Rescattering corrections and self-consistent metric in Planckian scattering

Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles' motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles' shock-waves undergo calculable trajectory shifts and time delays during the scattering process --- which turns out to be consistently described by both action and metric, up to relative order $R^2/b^2$ in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutions --- not fully investigated here --- are also presented.Comment: 39 pages, 14 figure

The NLO jet vertex in the small-cone approximation for kt and cone algorithms

We determine the jet vertex for Mueller-Navelet jets and forward jets in the small-cone approximation for two particular choices of jet algoritms: the kt algorithm and the cone algorithm. These choices are motivated by the extensive use of such algorithms in the phenomenology of jets. The differences with the original calculations of the small-cone jet vertex by Ivanov and Papa, which is found to be equivalent to a formerly algorithm proposed by Furman, are shown at both analytic and numerical level, and turn out to be sizeable. A detailed numerical study of the error introduced by the small-cone approximation is also presented, for various observables of phenomenological interest. For values of the jet "radius" R=0.5, the use of the small-cone approximation amounts to an error of about 5% at the level of cross section, while it reduces to less than 2% for ratios of distributions such as those involved in the measure of the azimuthal decorrelation of dijets.Comment: 22 pages, 7 figures, 13 eps file

Emerging Hawking-like Radiation from Gravitational Bremsstrahlung Beyond the Planck Scale

We argue that, as a consequence of the graviton's spin-2, its bremsstrahlung in trans-planckian-energy ($E\gg M_P$) gravitational scattering at small deflection angle can be nicely expressed in terms of helicity-transformation phases and their transfer within the scattering process. The resulting spectrum exhibits deeply sub-planckian characteristic energies of order $M_P^2/E \ll M_P$ (reminiscent of Hawking radiation), a suppressed fragmentation region, and a reduced rapidity plateau, in broad agreement with recent classical estimates.Comment: 5 pages, 3 figures. Comments and references added. Typos corrected. Fig. 3 modified. Title modified. Same as published articl

On factorisation at small x

We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a collinear model which includes higher twist terms. Unlike the simplest collinear model, the BFKL equation leads to effective anomalous dimensions containing higher-twist pieces which grow as a (non-perturbative) power at small x. While these pieces dominate the effective splitting function at very small x they do not lead to a break-down of factorisation insofar as their effect on the predicted scaling violations remains strongly suppressed.Comment: 17 pages, LaTeX. Updated version corrects some small misprints and adds extra preprint number

Unified limiting form of graviton radiation at extreme energies

We derive the limiting form of graviton radiation in gravitational scattering at transplanckian energies ($E\gg M_P$) and small deflection angles. We show that --- owing to the graviton's spin 2 --- such limiting form unifies the soft- and Regge- regimes of emission, by covering a broad angular range, from forward fragmentation to deeply central region. The single-exchange emission amplitudes have a nice expression in terms of the transformation phases of helicity amplitudes under rotations. As a result, the multiple-exchange emission amplitudes can be resummed via an impact parameter $b$-space factorization theorem that takes into account all coherence effects. We then see the emergence of an energy spectrum of the emitted radiation which, being tuned on $\hbar/R \sim M_P^2/E \ll M_P$, is reminiscent of Hawking's radiation. Such a spectrum is much softer than the one na\"ively expected for increasing input energies and neatly solves a potential energy crisis. Furthermore, by including rescattering corrections in the (quantum) factorization formula, we are able to recover the classical limit and to find the corresponding quantum corrections. Perspectives for the extrapolation of such limiting radiation towards the classical collapse regime (where $b$ is of the order of the gravitational radius $R$) are also discussed.Comment: 45 pages, 15 figures, new result, some corrections and additional comment