Soft-gluon Resummation Research Articles

Resummation effects in vector-boson and Higgs associated production

Fixed-order QCD radiative corrections to the vector-boson and Higgs associated production channels, $pp\ensuremath{\rightarrow}VH$ ($V={W}^{\ifmmode\pm\else\textpm\fi{}}$, $Z$), at hadron colliders are well understood. We combine higher-order perturbative QCD calculations with soft gluon resummation of both threshold logarithms and logarithms which are important at a low transverse momentum of the $VH$ pair. We study the effects of both types of logarithms on the scale dependence of the total cross section and on various kinematic distributions. The next-to-next-to-next-to-leading logarithmic resummed total cross sections at the LHC are almost identical to the fixed-order perturbative next-to-next-to-leading order rates, indicating the excellent convergence of the perturbative QCD series. Resummation of the $VH$ transverse momentum (${p}_{T}$) spectrum provides reliable results for small values of ${p}_{T}$ and suggests that implementing a jet veto will significantly decrease the cross sections.

Percent-Level-Precision Physics at the Tevatron: Next-to-Next-to-Leading Order QCD Corrections toqq¯→tt¯+X

We compute the next-to-next-to-leading order QCD corrections to the partonic reaction that dominates top-pair production at the Tevatron. This is the first ever next-to-next-to-leading order calculation of an observable with more than two colored partons and/or massive fermions at hadron colliders. Augmenting our fixed order calculation with soft-gluon resummation through next-to-next-to-leading logarithmic accuracy, we observe that the predicted total inclusive cross section exhibits a very small perturbative uncertainty, estimated at ±2.7%. We expect that once all subdominant partonic reactions are accounted for, and work in this direction is ongoing, the perturbative theoretical uncertainty for this observable could drop below ±2%. Our calculation demonstrates the power of our computational approach and proves it can be successfully applied to all processes at hadron colliders for which high-precision analyses are needed.

Soft-gluon resummation for boosted top-quark production at hadron colliders

We investigate the production of highly energetic top-quark pairs at hadron colliders, focusing on the case where the invariant mass of the pair is much larger than the mass of the top quark. In particular, we set up a factorization formalism appropriate for describing the differential partonic cross section in the double soft and small-mass limit, and explain how to resum simultaneously logarithmic corrections arising from soft gluon emission and from the ratio of the pair-invariant mass to that of the top quark to next-to-next-to-leading logarithmic accuracy. We explore the implications of our results on approximate next-to-next-to-leading order formulas for the differential cross section in the soft limit, pointing out that they offer a simplified calculational procedure for determining the currently unknown delta-function terms in the limit of high invariant mass.

Soft-gluon resummation for slepton-pair production at hadron colliders

We use a recent approach to soft-gluon resummation based on effective field theory to implement soft-gluon resummation at NNNLL order for slepton-pair production in SUSY extensions of the Standard Model. This approach resums large logarithmic correc- tions arising from the dynamical enhancement of the partonic threshold region caused by steeply falling parton luminosities. We evaluate the resummed invariant-mass distribution and total cross section for slepton-pair production at the Tevatron and LHC, matching our results onto NLO fixed-order calculations. As a byproduct, we also study virtual SUSY effects in the context of soft-gluon resummation for the Drell-Yan process.

Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation

Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total tt¯ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin N-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to the NLL approximation, and a small shift in the central value, consistent with the quoted uncertainties. These numerical predictions agree with the currently available measurements from the Tevatron and LHC and have uncertainty of similar size. We conclude that significant improvements in the tt¯ cross-sections can potentially be expected only upon inclusion of the complete NNLO corrections.

QCD Resummation for Single Spin Asymmetries

We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme-independent coefficients are calculated up to one-loop order.

Top-pair forward-backward asymmetry beyond next-to-leading order

We make use of recent results in effective theory and higher-order perturbative calculations to improve the theoretical predictions of the QCD contribution to the top-quark pair production forward-backward asymmetry at the Tevatron. In particular, we supplement the fixed-order next-to-leading order calculation with higher-order corrections from soft-gluon resummation at next-to next-to-leading order accuracy performed in two different kinematic schemes, which allows us to make improved predictions for the asymmetry in the $p\overline{p}$ and $t\overline{t}$ rest frames as a function of the rapidity and invariant mass of the $t\overline{t}$ pair. Furthermore, we provide binned results which can be compared with the recent measurements of the forward-backward asymmetry in events with a large pair invariant mass or rapidity difference. Finally, we calculate at $\mathrm{NLO}+\mathrm{NNLL}$ order the top-quark charge asymmetry at the LHC as a function of a lower rapidity cutoff for the top and antitop quarks.

A model for probing large distance behaviour in high energy collisions

We apply to total cross-sections our model for soft gluon resummation in the infrared region. The model aims to probe large distance interactions in QCD. Our ansatz for an effective coupling for gluons and quarks in the infrared region follows an inverse power law which is singular but integrable. In the context of an eikonal formalism with QCD mini-jets, we study total hadronic cross-sections for protons, pions, photons. We estimate the total inelastic cross-section at LHC comparing with recent measurements and update previous results for survival probability.

Precision predictions for the [formula omitted] production cross section at hadron colliders

We make use of recent results in effective theory and higher-order perturbative calculations to improve the theoretical predictions of the top-quark pair production cross section at hadron colliders. In particular, we supplement the fixed-order NLO calculation with higher-order corrections from soft gluon resummation at NNLL accuracy. Uncertainties due to power corrections to the soft limit are estimated by combining results from single-particle inclusive and pair invariant-mass kinematics. We present our predictions as functions of the top-quark mass in both the pole scheme and the MS¯ scheme. We also discuss the merits of using threshold masses as an alternative, and calculate the cross section with the top-quark mass defined in the 1S scheme as an illustrative example.

Soft gluon resummation of Drell–Yan rapidity distributions: Theory and phenomenology

We examine critically the theoretical underpinnings and phenomenological implications of soft gluon (threshold) resummation of rapidity distributions at a hadron collider, taking Drell–Yan production at the Tevatron and the LHC as a reference test case. First, we show that in perturbative QCD soft gluon resummation is necessary whenever the partonic (rather the hadronic) center-of-mass energy is close enough to threshold, and we provide tools to assess when resummation is relevant for a given process. Then, we compare different prescriptions for handling the divergent nature of the series of resummed perturbative corrections, specifically the minimal and Borel prescriptions. We assess the intrinsic ambiguities of resummed results, both due to the asymptotic nature of their perturbative expansion, and to the treatment of subleading terms. Turning to phenomenology, we introduce a fast and accurate method for the implementation of resummation with the minimal and Borel prescriptions using an expansion on a basis of Chebyshev polynomials. We then present results for W and Z production as well as both high- and low-mass dilepton pairs at the LHC, and show that soft gluon resummation effects are generally comparable in size to NNLO corrections, but sometimes affected by substantial ambiguities.

Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.

Threshold resummation for pair production of coloured heavy (s)particles at hadron colliders

We derive a factorization formula for the production of pairs of heavy coloured particles in hadronic collisions near the production threshold that establishes factorization of soft and Coulomb effects. This forms the basis for a combined resummation of Coulomb and soft corrections, including the non-trivial interference of the two effects. We develop a resummation formalism valid at NNLL accuracy using the momentum-space approach to soft gluon resummation. We present numerical results for the NLL resummed squark–antisquark production cross section at the LHC and Tevatron, including also the contribution of squark–antisquark bound states below threshold. The total correction on top of the next-to-leading order approximation is found to be sizeable, and amounts to (4–20)% in the squark mass region 200 GeV–3 TeV at the 14 TeV LHC. The scale dependence of the total cross section is also reduced.

Two-loop soft anomalous dimensions for single top quark associated production with aW−orH−

I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a W boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for bg -> tW- and bg -> tH- at LHC energies of 7, 10, and 14 TeV.

Infrared Singularities and Soft Gluon Resummation with Massive Partons

Infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension matrix, which is also an essential ingredient for the resummation of large logarithms due to soft gluon emissions. We report a recent analytical calculation of the anomalous dimension matrix with both massless and massive partons at two-loop level, which describes the two-loop infrared singularities of any scattering amplitudes with an arbitrary number of massless and massive partons, and also enables soft gluon resummation at next-to-next-to-leading-logarithmic order. As an application, we calculate the infrared poles in the q qbar -> t tbar and gg -> t tbar scattering amplitudes at two-loop order.

Non-global logarithms and jet algorithms in high-p T jet shapes

We consider jet-shape observables of the type proposed recently, where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to-leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc limit and emphasising their properties. We also point out differences between jet algorithms in the context of soft gluon resummation for such observables.

QCD corrections to scalar diquark production at hadron colliders

We calculate the next-to-leading order QCD corrections to quark-quark annihilation to a scalar resonant state ("diquark") in a color representation of antitriplet or sextet at the Tevatron and LHC energies. At the LHC, we find the enhancement (K-factor) for the antitriplet diquark is typically about 1.31--1.35, and for the sextet diquark is about 1.22--1.32 for initial-state valence quarks. The full transverse-momentum spectrum for the diquarks is also calculated at the LHC by performing the soft gluon resummation to the leading logarithm and all orders in the strong coupling.

Soft-gluon resummation for squark and gluino hadroproduction

We consider the resummation of soft gluon emission for squark and gluino hadroproduction at next-to-leading-logarithmic (NLL) accuracy in the framework of the minimal supersymmetric standard model. We present analytical results for squark-squark and squark-gluino production and provide numerical predictions for all squark and gluino pair-production processes at the Tevatron and at the LHC. The size of the soft-gluon corrections and the reduction in the scale uncertainty are most significant for processes involving gluino production. At the LHC, where the sensitivity to squark and gluino masses ranges up to 3 TeV, the corrections due to NLL resummation over and above the NLO predictions can be as high as 35% in the case of gluino-pair production, whereas at the Tevatron, the NLL corrections are close to 40% for squark-gluino final states with sparticle masses around 500 GeV.

SCALE EVOLUTION OF UNINTEGRATED DISTRIBUTIONS AND THE Pt-SPECTRUM OF GAUGE BOSONS

We present predictions for the Z-boson pt-spectrum at Tevatron within the framework of unintegrated distributions evolved according to evolution equations recently proposed by us. We discuss the dependence of the results on the choice of non-perturbative parameters, the coupling constant and the impact of soft gluon resummation.

Soft gluon resummation for the production of gluino-gluino and squark-antisquark pairs at the LHC

We study the effect of soft gluon emission in the hadroproduction of gluino-gluino and squark-antisquark pairs at the next-to-leading logarithmic accuracy within the framework of the minimal supersymmetric model. We present the calculation of the one-loop soft anomalous dimension matrices controlling the color evolution of the underlying hard-scattering processes. The numerical results for resummed cross sections for proton-proton collisions at the Large Hadron Collider are discussed in detail.

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.