Higher order leading logarithmic QED corrections to deep inelasticep scattering at very high energies

Higher order electromagnetic radiative corrections to neutral current deep inelastic electron proton scattering are studied in collinear approximation. Second order corrections show qualitatively new features compared to the first order ones and are non-negligible for largey and smallx. We also show how kinematical cuts on the recoil quark jet, in particular the jet angle, will allow a strong reduction of the contribution from radiative events for smallx and largey.     

QED radiative corrections to impact factors

We consider radiative corrections to the electron and photon impact factors. The generalized eikonal representation for the e ⁺ e ^? scattering amplitude at high energies and fixed momentum transfers is violated by nonplanar diagrams. An additional contribution to the two-loop approximation appears from the Bethe-Heitler mechanism of fermion pair production with the identity of the fermions in the final state taken into account. The violation of the generalized eikonal representation is also related to the charge parity conservation in QED. A one-loop correction to the photon impact factor for small virtualities of the exchanged photon is obtained using the known results for the cross section of the e ⁺ e ^? production during photon-nuclei interactions.     

Tagged-photon events in polarized deep inelastic scattering

Deep inelastic scattering events of a longitudinally polarized electron by a polarized proton with a tagged collinear photon radiated from the initial-state electron are considered. The corresponding cross section is derived in the Born approximation. The model-independent radiative corrections to the Born cross section are also calculated. The obtained result is applied to the elastic scattering.     

Binding corrections for reactions on the deuteron in the 3-3 resonance region

Binding corrections evaluated to all orders in a phenomenological nucleon-nucleon potential are compared with the leading term and with a double scattering correction in the Watson expansion for breakup and for coherent reactions on the deuteron at intermediate pion or photon energies. As principal result, we establish that for charged pion photoproduction, and for certain pion induced “spectator” reactions, the binding correction remains sufficiently small that truncation of the Watson expansion at terms of second order in the projectile-nucleon amplitudes is justifiable, but sufficiently large that it cannot be neglected in comparison with multiple scattering corrections. For the reactions π⁺d → π⁺p + spectator neutron and π^?d → π^?n + spectator proton, our theory predicts deviations from the simplest impulse approximation which become very large in well-defined kinematical regions, and should be easily accessible to experimental investigation.     

Scanning of the e + e − → π+π− cross section below 1 GeV at DAΦNE by radiative events

The tagged photon events for the measurement of the e ⁺ e ^? → π⁺π^? total cross section by the radiative return method at DAΦNE is discussed. The effects caused by the not exactly head-on collision of beams and by the QED radiative corrections are investigated. The essential part consists of the analysis of the event selection rules that ensure the rejection of the 3-pion hadronic state and take the main properties of the multiple purpose KLOE detector into account. The study of the non-head-on effect is performed in the Born approximation by integrating over the tagged photon angles, whereas the radiative corrections are calculated neglecting this effect. Together with the quasireal electron approach, this allows us to derive analytical formulas for the correction to the cross section of the initial-state radiative process. Some numerical calculations illustrate our analytical results.     

Model dependence of the electromagnetic corrections to lepton pair production in electron-positron collisions

The electromagnetic radiative corrections toe ⁺ e ^? -annihilation into lepton pairs are calculated including hard photon bremsstrahlung in the standard and extended electroweak models. For \(\sqrt s \) = 38 GeV we find for the standard model, that the radiative corrections toZ-exchange reduce the charge asymmetry up to 1% which is mainly caused by the virtual and soft photon parts of the corrections. For models with a higher forward-backward asymmetry the situation is found to be quite similar.     

Hawking radiation due to photon and gravitino tunneling

Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking’s periodicity argument, the modified metric for the Schwarzschild black hole is given. This corrected version of the metric, up to ? order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

Quantum transport theory for abelian plasmas

The gauge invariant relativistic quantum equations of motion for the fermion and photon Wigner operators are derived from QED. In the mean field (Hartree) approximation, we extract the generalized quantum Vlasov and mass-shell constraint equations for fermions. In addition, a complete spinor decomposition is performed. A systematic method for computing quantum corrections to all orders in h is developed. First order quantum (spin) corrections are computed explicitly. Finally, the relations between gauge dependent and independent definitions of the photon Wigner function and their corresponding transport equations are discussed.     

Finite temperature radiative corrections to neutron decay and related processes

We present a detailed calculation of the radiative corrections at finite temperature to the processes nν ? pe, ne ? pν. and n ? peν. The temperature range considered is approximately 100 keV to 3 MeV, which is the range relevant for nucleosynthesis calculations. Photon absorption and emission, photonic corrections to the vertex and fermion wave-function renormalizations, as well as the correction to the electron “mass” are calculated explicitly. It is shown that infrared divergences are only cancelled when absorption and induced photon emission are included. We analyze the effect of these processes on the various reaction rates, and discuss the effects of these corrections on the calculated helium abundance in the universe.     

Radiative muon capture in medium-heavy nuclei

Radiative muon capture in nuclei is thoroughly investigated in view of its sensitivity to the pseudoscalar coupling constant g_P. In the photon energy domain of interest (k ? 60 MeV) the effective one-body hamiltonian in use is shown essentially to hold true, with minor corrections due to the muon propagator in the nuclear field and to the two-step process. The closure approximation is avoided by appropriately integrating the response function calculated in the Fermi gas model, in the energy-momentum transfer plane.Theoretical predictions in medium-heavy nuclei of the high-energy photon spectrum, of photon polarization, and of muon-spin photon angular correlation are given for various values of the pseudoscalar coupling constant.     

A relativistic quark model for baryons

The Bethe-Salpeter equation for the relativistic three quark bound state is solved for an instantaneous interaction in the ladder approximation. The particular solution obtained is valid for simple potentials in both the weak and strong binding situations. The general method for calculating matrix elements for the interaction of the bound state with an external electromagnetic field is presented. Particular attention is paid to the emergence of the nonrelativistic quark model interaction as the lowest order approximation in a perturbative expansion in the inverse quark mass. Relativistic corrections to this approximation are investigated, and their importance is seen to depend on the quark mass. For light quarks these corrections can be large, and to reproduce the proton magnetic moment, for instance, a substantial anomalous moment is necessary. The model has several encouraging features. The form factors with a harmonic potential have an asymptotic k^?2 behavior, and the relativistic corrections to the SU(6) results for the form factors are of the correct order of magnitude.     

Radiative effects in deep inelastic scattering of polarized leptons by polarized nucleons

Low-order electromagnetic corrections to deep inelastic scattering of polarized leptons by polarized nucleons are derived and investigated using a covariant method. Thorough numerical calculations of the corrections to cross sections and to the measured asymmetry are carried out for μp (ep) scattering in the range of lepton energy E = 200–500 GeV (10–16 GeV). The sensitivity of the corrections to the choice of the structure functions is investigated. The electromagnetic corrections to the asymmetry are found to be less than 10% within the greatest part of the kinematical region, but if x ～ 0, y ～ 1 they can reach a few tens of percent. The lowest order neutral current contribution to the asymmetry is obtained within the framework of standard electroweak interaction theory and the quark parton model. It is found this effect may be significant, especially in the kinematical range where electromagnetic corrections are negligible.     

Inclusive jet production with virtual photons in next-to-leading order QCD

We present a next-to-leading order calculation for the virtual photoproduction of one and two jets inep collisions. Soft and collinear singularities are extracted using the phase space slicing method. The collinear photon initial state singularity depends logarithmically on the mass of the virtual photon and is absorbed into the virtual photon structure function. An $\overline {MS} $ factorization scheme is defined similarly to the real photon case. Numerical results are presented for HERA conditions using the Snowmass jet definition for inclusive single jet and dijet cross sections. We study the dependence of these cross sections on the transverse energies and rapidities of the jets. Finally, we compare the ratio of the experimentally defined resolved and direct cross sections with recent ZEUS data as a function of the photon virtualityP ².     

Absorptive corrections to the reaction γp→nπ in the one pion exchange model with gauge invariant extension

Absorptive corrections have been calculated for photoproduction ofN ^*. Two versions for the uncorrected production amplitude are used. First, the one pion exchange Born approximation in the Coulomb gauge and second, a gauge invariant extension, restricted to the orbital electromagnetic current and to the isospinI=1-amplitude in thet-channel. We found the second restriction to be unimportant. Numerical values for cross sections and decay correlations in the BeV region are given in diagram form. Present day experimental accuracy does not allow to test the effects of absorption.     

Hard photon next-to-leading corrections to two-fermion production in e + e − collisions above the Z 0 peak

A complete next-to-leading order calculation of the initial-state O (α) photonic corrections to hadron and lepton-pair production in e ⁺ e ^?. collisions is presented. The impact of the next-to-leading order corrections on the twofermion cross section and forward-backward asymmetry is studied in detail for several event selections, with special emphasis on hard photon effects at LEP1.5 and LEP2 energies. It is shown that for typical realistic event selections, initial-state next-to-leading order corrections in the soft approximation can be safely extrapolated to energies above the Z ⁰ peak without significant loss of precision.     

Unnaturalness in the higgs-Fermion sector

The Higgs-fermion-antifermion coupling is examined at one-loop level. It is shown that for a process like e⁺e⁻ → Hγ the one-loop radiative corrections can be several orders of magnitude larger than the Born approximation provided that the photon is sufficiently hard.     

Monte-Carlo generator photon jets for the process e+e?→γγ

Monte-Carlo generator with photon jets radiation in collinear regions for the process e ⁺ e ⁻→γγ is described in detail. Radiative corrections in the first order of α are treated exactly. Large leading logarithmic corrections coming from collinear regions are taken into account in all orders of α by applying the Structure Function approach. Theoretical precision of the cross section with radiative corrections is estimated to be 0.2%. This process is considered as an additional tool to measure luminosity in forthcoming experiments with the CMD-3 detector at the e ⁺ e ⁻ collider VEPP-2000.     

Higher order QCD contributions to electron structure functions

We study deep inelastice ⁺ e ^? scattering with untagged throughgoing target electrons. The corresponding electron structure functions are not trivially related to photon structure functions. Both can be calculated in QCD perturbation theory but the first ones can be measured more easily. In studying next-to-leading log contributions to electron structure functions we find that the leading logQ ² approximation completely fails at present energies. This is due to different scales λ andm _e . A modified leading-log approximation is introduced. Higher order corrections to this approximation are small away fromx=0 or 1.