Vacuum polarization radiative correction to the parity violating electron scattering on heavy nuclei

The effect of vacuum polarization on the parity violating asymmetry in the elastic electron-nucleus scattering is considered. Calculations are performed in the high-energy approximation with an exact account for the electric field of the nucleus. It is shown that the radiative correction to the parity violating asymmetry is logarithmically enhanced and the value of the correction is about -1%.Comment: 6 pages, 3 figures, REVTex

Bremsstrahlung and pair production processes at low energies, multi-differential cross section and polarization phenomena

Radiative electron-proton scattering is studied in peripheral kinematics, where the scattered electron and photon move close to the direction of the initial electron. Even in the case of unpolarized initial electron the photon may have a definite polarization. The differential cross sections with longitudinally or transversal polarized initial electron are calculated. The same phenomena are considered for the production of an electron-positron pair by the photon, where the final positron (electron) can be also polarized. Differential distributions for the case of polarized initial photon are given. Both cases of unscreened and completely screened atomic targets are considered.Comment: 15 pages, 6 figure

Charge-odd correlation of lepton and pion pair production in electron-proton scattering

Charge-odd correlation of the charged pair components produced at electron-proton scattering can measure three current correlation averaged by proton state. In general these type correlation can be described by 14 structure functions. We restrict here by consideration of inclusive distributions of a pair components, which is the light-cone projection of the relevant hadronic tensor. Besides we consider the point-like approximation for proton and pion. Numerical estimations show that charge-odd effects can be measured in exclusive ep -> 2 pi X experiments.Comment: 10 pages, 4 figure

Soft gluon radiation and energy dependence of total hadronic cross-sections

An impact parameter representation for soft gluon radiation is applied to obtain both the initial decrease of the total cross-section ($\sigma_{tot}$) for proton-proton collisions as well as the later rise of $\sigma_{tot}$ with energy for both $pp$ and $p\bar{p}$. The non-perturbative soft part of the eikonal includes only limited low energy gluon emission and leads to the initial decrease in the proton-proton cross- section. On the other hand, the rapid rise in the hard, perturbative jet part of the eikonal is tamed into the experimentally observed mild increase by soft gluon radiation whose maximum energy rises slowly with energy.Comment: 30 pages, 6 figures. Version accepted for publication in Physical Review D. Additional section with explanatory material added making the paper more self contained and two figures changed to have a complete summary of the available accelerator dat

Two-Loop Sudakov Form Factor in a Theory with Mass Gap

The two-loop Sudakov form factor is computed in a U(1) model with a massive gauge boson and a $U(1)\times U(1)$ model with mass gap. We analyze the result in the context of hard and infrared evolution equations and establish a matching procedure which relates the theories with and without mass gap setting the stage for the complete calculation of the dominant two-loop corrections to electroweak processes at high energy.Comment: Latex, 5 pages, 2 figures. Bernd Feucht is Bernd Jantzen in later publications. (The contents of the paper is unchanged.

On a problem of Erd\H{o}s and Rothschild on edges in triangles

Erd\H{o}s and Rothschild asked to estimate the maximum number, denoted by H(N,C), such that every N-vertex graph with at least CN^2 edges, each of which is contained in at least one triangle, must contain an edge that is in at least H(N,C) triangles. In particular, Erd\H{o}s asked in 1987 to determine whether for every C>0 there is \epsilon >0 such that H(N,C) > N^\epsilon, for all sufficiently large N. We prove that H(N,C) = N^{O(1/log log N)} for every fixed C < 1/4. This gives a negative answer to the question of Erd\H{o}s, and is best possible in terms of the range for C, as it is known that every N-vertex graph with more than (N^2)/4 edges contains an edge that is in at least N/6 triangles.Comment: 8 page

A model of a transition neutral pion formfactor measured in annihilation and scattering channels

We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and annihilation channels are considered including the relevant experiments with lepton-proton scattering.Comment: 5 pages, 4 figur

Resummation of double logarithms in electroweak high energy processes

At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes.Comment: 26 pages, 3 figures, Latex2

Off-shell scattering amplitudes in the double-logarithmic approximation

When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and the ElectroWeak Standard Model. The off-shell amplitudes are considered in the hard and the Regge kinematic limits. We compare our results in both the Feynman and Coulomb gauges.Comment: 15 pages, 3 figures; RevTeX

Thermodynamic Geometric Stability of Quarkonia states

We compute exact thermodynamic geometric properties of the non-abelian quarkonium bound states from the consideration of one-loop strong coupling. From the general statistical principle, the intrinsic geometric nature of strongly coupled QCD is analyzed for the Columbic, rising and Regge rotating regimes. Without any approximation, we have obtained the non-linear mass effect for the Bloch-Nordsieck rotating strongly coupled quarkonia. For a range of physical parameters, we show in each cases that there exists a well-defined, non-degenerate, curved, intrinsic Riemannian manifold. As the gluons become softer and softer, we find in the limit of the Bloch-Nordsieck resummation that the strong coupling obtained from the Sudhakov form factor possesses exact local and global thermodynamic properties of the underlying mesons, kaons and $D_s$ particles.Comment: 45 pages, 17 figures, Keywords: Thermodynamic Geometry, Quarkonia, Massive Quarks, QCD Form Factor. PACS: 02.40.-k; 14.40.Pq; 12.40.Nn; 14.70.D