supersymmetric models with grand unification. We consider models wherein the standard model (SM) gauge group SU(3)c×SU(2)L×U(1)Yis unified into the grand unified gauge groups SU(5) or SO(10). We study this process at energies that may be accessible at a future International Linear Collider (ILC). We compare and contrast the dependence of the signal cross-section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the SM gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher-order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the SM radiative neutrino production [Formula: see text], as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) [Formula: see text]. The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly. It is likely that the radiative production of the lightest neutralinos may be a viable channel to study supersymmetric partners of the SM particles at the first stage of an ILC, where heavier sparticles may be too heavy to be produced in pairs.

Theoretical study on the 1s22s-1s2 np transitions for Ni25+ ion

The transition energies, wavelengths and oscillator strengths for the 1s22s-1s2np (n ⩽ 9) transitions of Ni25+ ion are calculated. In calculation of the energies, we not only take account of the firstorder corrections from relativistic and mass-polarization effects, but also estimate the higher-order relativistic contribution and QED correction by introducing the effective nuclear charge. The results agree with experimental data available in literature satisfactorily. Grotrian diagram showing these transitions is given.