Arif I. Shoshi

S-matrix unitarity, impact parameter profiles, gluon saturation and high-energy scattering

Abstract A model combining perturbative and non-perturbative QCD is developed to compute high-energy reactions of hadrons and photons and to investigate saturation effects that manifest the S-matrix unitarity. Following a functional integral approach, the S-matrix factorizes into light-cone wave functions and the universal amplitude for the scattering of two color-dipoles which are represented by Wegner–Wilson loops. In the framework of the non-perturbative stochastic vacuum model of QCD supplemented by perturbative gluon exchange, the loop–loop correlation is calculated and related to lattice QCD investigations. With a universal energy dependence motivated by the two-pomeron (soft + hard) picture that respects the unitarity condition in impact parameter space, a unified description of pp, πp, Kp, γ ∗ p , and γγ reactions is achieved in good agreement with experimental data for cross sections, slope parameters, and structure functions. Impact parameter profiles for pp and γ ∗ L p reactions and the gluon distribution of the proton xG(x,Q 2 ,| b → ⊥ |) are calculated and found to saturate in accordance with S-matrix unitarity. The c.m. energies and Bjorken x at which saturation sets in are determined.

Confining QCD strings, Casimir scaling, and a Euclidean approach to high-energy scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaros analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.

Decomposition of the QCD string into dipoles and unintegrated gluon distributions

We present the perturbative and non-perturbative QCD structure of the dipole-dipole scattering amplitude in momentum space. The perturbative contribution is described by the two-gluon exchange and the non-perturbative contribution by the stochastic vacuum model which leads to confinement of the quark and antiquark in the dipole via a string of color fields. This QCD string gives important nonperturbative contributions to high-energy reactions. A new structure different from the perturbative dipole factors is found in the string-string scattering amplitude. The string can be represented as an integral over stringless dipoles with a given dipole number density. This decomposition of the QCD string into dipoles allows us to calculate the unintegrated gluon distribution of hadrons and photons from the dipole-hadron and dipole-photon cross section via

Saturation Effects in Hadronic Cross Sections

|{k}_{\ensuremath{\perp}}|

\(\mbox{Log}(1/x)\) gluon distribution and structure functionsin the loop-loop correlation model

factorization.

Anatomy of QCD Strings and Saturation Effects in High-Energy Scattering

The steep rise of the gluon distribution xG(x,Q 2) and structure function F 2(x, Q 2) of the proton towards small Bjorken x = Q 2/s is one of the most exciting observations at the HERA experiments [1]. The experimental results show a rise of the total γ*p cross section, \( \sigma \begin{array}{*{20}{c}} {tot} \\ {\gamma *p} \end{array}\left( {s,{Q^2}} \right), \) with increasing c.m. energy √s which becomes stronger with increasing photon virtuality Q 2.

Gluon saturation and S matrix unitarity

Abstract.We consider the interaction of the partonic fluctuation of a scalar “photon” with an external color field to calculate the leading and next-to-leading order gluon distribution of the proton following the work done by Dosch-Hebecker-Metz-Pirner. We relate these gluon distributions to the short and long distance behavior of the cross section of an adjoint dipole scattering off a proton. The leading order result is a constant, while the next-to-leading order result shows a

Fluctuation Effects on R_pA at High Energy

\ln(1/x)

On the behaviour of R

enhancement at small x. To get numerical results for the gluon distributions at the initial scale Q20 = 1.8 GeV2, we compute the adjoint dipole-proton cross section in the loop-loop correlation model. Quark distributions at the same initial scale are parameterized according to Regge theory. We evolve quark and gluon distributions to higher Q2 values using the DGLAP equation and compute charm and proton structure functions in the small-x region for different Q2 values.