QED Effects Research Articles

Development of a new database for Auger electron and X-ray spectra

An energy correction method is described to account for the Breit and QED effects on Auger electrons and X-ray energies in the recently developed atomic relaxation model BrIccEmis. The results are compared with literature and new experimental data for Z = 52. Overall this improves the agreement of the calculated energies with the literature values. A new atomic radiation database NS_Radlist, will contain atomic transition energies from the BrIccEmis program with these energy corrections.

Concept and simulations of a high-resolution asymmetric von Hamos X-ray spectrometer for CRYRING@ESR electron cooler

SynopsisA concept of a high resolution asymmetric von Hamos X-ray spectrometer for the CRYRING@ESR electron cooler is described and its characteristics obtained by ray-tracing Monte-Carlo simulations are presented. The spectrometer will be used to study the QED effects in H-like medium-Z ions by measuring the energies of X-rays from radiative recombination of highly charged ions with cooling electrons, with a ppm precision of energy determination.

On the importance of NNLO QCD and isospin-breaking corrections in varepsilon '/varepsilon

Following the 1999 analysis of Gambino, Haisch and one of us, we stress that all the recent NLO analyses of varepsilon '/varepsilon in the Standard Model (SM) suffer from the renormalization scheme dependence present in the electroweak penguin contributions as well as from scale uncertainties in them related to the matching scale mu _W and in particular to mu _t in m_t(mu _t). We also reemphasize the important role of isospin-breaking and QED effects in the evaluation of varepsilon '/varepsilon . Omitting all these effects, as done in the 2015 analysis by RBC-UKQCD collaboration, and choosing as an example the QCD penguin (Q_6) and electroweak penguin (Q_8) parameters B_6^{(1/2)} and B_8^{(3/2)} to be B_6^{(1/2)}= 0.80 pm 0.08 and B_8^{(3/2)}= 0.76 pm 0.04 at mu = m_c=1.3,, text {GeV}, we find (varepsilon '/varepsilon )_mathrm{SM} = (9.4 pm 3.5) times 10^{-4}, whereas including them results in (varepsilon '/varepsilon )_mathrm{SM} = (5.6pm 2.4)times 10^{-4}. This is an example of an anomaly at the 3.3,sigma level, which would be missed without these corrections. NNLO QCD contributions to QCD penguins are expected to further enhance this anomaly. We provide a table for varepsilon '/varepsilon for different values of B_6^{(1/2)} and the isospin-breaking parameter {widehat{Omega }}_text {eff}, that should facilitate monitoring the values of varepsilon '/varepsilon in the SM when the RBC-UKQCD calculations of hadronic matrix elements including isospin-breaking corrections and QED effects will improve with time.

MBPT Calculations of Energy Levels for 1s2 and 1snl (N=2-5) Configuration of Helium Like Lithium Ion

In this paper, we carried out accurate energy levels calculations among the lowest 49 levels arising from the 1s2 and 1snl (n=2-5) configuration of the He-like-Li ion using the standard relativistic configuration interaction (RCI) approach and the second-order many body perturbation theory (MBPT). Both methods were implemented in the relativistic atomic code FAC. The self-consistent field approximation and the Hamiltonian effects of the Breit interaction as well as the QED effects were included to the different calculation methods. To assess the accuracy of our calculations, we performed comparison to available experimental (NIST database) and previous theoretical results. Comparisons are made with the available data in the literature and good agreement has been found which confirms the reliability of our results. Comparatively to the NIST database, it was found that our calculated energy levels using three methods, mainly standard FAC, RCI and MBPT are assessed to be mainly accurate to better than 1.33%, 0.47% and 0.06%. Our data are with great interest in plasma diagnostics.

Renormalizing vector currents in lattice QCD using momentum-subtraction schemes

We examine the renormalisation of flavour-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artefacts associated with the use of intermediate momentum-subtraction schemes. Our study uses the Highly Improved Staggered Quark (HISQ) action on gluon field configurations that include $n_f=2+1+1$ flavours of sea quarks, but our results have applicability to other quark actions. Renormalisation schemes that make use of the exact lattice vector Ward-Takahashi identity for the conserved current also have renormalisation factors, $Z_V$, for nonconserved vector currents that are free of contamination by nonperturbative condensates. We show this by explicit comparison of two such schemes: that of the vector form factor at zero momentum transfer and the RI-SMOM momentum-subtraction scheme. The two determinations of $Z_V$ differ only by discretisation effects (for any value of momentum-transfer in the RI-SMOM case). The RI$^{\prime}$-MOM scheme, although widely used, does not share this property. We show that $Z_V$ determined in the standard way in this scheme has $\mathcal{O}(1\%)$ nonperturbative contamination that limits its accuracy. Instead we define an RI$^{\prime}$-MOM $Z_V$ from a ratio of local to conserved vector current vertex functions and show that this $Z_V$ is a safe one to use in lattice QCD calculations. We also perform a first study of vector current renormalisation with the inclusion of quenched QED effects on the lattice using the RI-SMOM scheme.

Ad Lucem: QED parton distribution functions in the MMHT framework

We present the MMHT2015qed PDF set, resulting from the inclusion of QED corrections to the existing set of MMHT Parton Distribution Functions (PDFs), and which contain the photon PDF of the proton. Adopting an input distribution from the LUXqed formulation, we discuss our methods of including QED effects for the full, coupled DGLAP evolution of all partons with QED at {mathcal {O}}(alpha ), {mathcal {O}}(alpha alpha _{S}), {mathcal {O}}(alpha ^2). While we find consistency for the photon PDF of the proton with other recent sets, building on this we also present a set of QED corrected neutron PDFs and provide the photon PDF separated into its elastic and inelastic contributions. The effect of QED corrections on the other partons and the fit quality is investigated, and the sources of uncertainty for the photon are outlined. Finally we explore the phenomenological implications of this set, giving the partonic luminosities for both the elastic and inelastic contributions to the photon and the effect of our photon PDF on fits to high mass Drell–Yan production, including the photon-initiated channel.

QED challenges at FCC-ee precision measurements

The expected experimental precision of the rates and asymmetries in the Future Circular Collider with electron–positron beams (FCC-ee) in the center of the mass energy range 88–365 GeV considered for construction in CERN, will be better by a factor 5–200. This will be thanks to the very high luminosity, a factor up to 10^5 higher than in the past LEP experiments. Consequently, it poses the extraordinary challenge of improving the precision of the Standard Model predictions by a comparable factor. In particular the perturbative calculations of the trivial QED effects, which have to be removed from the experimental data, are considered to be a major challenge for almost all quantities to be measured at FCC-ee. The task of this paper is to summarize the “state of the art” in this class of the calculations left over from the LEP era and to examine what is to be done to match the precision of the FCC-ee experiments – what kind of technical advancements are necessary. The above analysis will be done for most important observables of the FCC-ee, like the total cross sections near Z and WW threshold, charge asymmetries, the invisible width of Z boson, the spin asymmetry from tau lepton decay and the luminosity measurement.

Theoretical Energy Levels of 1sns and 1snp States of Helium-Like Ions

Energy levels of the 1sns and 1snp states of ions along the helium isoelectronic sequence from carbon to uranium are calculated, with n = 3–7. The computation is performed within the relativistic configuration-interaction method, including the relativistic nuclear recoil effect, the leading quantum electrodynamics effects, and the frequency dependence of the Breit interaction. All theoretical energies are supplied with uncertainty estimates.

Few-electron atomic ions in non-relativistic QED: The ground state

Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for Z≤20 the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy. It is demonstrated that for both helium-like and lithium-like ions with Z≤20 the finite nuclear mass effects do not change 4–5 significant digits (s.d.), and the leading relativistic and QED effects leave unchanged 3–4 s.d. in the ground state energy. It is shown that the non-relativistic ground state energy can be interpolated with accuracy not less than 13 s.d. for Z≤12, and not less than 12 s.d. for Z≤50 for helium-like as well as for Z≤20 for lithium-like ions by a compact meromorphic function in variable λ=Z−ZB (here ZB is the 2nd critical charge (Turbiner et al., 2016)), P9(λ)∕Q5(λ). It is found that both the Majorana formula – a second degree polynomial in Z with two free parameters – and a fourth degree polynomial in λ (a generalization of the Majorana formula) reproduce the ground state energy of the helium-like and lithium-like ions for Z≤20 in the domain of applicability of NRQED, thus, at least, 3 s.d. It is noted that ≳99.9% of the ground state energy is given by the variational energy for properly optimized trial function of the form of (anti)-symmetrized product of three (six) screened Coulomb orbitals for two-(three) electron system with 3 (7) free parameters for Z≤20, respectively. It may imply that these trial functions are, in fact, exact wavefunctions in non-relativistic QED, thus, the NRQED effective potential can be derived. It is shown that the sum of relativistic and QED effects in leading approximation - 3 s.d. - for both 2 and 3 electron systems is interpolated by 4th degree polynomial in Z for Z≤20.

Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity

Here we present a fundamental study on how the ground-state chemical reactivity of a molecule can be modified in a QED scenario, i.e., when it is placed inside a cavity and there is strong coupling between the cavity field and vibrational modes within the molecule. We work with a model system for the molecule (Shin-Metiu model) in which nuclear, electronic and photonic degrees of freedom are treated on the same footing. This simplified model allows the comparison of exact quantum reaction rate calculations with predictions emerging from transition state theory based on the cavity Born-Oppenheimer approach. We demonstrate that QED effects are indeed able to significantly modify activation barriers in chemical reactions and, as a consequence, reaction rates. The critical physical parameter controlling this effect is the permanent dipole of the molecule and how this magnitude changes along the reaction coordinate. We show that the effective coupling can lead to significant single-molecule energy shifts in an experimentally available nanoparticle-on-mirror cavity. We then apply the validated theory to a realistic case (internal rotation in the 1,2-dichloroethane molecule), showing how reactions can be inhibited or catalyzed depending on the profile of the molecular dipole. Furthermore, we discuss the absence of resonance effects in this process, which can be understood through its connection to Casimir-Polder forces. Finally, we treat the case of many-molecule strong coupling, and find collective modifications of reaction rates if the molecular permanent dipole moments are oriented with respected to the cavity field. This demonstrates that collective coupling can also provide a mechanism for modifying ground-state chemical reactivity of an ensemble of molecules coupled to a cavity mode.

Documentation of TauSpinner approach for electroweak corrections in LHC Z rightarrow ll observables

The LHC Standard Model Z-boson couplings measurements approach the LEP legacy precision. The calculations of electroweak (EW) corrections available for the Monte Carlo generators become of relevance. Predictions of Z-boson production and decay require classes of QED/EW/QCD corrections and separatly from the production process QCD dynamics. At the LEP time electroweak form-factors and Improved Born Approximation were introduced for non QED genuine weak and line-shape corrections. This formalism was well suited for observables, so-called doubly-deconvoluted the Z-pole region where initial- and final-state QED real and virtual emissions were treated separately or were integrated over. The approach was convenient for implementation into Monte Carlo programs for LEP, Belle-BaBar and other future e^+e^- colliders and for invariant mass of outgoing lepton pair from a few GeV to well above WW and even t{bar{t}} threshold. We attempt now to profit from that, for the LHC pp and 70–150 GeV window for the outgoing lepton pair invariant mass. Our technical focus is on the EW corrections for LHC Z rightarrow ell ell observables. For this purpose the TauSpinner package, for the reweighting of previously generated events, is enriched with the genuine EW corrections (QED effects subtracted) of the Dizet electroweak library, taken from the LEP era KKMC Monte Carlo. Complete genuine EW O(alpha ) weak loop corrections and dominant higher-order terms are taken into account. For the efficiency and numerical stability look-up tables are used. For LHC observables: the Z-boson line-shape, the outgoing leptons forward-backward asymmetry, the effective leptonic weak mixing angles and finally for the spherical harmonic expansion coefficients of the lepton distributions, corrections are evaluated. Simplified calculations of Effective Born of modified EW couplings are compared with of Improved Born Approximation of complete set of EW form-factors. Approach uses LEP precision tests definitions and thus offers consistency checks. The package can be useful to evaluate of observables precision limits and to determine which corrections are then important for LHC and FCC projects phenomenology.

The path to 0.01% theoretical luminosity precision for the FCC-ee

The current status of the theoretical precision for the Bhabha luminometry is critically reviewed and pathways are outlined to the requirement targeted by the FCC-ee precision studies. Various components of the pertinent error budget are discussed in detail – starting from the context of the LEP experiments, through their current updates, up to prospects of their improvements for the sake of the FCC-ee. It is argued that, with an appropriate upgrade of the Monte Carlo event generator BHLUMI and/or other similar MC programs calculating QED effects in the low angle Bhabha process, the total theoretical error of 0.01% for the FCC-ee luminometry can be reached. A new study of the Z and s-channel γ exchanges within the angular range of the FCC-ee luminometer using the BHWIDE Monte Carlo was instrumental in obtaining the above result. Possible ways of BHLUMI upgrade are also discussed.

Estimating the radiative part of QED effects in systems with supercritical charge

The effective interaction of the electron magnetic moment anomaly with the Coulomb fileld of superheavy nuclei is investigated by taking into account its dynamical screening at small distances. The shift of the electronic levels, caused by this interaction, is considered for H-like atoms and for compact nuclear quasi-molecules, non-perturbatively both in Zα and (partially) in α/π. It is shown that the levels shift reveals a non-monotonic behavior in the region Zα 1 and near the threshold of the lower continuum decreases both with the increasing the charge and with enlarging the size of the system of Coulomb sources. The last result is generalized to the total self-energy contribution to the levels shift and so to the possible behavior of radiative QED effects with virtual photon exchange near the lower continuum in the supercritical region.

Theory of the Lamb Shift in Hydrogen and Light Hydrogen‐Like Ions

AbstractTheoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high‐precision determination of the proton charge radius drastically reduces the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two‐ and three‐loop QED effects, which calls for further advances in their calculations. The present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen‐like ions with the nuclear charge number up to is reviewed. Theoretical errors due to various effects are critically examined and estimated.

The enhanced X-ray Timing and Polarimetry mission—eXTP

In this paper we present the enhanced X-ray Timing and Polarimetry mission - eXTP. eXTP is a space science mission designed to study fundamental physics under extreme conditions of density, gravity and magnetism. The mission aims at determining the equation of state of matter at supra-nuclear density, measuring effects of QED, and understanding the dynamics of matter in strong-field gravity. In addition to investigating fundamental physics, eXTP will be a very powerful observatory for astrophysics that will provide observations of unprecedented quality on a variety of galactic and extragalactic objects. In particular, its wide field monitoring capabilities will be highly instrumental to detect the electro-magnetic counterparts of gravitational wave sources. The paper provides a detailed description of: (1) the technological and technical aspects, and the expected performance of the instruments of the scientific payload; (2) the elements and functions of the mission, from the spacecraft to the ground segment.

Relativistic full-configuration-interaction calculations of magic wavelengths for the 2 3S1→2 1S0 transition of helium isotopes

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.

Allowed and forbidden transition rates and corresponding wavelengths for Si-like Au ion (Au65+) by relativistic configuration interaction method

Large-scale atomic calculations are carried out to produce data of atomic structure and transitions rates for Si-like Au ion (Au65+). Generated atomic data are essential for modeling of M-shell spectra of gold ions in Au plasma, and fusion research. Energy levels are calculated by applying two methods: the relativistic configuration interaction method (RCI) of the flexible atomic code (FAC) and the multi-reference many body perturbation theory method (MR-MBPT). Energy levels, oscillator strengths, and transition rates are calculated for transitions between excited and ground states from n = 3l to n′l′, where n′ = 4, 5, 6, and 7; and l and l′ are the proper angular momenta of shells n and n′, respectively. The electric dipole (E1), electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1), magnetic quadrupole (M2), and magnetic octupole (M3) transitions are all considered in the calculations. Correlation effects, relativistic effects, and QED effects are also included in the calculations. The two methods yield comparable values of energy levels. Data of energy levels of low-lying states and data for inner shell transitions reported in this study demonstrate good agreement with published experimental and theoretical data.

Room temperature continuous-wave nanolaser diode utilized by ultrahigh-Q few-cell photonic crystal nanocavities

Few-cell point-defect photonic crystal (PhC) nanocavities (such as LX and H1 type cavities), have several unique characteristics including an ultra-small mode volume (Vm), a small device footprint advantageous for dense integration, and a large mode spacing advantageous for high spontaneous-emission coupling coefficient (β), which are promising for energy-efficient densely-integratable on-chip laser light sources enhanced by the cavity QED effect. To achieve this goal, a high quality factor (Q) is essential, but conventional few-cell point-defect cavities do not have a sufficiently high Q. Here we adopt a series of modified designs of LX cavities with a buried heterostructure (BH) multi-quantum-well (MQW) active region that can achieve a high Q while maintaining their original advantages and fabricate current-injection laser devices. We have successfully observed continuous-wave (CW) lasing in InP-based L1, L2, L3 and L5 PhC nanocavities at 23°C with a DC current injection lower than 10 μA and a bias voltage lower than 0.9 V. The active volume is ultra-small while maintaining a sufficiently high confinement factor, which is as low as ~10-15 cm3 for a single-cell (L1) nanocavity. This is the first room-temperature current-injection CW lasing from any types of few-cell point-defect PhC nanocavities (LX or H1 types). Our report marks an important step towards realizing a nanolaser diode with a high cavity-QED effect, which is promising for use with on-chip densely integrated laser sources in photonic networks-on-chip combined with CMOS processors.

Five-particle contributions to the inclusive rare bar{B} rightarrow X_{s(d)} , ell ^+ell ^- decays

We calculate tree-level contributions to the inclusive rare bar{B} rightarrow X_{s(d)} , ell ^+ell ^- decays. At the partonic level they stem from the five-particle process b rightarrow s(d) , q bar{q} , ell ^+ell ^-, with q in {u,d,s}. While for b rightarrow d transitions such five-body final states contribute at the same order in the Wolfenstein expansion compared to the three-body partonic decay, they are CKM suppressed in b rightarrow s decays. In the perturbative expansion, we include all leading-order contributions, as well as partial next-to-leading order QCD and QED effects. In the case of the differential branching ratio, we present all results completely analytically in terms of polylogarithmic functions of at most weight three. We also consider the differential forward-backward asymmetry, where all except one interference could be obtained analytically. From a phenomenological point of view the newly calculated contributions are at the percent level or below.

Essentially non-perturbative and peculiar polarization effects in planar QED with strong coupling

The essentially non-perturbative polarization effects are considered for a planar supercritical Dirac-Coulomb system with strong coupling (similar to graphene and graphene-based heterostructures) in terms of induced charge density ρVP(r→). The main attention is paid to the renormalization, convergence of the partial expansion and the behavior of ρVP(r→) and the integral induced charge QVP in the overcritical region. The dependence of the induced density on the screening of the Coulomb asymptotics of the external source is also explored in detail. Some peculiar effects in the discrete spectrum with the lowest rotational numbers mj = ±1∕2, ±3∕2 in the screened case are detected and their possible role in the transition through corresponding Zcr is also discussed.