Calculation Of Radiative Corrections Research Articles

Precise calculation of one-loop radiative corrections in møller scattering

Precise calculation of one-loop radiative corrections in møller scattering

Precise Calculations of One-Loop Radiative Corrections in Møller Scattering

Precise Calculations of One-Loop Radiative Corrections in Møller Scattering

Analytical calculations of the tenth order QED radiative corrections to lepton anomalies within the Mellin–Barnes representation

We investigate the radiative QED corrections to the lepton (L = e, μ and τ) anomalous magnetic moment due to the contributions of diagrams with insertions of the photon vacuum polarisation operator consisting solely of four closed lepton (l = e, μ and τ) loops. Moreover, we focus on specific operators with two loops formed by leptons L of the same type as the external one, the other two formed by leptons ℓ different from L. The approach is essentially based on the employment of the Mellin–Barnes representation of the x-parametrization of the corresponding Feynman diagrams. This allows one to obtain, for the first time, exact analytical expressions for the radiative corrections of the tenth order w.r.t. the electromagnetic coupling constant e. Analytically, the radiative corrections are expressed in terms of the ratio r = m ℓ /m L of the internal to external lepton masses. The dependence on r is investigated numerically in the whole interval of r, 0 < r < ∞ . To make comparisons with earlier published results possible, our exact analytical expressions are expanded as r → 0 and r → ∞ and compared with the corresponding asymptotic expansions known in the literature.

Radiative corrections to neutron and nuclear β-decays: a serious kinematics problem in the literature

We report a serious kinematics problem in the bremsstrahlung photon part of the order-α outer (model independent) radiative correction calculations for those neutron (and nuclear beta) decay observables (like electron-neutrino correlation parameter measurement) where the proton (recoil particle) is detected. The so-called neutrino-type radiative correction calculations, which fix the neutrino direction in the bremsstrahlung photon integrals, use 3-body decay kinematics to connect the unobserved neutrino direction with the observed electron and proton (recoil particle) momenta. But the presence of the bremsstrahlung photon changes the kinematics from 3-body to 4-body one, and the accurate information about the recoil particle momentum is lost due to the integration with respect to the photon momentum. Therefore the application of the abovementioned 3-body decay kinematics connection for the radiative correction calculations, rather prevalent in the literature, is not acceptable. We show that the correct, so-called recoil-type radiative correction calculations, which fix the proton (recoil particle) momentum instead of the neutrino direction and use rather involved analytical, semianalytical or Monte Carlo bremsstrahlung integration methods, result usually in much larger corrections than the incorrect neutrino-type analytical methods.

Radiative corrections and new physics tests in semileptonic tau decays

I review recent advances in the computation of radiative corrections in one- and two-meson tau decays and sketch their main applications in new physics tests: of lepton universality and CKM unitarity, as well as searching for non-standard interactions.

Contribution of nuclear excitation electromagnetic form factors in C12 and O16 to the Coulomb sum rule

We report on empirical parameterizations of longitudinal and transverse nuclear excitation electromagnetic form factors in ${\rm ^{12}C}$ and ${\rm ^{16}O}$. We extract the contribution of nuclear excitations to the Normalized Inelastic Coulomb Sum Rule (\csr) as a function of momentum transfer $\bf q$ and find that it is significant (0.29$\pm$0.030 at $\bf q$= 0.22 GeV). The total contributions of nuclear excitations to $S_L({\bf q})$ in ${\rm ^{12}C}$ and ${\rm ^{16}O}$ are found to be equal within the uncertainties. Since the cross sections for nuclear excitations are significant, the radiative tails from nuclear excitations should be included in precise calculations of radiative corrections to quasielastic electron scattering at low $\bf q$ and deep-inelastic electron scattering at large energy transfers $\nu$. The parameterizations also serve as a benchmark in testing theoretical modeling of cross sections for excitation of nuclear states in electron and neutrino interactions on nuclear targets at low energies.

The fate of infrared divergences in a finite formulation of field theory: QED revisited

Within the framework of the recently proposed Taylor–Lagrange regularization procedure, we reanalyze the calculation of radiative corrections in quantum electrodynamics (QED) at next to leading order. Starting from a well-defined local bare Lagrangian, the use of this regularization procedure enables us to manipulate fully finite elementary amplitudes in the ultra-violet (UV) as well as infrared (IR) regimes, in physical [Formula: see text] space–time dimensions and for physical massless photons, as required by gauge invariance. We can thus separately calculate the electromagnetic form factors of the electron and the cross-section for real photon emission, each quantity being finite in these physical conditions. We then discuss the renormalization group (RG) equations within this regularization procedure. Thanks to the taming of IR divergencies, the RG equation associated to the (physical) effective charge exhibits an UV stable fixed point at [Formula: see text], showing an asymptotic freedom-type behavior. We finally consider the case of two mass scales, one low and one heavy, paying particular attention to the natural decoupling properties between heavy and light degrees of freedom. As a direct consequence, the fine structure constant should be zero in the limit of massless electrons.

Peculiarities of pancreatic dysfunction in patients with chronic obstructive pulmonary disease

We consider the production of a Standard Model Higgs boson decaying to bottom quarks in association with a vector boson W±/Z in hadron collisions. We present a fully exclusive calculation of QCD radiative corrections both for the production cross section and for the Higgs boson decay rate up to next-to-next-to-leading order (NNLO) accuracy. Our calculation also includes the leptonic decay of the vector boson with finite-width effects and spin correlations. We consider typical kinematical cuts applied in the experimental analyses at the Large Hadron Collider (LHC) and we find that the full NNLO QCD corrections significantly decrease the accepted cross section and have a substantial impact on the shape of distributions. We point out that these additional effects are essential to obtain precise theoretical predictions to be compared with the LHC data.

Elastic positron–proton scattering at low Q$$^2$$

Systematic differences in the the proton's charge radius, as determined by ordinary atoms and muonic atoms, have caused a resurgence of interest in elastic lepton scattering measurements. The proton's charge radius, defined as the slope of the charge form factor at Q$^2$=0, does not depend on the probe. Any difference in the apparent size of the proton, when determined from ordinary versus muonic hydrogen, could point to new physics or need for the higher order corrections. While recent measurements seem to now be in agreement, there is to date no high precision elastic scattering data with both electrons and positrons. A high precision proton radius measurement could be performed in Hall B at Jefferson Lab with a positron beam and the calorimeter based setup of the PRad experiment. This measurement could also be extended to deuterons where a similar discrepancy has been observed between the muonic and electronic determination of deuteron charge radius. A new, high precision measurement with positrons, when viewed alongside electron scattering measurements and the forthcoming MUSE muon scattering measurement, could help provide new insights into the origins of the proton radius puzzle, and also provide new experimental constraints on radiative correction calculations.

Parton distributions in radiative corrections to the cross section of electron-proton scattering

The structure function approach and the parton picture, developed for the theoretical description of the deep inelastic electron-proton scattering, also proved to be very effective for calculation of radiative corrections in Quantum Electrodynamics. We use them to calculate radiative corrections to the cross section of electron-proton scattering due to electron-photon interaction, in the experimental setup with the recoil proton detection, proposed by A. A. Vorobyev to measure the proton radius. In the one-loop approximation, explicit expressions for these corrections are obtained for arbitrary momentum transfers. It is shown that, at momentum transfers small compared with the proton mass, various contributions to the corrections mutually cancel each other with power accuracy. In two loops, the corrections are obtained in the leading logarithmic approximation.

Following in Tini’s Giant Footsteps

This paper describes my personal appreciation of some of Tini Veltman's great research achievements and how my own research career has followed the pathways he opened. Among the topics where he has been the most influential have been the pursuit and study of the Higgs boson and the calculation of radiative corrections that enabled the masses of the top quark and the Higgs boson to be predicted ahead of their discoveries. The search for physics beyond the Standard Model may require a complementary approach, such as the search for non-renormalizable interactions via the Standard Model Effective Field Theory.

Modern methods of calculations of bremsstrahlung in the interaction of elementary particles

. The problem of real bremsstrahlung calculation is considered using the modern methods of regularization of divergencies. In particular, we calculate soft photon bremsstrahlung in the most general form using the method of dimensional regularization of infrared divergences. The general calculation algorithm of hard photon bremsstrahlung is described. It is shown that the contribution of hard bremsstrahlung can be separated into the finite and divergent parts. The divergent part can be factorized with the contribution of the initial process in the Born approximation. It is shown that a good choice of kinematic variables makes an analytic covariant calculation of the divergent part of the hard bremsstrahlung possible. In a particular case, an algorithm for determining the kinematic constraints on the invariants is described. A numerical analysis of the radiative corrections for gauge bosons production processes in the case of electron-photon collisions is performed. It is discovered that the contribution of the finite part of bremsstrahlung at high collision energies reaches 20 per cent and must be taken into account in calculations of radiative corrections. The results obtained can be used in various calculations, including covariant ones, performed in the context of confirmation of the Standard Model theoretical predictions or searching for manifestations of alternative gauge models.

Two-loop beta function for complex scalar electroweak multiplets

We present the general form of the renormalizable four-point interactions of a complex scalar field furnishing an irreducible representation of SU(2), and derive a set of algebraic identities that facilitates the calculation of higher-order radiative corrections. As an application, we calculate the two-loop beta function for the SM extended by a scalar multiplet, and provide the result explicitly in terms of the group invariants. Our results include the evolution of the Higgs-portal couplings, as well as scalar “minimal dark matter”. We present numerical results for the two-loop evolution of the various couplings.

Forward–backward asymmetry in electron–positron annihilation into pion or kaon pairs revisited

Forward–backward (charge) asymmetry in the processes of [Formula: see text] annihilation into a pair of charged pseudoscalar mesons is recalculated in the one-loop approximation. The exact dependence on the meson masses is taken into account. Results known in the literature are partially corrected. The bulk of the charge asymmetry appears due to double-photon exchange in [Formula: see text] channel. Experimental studies of the asymmetry can be used to verify the point-like approximation used in calculation of radiative corrections due to emission of photons by pions or kaons.

Nonrelativistic quantum electrodynamic approach to polarizabilities of light atoms

We derive polarizabilities for light atoms and their relativistic and radiative corrections by using nonrelativistic quantum electrodynamics (NRQED). We find out that if we use NRQED directly on the polarizabilities, it will lead to gauge-dependent terms which should be cancelled out by summing all the Feynman diagrams. The elimination of these gauge-dependent terms will become very cumbersome in the calculations of relativistic and radiative corrections. By combining the Power–Zienau–Woolley transformation with NRQED, we have simplified this process. In addition to this, the combination allows us to obtain not only the electric dipole polarizability but also other kinds of polarizabilities, such as magnetic, Coulomb-transversal and hyperpolarizabilities, in a unified way. In the following article we introduce this combined method and show a systematic procedure to derive the polarizabilities as well as the relativistic, radiative corrections to some of them.

QED radiative corrections to the P1/22−P3/22 fine structure in fluorinelike ions

Ab initio calculations of QED radiative corrections to the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure transition energy are performed for selected F-like ions. These calculations are nonperturbative in $\alpha Z$ and include all first-order and many-electron second-order effects in $\alpha$. When compared to approximate QED computations, a notable discrepancy is found especially for F-like uranium for which the predicted self-energy contributions even differ in sign. Moreover, all deviations between theory and experiment for the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure energies of F-like ions, reported recently by Li et al., Phys. Rev. A 98, 020502(R) (2018), are resolved if their highly accurate, non-QED fine-structure values are combined with the QED corrections ab initially evaluated here.

High-energy behavior of strong-field QED in an intense plane wave

Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches.

Radiative corrections to the jet quenching parameter in dilute and dense media

We extend the calculation of radiative corrections to momentum broadening in a QCD medium to include processes where single scattering dominates over multiple soft scatterings. Our analysis focusses on processes that are enhanced by a potentially large double logarithmic contribution. We demonstrate that such double logarithmic contributions emerge in calculations of momentum broadening in dilute systems where only single scattering occurs. We show how the different regimes, multiple versus single scattering, constrain different parts of the phase space.

Associated production of a Higgs boson decaying into bottom quarks at the LHC in full NNLO QCD

We consider the production of a Standard Model Higgs boson decaying to bottom quarks in association with a vector boson W±/Z in hadron collisions. We present a fully exclusive calculation of QCD radiative corrections both for the production cross section and for the Higgs boson decay rate up to next-to-next-to-leading order (NNLO) accuracy. Our calculation also includes the leptonic decay of the vector boson with finite-width effects and spin correlations. We consider typical kinematical cuts applied in the experimental analyses at the Large Hadron Collider (LHC) and we find that the full NNLO QCD corrections significantly decrease the accepted cross section and have a substantial impact on the shape of distributions. We point out that these additional effects are essential to obtain precise theoretical predictions to be compared with the LHC data.

Updated measurement of the e+e−→ωπ0→π0π0γ cross section with the SND detector

We analyze a 37 pb$^{-1}$ data sample collected with the SND detector at the VEPP-2000 $e^+e^-$ collider in the center-of-mass energy range 1.05--2.00 GeV and present an updated measurement of the $e^+e^- \to \omega \pi^0 \to \pi^0\pi^0\gamma$ cross section. In particular, we correct the mistake in radiative correction calculation made in our previous measurement based on a part of the data. The measured cross section is fitted with the vector meson dominance model with three $\rho$-like states and used to test the conserved vector current hypothesis in the $\tau^-\to\omega\pi^-\nu_{\tau}$ decay.