Quantum Tunneling and Unitarity Features of an S-matrix for Gravitational Collapse

Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate the S-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < b_c, a critical value of the order of the gravitational radius R = 2 G sqrt(s), thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < b_c is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling G s / hbar itself. Some features of the resulting unitary model are discussed.Comment: 28 pages, 11 figure

qqˉq\bar q interaction in light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions

A rectangular Wilson loop with sides parallel to space and time directions is perturbatively evaluated in two light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions, with ``instantaneous'' and ``causal'' interactions between static quarks. In the instantaneous formulation we get Abelian-like exponentiation of the area in terms of $C_F$. In the ``causal'' formulation the loop depends not only on the area, but also on the dimensionless ratio $\beta = {L \over T}$, $2L$ and $2T$ being the lengths of the rectangular sides. Besides it also exhibits dependence on $C_A$. In the limit $T \to \infty$ the area law is recovered, but dependence on $C_A$ survives. Consequences of these results are pointed out.Comment: 30 pages, latex, one figure included as a ps file, an Erratum include

A collinear model for small-x physics

We propose a simple model for studying small-x physics in which we take only the collinearly enhanced part of leading and subleading kernels, for all possible transverse momentum orderings. The small-x equation reduces to a second order differential equation in t=log k^2/Lambda^2 space, whose perturbative and strong-coupling features are investigated both analytically and numerically. For two-scale processes, we clarify the transition mechanism between the perturbative, non Regge regime and the strong-coupling Pomeron behavior.Comment: 22 pages, 8 figures, LaTeX file, uses JHEP.cl

The NLO Jet Vertex for Mueller-Navelet and Forward Jets: the Quark Part

We calculate the next-to-leading corrections to the jet vertex which is relevant for the Mueller-Navelet-jets production in p-pbar collisions and for the forward jet cross section in e-p collisions. In this first part we present the results of the vertex for an incoming quark. Particular emphasis is given to the separation of the collinear divergent part and the central region of the produced gluon.Comment: 28 pages, 8 eps figure

First complete NLL BFKL calculation of Mueller Navelet jets at LHC

For the first time, a next-to-leading BFKL study of the cross section and azimuthal decorrellation of Mueller Navelet jets is performed, i.e. including next-to-leading corrections to the Green's function as well as next-to-leading corrections to the Mueller Navelet vertices. The obtained results for standard observables proposed for studies of Mueller Navelet jets show that both sources of corrections are of equal and big importance for final magnitude and final behavior of observables, in particular for the LHC kinematics investigated here in detail. The astonishing conclusion of our analysis is that the observables obtained within the complete next-lo-leading order BFKL framework of the present paper are quite similar to the same observables obtained within next-to-leading logarithm DGLAP type treatment. The only noticeable difference is the ratio the azimuthal angular moments / which still differs in both treatments.Comment: 5 pages, 1 figure, to appear in the proceedings of 35th International Conference on High Energy Physics, (ICHEP 2010), Paris, France, July 22-28, 201

A complete NLL BFKL calculation of Mueller Navelet jets at LHC

For the first time, a next-to-leading BFKL study of the cross section and azimuthal decorrellation of Mueller Navelet jets is performed, i.e. including next-to-leading corrections to the Green's function as well as next-to-leading corrections to the Mueller Navelet vertices. The obtained results for standard observables proposed for studies of Mueller Navelet jets show that both sources of corrections are of equal and big importance for final magnitude and final behavior of observables, in particular for the LHC kinematics investigated here in detail. The astonishing conclusion of our analysis is that the observables obtained within the complete next-lo-leading order BFKL framework of the present paper are quite similar to the same observables obtained within next-to-leading logarithm DGLAP type treatment. This fact sheds doubts on general belief that the studies of Mueller Navelet jets at the LHC will lead to clear discrimination between the BFKL and the DGLAP dynamics.Comment: 5 pages, 2 figures, to appear in the proceedings of 18th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2010), Florence, Italy, 19-23 Apr 201

The NLO Jet Vertex for Mueller-Navelet and Forward Jets: the Gluon Part

In this paper we complete our calculation of the NLO jet vertex which is part of the cross section formulae for the production of Mueller Navelet jets at hadron hadron colliders and of forward jets in deep inelastic electron proton scattering.Comment: 16 pages, latex, epj style, 6 eps figure

The BFKL Equation at Next-to-Leading Order and Beyond

On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue that in this formulation the collinear properties of the kernel are taken into account to all orders, and that the ensuing next-to-leading truncation provides a much more stable estimate of hard Pomeron and of resummed anomalous dimensions.Comment: LaTex, 12 pages, 1 eps figur