Radiative corrections to the Bhabha scattering

In this review we consider the high energy processes in QED frames in peripherical kinematics. The key feature of this kinematics is that processes have a large cross section which do not decrease with the increasing of the initial center of mass energy. Two purposes to study peripheral processes are: the background processes with large total cross sections and the structure of jets in the fragmentation region.     

Measurement of cross sections for processes involving <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation to hadrons at the VEPP-2M collider

Results obtained by measuring, in experiments at the VEPP-2M e ⁺ e ^? collider with the CMD-2 and SND detectors at the Novosibirsk Institute of Nuclear Physics, cross sections for e ⁺ e ^? → hadrons annihilation processes at energies in the range 360 ≤ √s ≤ 1380 MeV are surveyed. The measured cross sections and the vector-meson parameters deduced from an analysis of these cross sections are presented. The cross section for the process e ⁺ e ^? → π ⁺ π ^? is compared with the spectral function for the decay τ ^? → π ^? π ⁰ ν _τ.     

Analysis of the production of Higgs boson pairs at the one-loop level in the minimal supersymmetric standard model

Within theminimal supersymmetric standardmodel, the amplitudes and total cross sections for the processes e ⁺ e ^? → hh, e ⁺ e ^? → hH, e ⁺ e ^? → HH, and e ⁺ e ^? → AA are calculated in the first order of perturbation theory with allowance for a complete set of one-loop diagrams in the m _e → 0 approximation. Analytic expressions are obtained for the quantities under consideration; numerical results are presented in a graphical form. It is shown that the cross section for the process e ⁺ e ^? → hh is larger than those for the other processes (and is on the same order of magnitude as the cross section for the corresponding processes in the Standard Model). In the case of the collision energy equal to √s = 500 GeV, an integrated luminosity in the region ∫ ? ≥ 500 fb^?1, and a longitudinal polarization of the e ⁺ e ? beams used, 520, 320, and 300 production events are possible in the processes e ⁺ e ^? → hh (at M _h = 115 GeV), e ⁺ e ^? → HH, and e ⁺ e ^? → AA (at M _H,A = 120 GeV), respectively. Even at M _H,A ≈ 500 GeV and √s = 1.5 TeV, not less than 200 events for each of the processes can be accumulated. The cross section for the process e ⁺ e ^? → hH is small (about 10^?2 fb), which complicates the detection of the sought signal significantly.     

Single-electron charge transfer and excitations at collisions between Bi<Superscript>4+</Superscript> ions in the kiloelectronvolt energy range

Pioneering theoretical data for single-electron charge transfer and excitations due to collisions between Bi⁴⁺ ions in the ground (6s) and metastable (6p) states are gained in the collision energy interval 5–75 keV in the center-of-mass frame. The cross sections of the processes are calculated in terms of the close-coupling method in the basis of two-electron quasi-molecular states for the Coulomb trajectory of nuclei. It is found that single-electron capture into the singlet 6s ² states of Bi³⁺ ions makes a major contribution to the charge transfer total cross section for Bi⁴⁺(6s) + Bi⁴⁺(6s) collisions (reaction 1), whereas single-electron capture into the singlet 6s6p states is the basic contributor to the total cross section in Bi⁴⁺(6s) + Bi⁴⁺(6p) collisions (reaction 2). In the collision energy interval mentioned above, the collision cross sections vary between 1.2 × 10^?17 and 1.9 × 10^?17 cm² for reaction 1 and between 3.8 × 10^?17 and 5.3 × 10^?17 cm² for reaction 2. In reaction 1, the 6s → 6p excitation cross sections vary from 0.6 × 10^?16 to 0.8 × 10^?16 cm² for the singlet channel and from 2.2 × 10^?16 to 2.8 × 10^?16 cm² for the triplet channel. The calculation results are compared with the data obtained in experiments with crossed ion beams of kiloelectronvolt energy. The fraction of metastable ions in the beams is estimated by comparing the experimental data with the weighted average theoretical results for the cross sections of reactions 1 and 2. From the data for the charge transfer cross sections, one can estimate particle losses in relativistic beams due to a change in the charge state of the ions colliding with each other in the beam because of betatron oscillations.     

Dissociative excitation of the odd quartet <Emphasis Type="Italic">S,P, D</Emphasis>, and <Emphasis Type="Italic">F</Emphasis> levels of the manganese atom in e-MnCl<Subscript>2</Subscript> collisions

The dissociative excitation of the ⁴ S°, ⁴ P°, ⁴ D°, and ⁴ F° levels of the manganese atom in collisions of slow electrons iwth manganese dichloride molecules is studied experimentally. It is found that the dissociative excitation cross sections for these levels are larger than the cross sections of direct excitation in the e-Mn collisions. The cross section ratios of the electron-atom and electron-molecule collisions, which characterize the effect of the chemical bond of the manganese atom with the halogen on the absolute excitation cross sections, are determined.     

Method for taking into account hard-photon emission in four-fermion processes

A method for taking into account hard-photon emission in four-fermion processes proceeding in the s channel is described. The application of this method is exemplified by numerically estimating one-loop electroweak corrections to observables (cross sections and asymmetries) of the reaction e^?e⁺ → μ^?μ⁺(γ) involving longitudinally polarized electrons and proceeding at energies below the Z-resonance energy.     

Dissociative Excitation of the Odd Sextet Levels of the Cobalt Atom by Collisions of Electrons with Cobalt Dichloride Molecules

Inelastic collisions of slow electrons with cobalt dichloride molecules, leading to the formation of excited cobalt atoms in odd sextet states, are experimentally studied. At an incident electron energy of 100 eV, thirty six dissociative excitation cross sections are measured for levels belonging to the z⁶D°, z⁶F°, and z⁶G° terms. In the electron energy range of 0–100 eV, ten optical excitation functions are recorded. The full cross sections for the dissociative excitation of the cobalt atom levels and the contribution of cascade transitions to their population are determined. The cross sections for electron–molecule and electron–atom collisions are compared.     

The 3–3–1 Model with RH Neutrinos and Associated ZH Production at High-Energy ${\bf \textit{e}}^{+}{\bf \textit{e}}^{-}$ Collider

In the context of SU(3) _C ?? SU(3) _L ?? U(1) _X (3–3–1) model with right-handed neutrinos, we study the Higgsstrahlung process e ^?+? e ^???→ZH and calculate the cross section of this process at leading order. Our numerical results showed that the production cross sections for this process can be significantly large as \(M_{Z'}\approx \sqrt{s}\). With reasonable values of the Z′ mass M _Z′, Z′ exchange can generate large corrections to the cross sections of this process, which might be detected in the future high-energy linear e ^?+? e ^??? collider experiments.     

Multiple exchanges in lepton pair production in high-energy heavy ion collisions

As an archetype reaction for pQCD multigluon hard processes in collisions of ultrarelativistic nuclei, we analyze generic features of lepton pair production via multiphoton processes in peripheral heavy ion scattering. We report explicit results for collisions of two photons from one nucleus with two photons from the other nucleus, 2γ + 2γ → l⁺l^?. The results suggest that the familiar eikonalization of Coulomb distortions breaks down for oppositely moving Coulomb centers. The breaking of eikonalization in QED suggests that multigluon pQCD processes cannot be described in terms of collective nuclear gluon distributions. We discuss a logarithmic enhancement of the contribution from the 2γ + 2γ → l⁺l^? process to production of lepton pairs with large transverse momentum; similar enhancement is absent for the nγ + mγ → l⁺l^? processes with m, n > 2. We comment on the general structure of multiphoton collisions and properties of higher-order terms that cannot be eikonalized.     

Double vector-charmonium production in electron-positron annihilation into two photons at $$\sqrt s = 10.6$$ GeV

In experimentally studying the exclusive production of two \(c\bar c\) mesons in electron-positron annihilation, the BELLE Collaboration obtained results that differ substantially from theoretical predictions. Recently, it was assumed that a significant part of this discrepancy can be explained by the process e⁺e^? → 2γ* → 2J/ψ, and its cross section was published. It is shown here that these results are incorrect (the cross sections are overestimated). The correct values of the cross sections for the double production of various vector charmonia are given.     

Proc ess es e+ e− → cccc and e+ e− → J/ψ + gg at $$\sqrt s = 10.59 G eV$$

Experimental data obtained by the BELLE Collaboration for inclusive J/ψ production in the processes e⁺e^? → J/ψ + gg and e⁺e^? → J/ψ + cc are discussed. These data are compared with the predictions of perturbative QCD that were obtained by two methods, that which employs information about the J/ψ wave function and that which relies on the hypothesis of quark-hadron duality exclusively. Both computational methods yield results that disagree with the experimental data considerably. The dependence of the cross section for the process e⁺e^? → J/ψ + gg on the effective gluon mass is studied. The cross section for the production of doubly charmed baryons Ξ _cc ^* is estimated.     

Calculation of the energy dependence of the fusion cross section and total cross sections for peripheral reactions on the basis of an analysis of data on elastic heavy-ion scattering: Strongly bound ions

A method is proposed for calculating the energy dependence of the fusion cross section (in general, the sum of the cross sections for complete and incomplete fusion, quasifission, and reactions of deep-inelastic scattering) σ _F (E) and the total cross section for peripheral (or quasielastic) reactions, σ _D (E). The method is based on an analysis of a limited set of angular distributions for the elastic scattering in a given pair of nuclei. The predictive power of the method is illustrated by considering the ¹⁶O + ²⁰⁸Pb, ¹⁶O + ⁴⁰Ca, and ¹⁶O + ²⁸Si systems. For each of these systems, the calculations were performed at energies in the range extending from subbarrier values to those exceeding the barrier height substantially. The results of the calculations are found to be in good agreement with relevant experimental data, whereby the reliability of the method is confirmed. By virtue of this, it is proposed to employ the method to study the energy dependences σ _F (E) and σ _D (E) in collisions involving unstable nuclei, for which it is difficult to determine experimentally the above dependences because of a low intensity of secondary beams.     

Subthreshold <Emphasis Type="Italic">K</Emphasis><Superscript>−</Superscript>-meson production in proton-nucleus reactions revisited

The inclusive K^?-meson production in proton-nucleus collisions in the subthreshold energy regime is studied in the framework of an appropriate spectral function approach for incoherent primary proton-nucleon and secondary pion-nucleon production processes, which takes properly into account the nuclear mean-field potential effects on these processes as well as the final state interaction (FSI) among the outgoing nucleons participating in the one-step antikaon creation process. A detailed comparison of the model calculations of the K^? differential cross sections is given for the reactions p + ⁹Be, p + ⁶³Cu, and p + ¹⁹⁷Au at subthreshold energies with the currently available experimental data obtained recently at the ITEP proton synchrotron and at SIS/GSI. It is found that the calculations with inclusion of the influence of both the nuclear density-dependent mean-field potentials and the elementary NN-FSI effects on the K^? production from direct mechanism are able to reproduce, contrary to previous estimates based on the use only of the density-dependent mean fields in calculating the K^? yield from this mechanism, the energy dependences of the invariant differential cross sections for “hard” antikaon creation in p⁹Be and p⁶³Cu collisions. It is further shown that the NN-FSI effects play a minor role in describing the data on the spectrum of relatively soft K^? mesons from p¹⁹⁷Au interactions at incident energy of 2.5 GeV. It is also shown that the relative strength of the proton-and pion-induced reaction channels in the subthreshold energy regime is governed by the kinematics of the experiment under consideration. The influence of the nucleon, kaon, and antikaon mean-field potentials on the K^? yield is explored. It is demonstrated that, in line with previous findings, the K^? optical potential has a strong effect on this yield at low antikaon momenta, which is greater than those from nucleon and kaon effective potentials. At high antikaon momenta, the K^? yield is found to be mainly determined, along with the elementary NN-FSI effects, by the nucleon mean field and the scenario with zero K⁺ potential is favorable.     

Integrated Cross Sections of High-Energy <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> Pair Electroproduction by an Electron in an Atomic Field

The integrated cross sections of e⁺e^– pair electroproduction by an ultrarelativistic electron in an atomic field are studied. The importance of various contributions to the integrated cross sections is discussed. The Coulomb corrections have turned out to make a large contribution to both differential and integrated cross sections even at moderate values of the nuclear charge number. The interaction of the electron emitting a virtual photon with the atomic field is shown to contribute significantly to the cross sections differential with respect to the electron transverse momentum. However, this interaction affects only slightly the cross section differential only with respect to the positron transverse momentum.     

VEPP-2000 project: Collider,detectors, and physics program

The new VEPP-2000 e⁺e^? collider of maximum energy 2000 MeV, which is under construction at the Budker Institute of Nuclear Physics (Siberian Division, Russian Academy of Sciences, Novosibirsk), is briefly described. Experiments at VEPP-2000 will be performed with two upgraded detectors, CMD-2M and SND. A precise measurement of the total cross section for the process e⁺e^? → hadrons and of the partial cross sections for its exclusive hadronic channels is the main point of the physics program for this machine. These measurements will be aimed at testing QCD and the VMD and CVC models, as well as at refining the hadron contribution to fundamental constants such as the muon anomalous magnetic moment \(a_\mu = \frac{{g - 2}}{2}\) and the fine-structure constant α_em(M _Z ² ). Measurements of the nucleon form factors in the reactions e⁺e^? → p\(\bar p\), n\(\bar n\) at their threshold will also be of great importance.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Energy scan of cross sections for <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> annihilation into quarkonia and light hadrons in the Belle experiment

The cross sections of the reactions e⁺e^– → ?(nS)π⁺π^? (n = 1, 2,3) and e⁺e^– → h _b (nP)π⁺π^? (n = 1, 2) are measured as a function of the cms collision energy from their thresholds up to 11.02 GeV using the data of the Belle experiment operating at the KEKB e⁺e^– collider. The peaks of the ?(10 860) and ?(11020) resonances are observed in the cross sections with an insignificant contribution of the continuum. The decay ?(11020) → h _b (nP)π⁺π^? is found to fully proceed through intermediate isovector states Z _b (10610) and Z _b (10650).     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Recent results on resolved photon processes

During the last 18 months, experiments at bothe ⁺ e ^? andep colliders have begun to test earlier predictions for processes that probe the hadronic structure of the photon. All the main qualitative predictions have already been verified; more detailed analyses are now starting to improve our quantitative understanding of photon structure functions. Some comments on minijets and total cross sections are also included.     

QCD and hybrid NBD on oscillating moments of multiplicity distributions in lepton-and hadron-initiated reactions

QCD predictions for moments of multiplicity distributions are compared with experimental data on e⁺e^? collisions and their two-NBD fits. Moments of the multiplicity distribution in a two-NBD model for 1.8-TeV pp collisions are considered. Three-NBD model predictions and fits for pp at LHC energies are also discussed. Analytic expressions for moments of hybrid NBD are derived and used to get insight into jet parameters and multicomponent structure of the processes. Interpretation of observed correlations is proposed.