Symmetry of Anomalous Dimension Matrices for Colour Evolution of Hard Scattering Processes

In a recent paper, Dokshitzer and Marchesini rederived the anomalous dimension matrix for colour evolution of $gg \to gg$ scattering, first derived by Kidonakis, Oderda and Sterman. They noted a weird symmetry that it possesses under interchange of internal (colour group) and external (scattering angle) degrees of freedom and speculated that this may be related to an embedding into a context that correlates internal and external variables such as string theory. In this short note, I point out another symmetry possessed by all the colour evolution anomalous dimension matrices calculated to date. It is more prosaic, but equally unexpected, and may also point to the fact that colour evolution might be understood in some deeper theoretical framework. To my knowledge it has not been pointed out elsewhere, or anticipated by any of the authors calculating these matrices. It is simply that, in a suitably chosen colour basis, they are complex symmetric matrices.Comment: 3 page

Color evolution of 2 -> 3 processes

The color structure needed for resummation of all colored 2 -> 3 processes is calculated using multiplet inspired s-channel bases. In this way the resulting matrices, describing the color structure, are guaranteed to obey simplifying symmetries.Comment: 25 page

Symmetry of anomalous dimension matrices explained

In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it is only true in a subset of all possible orthonormal bases, but that this subset is the natural one to use for physical calculations.Comment: 4 page

Circular embeddings of planar graphs in nonspherical surfaces

AbstractWe show that every 3-connected planar graph has a circular embedding in some nonspherical surface. More generally, we characterize those planar graphs that have a 2-representative embedding in some nonspherical surface

Gaps between Jets in the High Energy Limit

We use perturbative QCD to calculate the parton level cross section for the production of two jets that are far apart in rapidity, subject to a limitation on the total transverse momentum Q0 in the interjet region. We specifically address the question of how to combine the approach which sums all leading logarithms in Q/Q0 (where Q is the jet transverse momentum) with the BFKL approach, in which leading logarithms of the scattering energy are summed. This paper constitutes progress towards the simultaneous summation of all important logarithms. Using an "all orders" matching, we are able to obtain results for the cross section which correctly reproduce the two approaches in the appropriate limits.Comment: 29 pages, 9 figures, minor corrections to text and improved figure

Color structure for soft gluon resummation - a general recipe

A strategy for calculating the color structure needed for soft gluon resummation for processes with any number of colored partons is introduced using a N_c --> infinity inspired basis. In this basis a general formalism can be found at the same time as the calculations are simplified. The advantages are illustrated by recalculating the soft anomalous dimension matrix for the processes gg --> gg, q\qbar --> q \qbar g and q\qbar --> ggg.Comment: 16 page

Soft gluons in Higgs plus two jet production

We investigate the effects of an all order QCD resummation of soft gluon emissions for Higgs boson production in association with two hard jets. We consider both the gluon-gluon fusion and weak boson fusion processes and show how to resum a large part of the leading logarithms in the jet veto scale. Our resummation improves on previous analyses which also aim to include the effects of multiple soft gluon radiation. In addition we calculate the interference between weak boson fusion and gluon-gluon fusion and find that it is small.Comment: 15 pages and 5 figure

The resummation of inter-jet energy flow for gaps-between-jets processes at HERA

We calculate resummed perturbative predictions for gaps-between-jets processes and compare to HERA data. Our calculation of this non-global observable needs to include the effects of primary gluon emission (global logarithms) and secondary gluon emission (non-global logarithms) to be correct at the leading logarithm (LL) level. We include primary emission by calculating anomalous dimension matrices for the geometry of the specific event definitions and estimate the effect of non-global logarithms in the large $N_c$ limit. The resulting predictions for energy flow observables are consistent with experimental data.Comment: 31 pages, 4 figures, 2 table

Jet vetoing at the LHC

We study the effect of a veto on additional jets in the rapidity region between a pair of high transverse momentum jets at the LHC. We aim to sum the most important logarithms in the ratio of the jet transverse momentum to the veto scale and to that end we attempt to assess the significance of the super-leading logarithms that appear at high orders in the perturbative expansion. We also compare our results to those of HERWIG++, in an attempt to ascertain the accuracy of the angular ordered parton shower. We find that there are large corrections that arise for large enough jet transverse momenta as a consequence of Coulomb gluon exchanges.Comment: 25 page

Towards Jetography

As the LHC prepares to start taking data, this review is intended to provide a QCD theorist's understanding and views on jet finding at hadron colliders, including recent developments. My hope is that it will serve both as a primer for the newcomer to jets and as a quick reference for those with some experience of the subject. It is devoted to the questions of how one defines jets, how jets relate to partons, and to the emerging subject of how best to use jets at the LHC.Comment: 95 pages, 28 figures, an extended version of lectures given at the CTEQ/MCNET school, Debrecen, Hungary, August 2008; v2 includes additional discussion in several places, as well as other clarifications and additional references