On the Resummation of Subleading Logarithms in the Transverse Momentum Distribution of Vector Bosons Produced at Hadron Colliders

The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading logarithms resummed in each case and the numerical differences in the cross sections which result.Comment: 13 (Latex) pages, including 5 embedded figures, uses epsfig.st

Dihedral symmetries of multiple logarithms

This paper finds relationships between multiple logarithms with a dihedral group action on the arguments. I generalize the combinatorics developed in Gangl, Goncharov and Levin's R-deco polygon representation of multiple logarithms to find these relations. By writing multiple logarithms as iterated integrals, my arguments are valid for iterated integrals as over an arbitrary field

Non-global logarithms in inter-jet energy flow with kt clustering requirement

Recent work in inter-jet energy flow has identified a class of leading logarithms previously not considered in the literature. These so-called non-global logarithms have been shown to have significant numerical impact on gaps-between-jets calculations at the energies of current particle colliders. Here we calculate, at fixed order and to all orders, the effect of applying clustering to the gluonic final state responsible for these logarithms for a trivial colour flow 2 jet system. Such a clustering algorithm has already been used for experimental measurements at HERA. We find that the impact of the non-global logarithms is reduced, but not removed, when clustering is demanded, a result which is of considerable interest for energy flow observable calculations.Comment: 13 pages, 4 figure

Threshold Resummation for Higgs Production in Effective Field Theory

We present an effective field theory to resum the large double logarithms originated from soft-gluon radiations at small final-state hadron invariant masses in Higgs and vector boson (\gamma^*, $W$ and $Z$) production at hadron colliders. The approach is conceptually simple, indepaendent of details of an effective field theory formulation, and valid to all orders in sub-leading logarithms. As an example, we show the result of summing the next-to-next-to-next leading logarithms is identical to that of standard pQCD factorization method.Comment: A version to appear in Phys. Rev.

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

On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections

We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell-Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved collinear evolution recently proposed by Dokshitzer, Marchesini and Salam (DMS). We compare our ansatz to existing exact results at two and three loops, finding evidence for the exponentiation of leading NE logarithms and confirming the predictivity of DMS evolution.Comment: 17 page