Particle theory

Abstract:

Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the conditions that the observable should satisfy for the approach to be valid, in particular continuous globalness and recursive infrared and collinear safety. The resulting resummation formula is expressed in terms of certain well-defined characteristics of the observable. We have written a computer program, CAESAR, which, given a subroutine for an arbitrary observable, determines those characteristics, enabling full automation of a large class of final-state resummations, in a range of processes. © SISSA 2005.

Abstract:

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N → ∞. We calculate the latent heat, Lh, in the continuum limit, and find the expected behaviour, Lh ∝ N², at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N ≥ 4 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T ≃ Tc confirming the discontinuous nature of the transition for N ≥ 3. We explicitly show that the large-N 'spatial' string tension does not vary with T for T ≤ Tc and that it is discontinuous at T = Tc. For T ≥ Tc it increases ∝ T² to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single T c at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between the ∝ N or ∝ N ² variations, each of which can lead to a striking but different N = ∞ deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed. © SISSA/ISAS 2005.

Abstract:

We review the work discussed and developed under the topic "Resummation" at Working Group 2 "Multijet final states and energy flow", of the HERA-LHC Workshop. We emphasise the role played by HERA observables in the development of resummation tools via, for instance, the discovery and resummation of non-global logarithms. We describe the event-shapes subsequently developed for hadron colliders and present resummed predictions for the same using the automated resummation program CAESAR. We also point to ongoing studies at HERA which can be of benefit for future measurements at hadron colliders such as the LHC, specifically dijet Et and angular spectra and the transverse momentum of the Breit current hemisphere.