Jet-shape observables

Studies of jet-shape observables in hard processes are summarized together with future developmentsComment: 4 pages, talk at ICHEP2004, Beijing, August 200

High energy gravitational scattering: a numerical study

The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.Comment: 11 pages, 6 figure

Soft gluons at large angles in hadron collisions

A general discussion is presented of the single logarithmic soft factor that appears in two scale QCD observables in processes involving four partons. We treat it as the ``fifth form factor'', accompanying the four collinear singular Sudakov form factors attached to colliding and outgoing hard partons. The fifth form factor is expressed in terms of the Casimir operators (squared colour charges) of irreducible representations in the crossing $t$- and $u$-channels. As an application we revisit the problem of large angle radiation in $gg\to gg$ and give a relatively simple solution and interpretation of the results. We found an unexpected symmetry of the soft anomalous dimension under exchange of internal and external variables of the problem whose existence calls for explanation.Comment: 29 pages, pictures generated with feynmf graphic packag

QCD coherence in the structure function and associated distributions at small xx

We recall the origin of angular ordering of soft parton emission in the region of small $x$ and show that this coherent structure can be detected in associated distributions. For structure functions at small $x$ and at fixed transverse momentum the angular ordering is masked because of the complete inclusive cancellations of collinear singularities for \xt0. Therefore, in this case the dependence on the hard scale is lost and the angular ordered region becomes equivalent to multi-Regge region in which all transverse momenta are of the same order. In this limit one derives the BFKL equation. In general such a complete cancellation does not hold for the associated distributions at small $x$. The calculation, which requires an analysis without any collinear approximation, is done by extending to small $x$ the soft gluon factorization techniques largely uses in the region of large $x$. Since one finds angular ordering in the both regions of small and large $x$, one can formulate a unified evolution equation for the structure function, a unified coherent branching and jet algorithm which allows the calculation of associated distributions in all $x$ regions. Such a unified formulation valid for all $x$ is presented and compared with usual treatments. In particular we show that the associated distributions at small $x$ are sensitive to coherence. By replacing angular ordering with the multi-Regge region one neglects large singular contributions in the associated distributions.Comment: LaTeX file of 27 page

On large angle multiple gluon radiation

Jet shape observables which involve measurements restricted to a part of phase space are sensitive to multiplication of soft gluon with large relative angles and give rise to specific single logarithmically enhanced (SL) terms (non-global logs). We consider associated distributions in two variables which combine measurement of a jet shape V in the whole phase space (global) and that of the transverse energy flow away from the jet direction, Eout (non-global). We show that associated distributions factorize into the global distribution in V and a factor that takes into account SL contributions from multi-gluon ``hedgehog'' configurations in all orders. The latter is the same that describes the single-variable Eout distribution, but evaluated at a rescaled energy VQ.Comment: 16 page