Effects of threshold resummation

We investigate effects of threshold resummation of logarithmic corrections $\ln N$ in Mellin space quantitatively. Threshold resummation leads to enhancement of next-to-leading-order QCD predictions for jet production at large jet transverse energy, which is in the trend indicated by experimental data. We show that this enhancement is completely determined by the behavior of threshold resummation at small $N$, the region where hierachy among different powers of $\ln N$ is lost and current next-to-leading-logarithm resummation is not reliable. Our analysis indicates that more accurate threshold resummation formalism should be developed in order to obtain convincing predictions.Comment: 12 pages, 2 figure

A numerical formulation of resummation in effective field theory

In this article we show how the resummation of infrared and collinear logarithms within Soft-Collinear Effective Theory (SCET) can be formulated in a way that makes it suitable for a Monte-Carlo implementation. This is done by applying the techniques developed for automated resummation using the branching formalism, which have resulted in the general resummation approach CAESAR/ARES. This work builds a connection between the two resummation approaches, and paves the way to automated resummation in SCET. As a case study we consider the resummation of the thrust distribution in electron-positron collisions at next-to-leading logarithm (NLL). However, the results presented here are easily generalizable to more complicated observables and processes as well as to higher orders in the logarithmic accuracy.Comment: 47 page

Resummation

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 $E_t$ and angular spectra and the transverse momentum of the Breit current hemisphere.Comment: 15 pages, 6 figures. Submitted to the HERA-LHC workshop proceeding

Unification of the kTk_T and threshold resummations

We derive a resummation formula for a $k_T$-dependent parton distribution function at threshold, where $k_T$ is a parton transverse momentum. The derivation requires infrared cutoffs for both longitudinal and transverse loop momenta as evaluating soft gluon emissions in the Collins-Soper resummation framework. This unified resummation exhibits suppression at large $b$, $b$ being the conjugate variable of $k_T$, which is similar to the $k_T$ resummation, and exhibits enhancement at small $b$, similar to the threshold resummation.Comment: 13 pages in latex, 1 figure in postscrip

Sudakov Logarithm Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders

A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.Comment: 32 pages, Latex, epsfig, 17 figure

Vector boson production in joint resummation

We study the transverse momentum ($Q_T$) distribution of an electro-weak vector boson produced via the Drell-Yan mechanism, in the context of joint resummation. This formalism allows for the simultaneous resummation of logarithmic contributions that are enhanced at small $Q_T$ and at partonic threshold. We extend joint resummation to next-to-next-to leading logarithmic accuracy and we present resummed and matched results for three different phenomenological setups. In particular, we study the production of a $Z$ boson at the Tevatron and at the Large Hadron Collider (LHC), as well as the production of a heavier $Z^\prime$ at the LHC. We compare our findings to standard $Q_T$ resummation, as well as to fixed-order perturbation theory. We find that joint resummation provides a moderate (but not flat) correction with respect to $Q_T$ resummation and it leads to a reduction of the scale dependence of the results. However, our study also shows some limitations of this formalism. While the use of joint resummation for $Z$ production at the Tevatron and $Z^\prime$ production at the LHC appears to be justified, our implementation suffers from a stronger dependence on power corrections for processes which are further away from threshold, such as $Z$ production at the LHC, for which we cannot claim an improvement over standard $Q_T$ resummation.Comment: 28 pages, 10 figures, published versio

Renormalization of 2PI resummation: a renormalization scheme approach

A practical method is suggested for performing renormalized 2PI resummation at finite temperature using specific momentum dependent renormalization schemes. In this method there is no need to solve Bethe-Salpeter equations for 2PI resummation. We examine the consistency of such schemes in the paper. The proposed method is used to perform a two-loop renormalized 2PI resummation in the finite temperature Phi^4 model.Comment: 14 pages revtex, 8 figure

A new prescription for soft gluon resummation

We present a new prescription for the resummation of the divergent series of perturbative corrections, due to soft gluon emission, to hard processes near threshold in perturbative QCD (threshold resummation). This prescription is based on Borel resummation, and contrary to the commonly used minimal prescription, it does not introduce a dependence of resummed physical observables on the kinematically unaccessible x->0 region of parton distributions. We compare results for resummed deep-inelastic scattering obtained using the Borel prescription and the minimal prescription and exploit the comparison to discuss the ambiguities related to the resummation procedure.Comment: 15 pages, 3 figures. Final version, to be published in Phys. Lett. B. Several typos corrected (in particular eqs 26,41,53); fig. 3 adde

Renormalization and resummation in finite temperature field theories

Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of counterterms: one is a direct method where the necessary counterterms are constructed order by order; the other is a general one, based on renormalization group arguments. We demonstrate at one hand that, in mass independent schemes, mass resummation can be performed by gap equations renormalized prior to the substitution of the resummed mass for its argument. On the other hand it is shown that any (momentum-independent) form of mass and coupling constant resummation is compatible with renormalization, and one can explicitly construct the corresponding counterterms.Comment: 10 pages, 4 figures, revtex