Large logarithms that arise in cross sections due to the collinear and soft singularities of QCD are traditionally treated using parton showers or analytic resummation. Parton showers provide a fully-differential description of an event but are challenging to extend beyond leading logarithmic accuracy. On the other hand, resummation calculations can achieve higher logarithmic accuracy but often for only a single observable. Recently, there have been many resummation calculations that jointly resum multiple logarithms. Here we investigate the benefits and limitations of joint resummation in a case study, focussing on the family of $e^+e^-$ event shapes called angularities. We calculate the cross section differential in n angularities at next-to-leading logarithmic accuracy. We investigate whether reweighing a flat phase-space generator to this resummed prediction, or the corresponding distributions from Herwig and Pythia, leads to improved predictions for other angularities. We find an order of magnitude improvement for n = 2 over n = 1, highlighting the benefit of joint resummation, but diminishing returns for larger values of n.
We study the application of the joint resummation to electroweak boson production at hadron colliders. The joint resummation formalism resums both threshold and transverse momentum corrections to the transverse momentum distribution at next-to-leading logarithmic accuracy. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.
We study the application of the joint resummation formalism to Higgs production via gluon-gluon fusion at the LHC, defining inverse transforms by analytic continuation. We work at next-to-leading logarithmic accuracy. We find that at low Q_T the resummed Higgs Q_T distributions are comparable in the joint and pure-Q_T formalisms, with relatively small influence from threshold enhancement in this range. We find a modest (about ten percent) decrease in the inclusive cross section, relative to pure threshold resummation.
We present joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We study the dependence of these distributions on the production channel, the color configurations and the differences with the pure threshold-resummed distribution.
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 produ…
The QCD predictions for single-inclusive jet production are computed with joint resummation of threshold and jet radius logarithms. The results are compared to those based on fixed order perturbation theory up to next-to-next-to-leading order and to data by the CMS collaboration measured in proton-proton collisions at the LHC at $\sqrt{S}=8$ TeV. The joint resummation results are in remarkable agreement with the data.
We present the joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We exhibit their dependence on the production channel and the color configurations, and compare these distributions to eachother and to NLO.
We present precision calculations of the transverse-momentum spectrum and the invariant-mass distribution for slepton pair production at hadron colliders. We implement the transverse-momentum, threshold and joint resummation formalisms at the next-to-leading logarithmic accuracy and consistently match the obtained result with the pure perturbative result at the first order in the strong coupling constant, i.e. at order alpha_s. We give numerical predictions for selectron and stau pair production, and compare the various resummed cross sections with the perturbative result.
We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we …
To describe the transverse momentum spectrum of heavy color-singlet production, the joint resummation of threshold and transverse momentum logarithms is investigated. We obtain factorization theorems for various kinematic regimes valid to all orders in the strong coupling, using Soft-Collinear Effective Theory. We discuss how these enable resummation and how to combine regimes. The new ingredients in the factorization theorems are calculated at next-to-leading order, and a range of consistency checks is performed. Our framework goes beyond the current next-to-leading logarithmic accuracy (NLL)…
We consider Drell-Yan production $pp \to Z/γ^* \to \ell^+\ell^-$ with the simultaneous measurement of the $Z$-boson transverse momentum $q_T$ and $0$-jettiness $\mathcal{T}_0$. Since both observables resolve the initial-state QCD radiation, the double-differential cross section in $q_T$ and $\mathcal{T}_0$ contains Sudakov double logarithms of both $q_T/Q$ and $\mathcal{T}_0/Q$, where $Q \sim m_Z$ is the dilepton invariant mass. We simultaneously resum the logarithms in $q_T$ and $\mathcal{T}_0$ to next-to-next-to-leading logarithmic order (NNLL) matched to next-to-leading fixed order (NLO). O…
We calculate direct gaugino pair production at hadron colliders at next-to-leading order of perturbative QCD, resumming simultaneously large logarithms in the small transverse-momentum and threshold regions to next-to-leading logarithmic accuracy. Numerical predictions are presented for transverse momentum and invariant mass spectra as well as for total cross sections and compared to results obtained at fixed order and with pure transverse-momentum and threshold resummation. We find that our new results are in general in good agreement with the previous ones, but often even more precise.
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for the process pp->gamma X at high transverse momentum of the photon.These corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We especially focus on the resummation effects for the contribution to the cross section where the photon is produced in jet fragmentation. Previous calculations in perturbation theory at fixed-order have established that this contribution is a subdominant part of the cross section. We find, however, tha…
We perform a detailed study of inclusive jet production cross sections at the LHC and compare the QCD theory predictions based on the recently developed formalism for threshold and jet radius joint resummation at next-to-leading logarithmic accuracy to inclusive jet data collected by the CMS collaboration at $\sqrt{S} = 7$ and $13$TeV. We compute the cross sections at next-to-leading order in QCD with and without the joint resummation for different choices of jet radii $R$ and observe that the joint resummation leads to crucial improvements in the description of the data. Comprehensive studies…
We present a precision calculation of the transverse-momentum and invariant-mass distributions for supersymmetric particle pair production at hadron colliders, focusing on Drell-Yan like slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement the joint resummation formalism at the next-to-leading logarithmic accuracy with a process-independent Sudakov form factor, thus ensuring a universal description of soft-gluon emission, and consistently match the obtained result with the pure perturbative result at the first order in the strong coupling con…
We apply QCD resummation techniques to study the transverse momentum distribution of Higgs bosons produced via gluon-gluon fusion at the LHC. In particular we focus on the joint resummation formalism which resums both threshold and transverse momentum corrections simultaneously. A comparison of results obtained in the joint and the standard recoil resummation frameworks is presented.
We construct an evolution equation for the pion wave function in the $k_T$ factorization theorem, whose solution sums the mixed logarithm $\ln x\ln k_T$ to all orders, with $x$ ($k_T$) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion wave function in the small $x$ and large $b$ regions, $b$ being the impact parameter conjugate to $k_T$, and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm $\ln^2…
We present the first threshold and jet radius jointly resummed cross section for single-inclusive hadronic jet production. We work at next-to-leading logarithmic accuracy and our framework allows for a systematic extension beyond the currently achieved precision. Longstanding numerical issues are overcome by performing the resummation directly in momentum space within Soft Collinear Effective Theory. We present the first numerical results for the LHC and observe an improved description of the available data. Our results are of immediate relevance for LHC precision phenomenology including the e…
We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled $β$ functions of two (or more) coupling constants $α_a$ and $α_b$, as well as anomalous dimensions that have joint perturbative series in $α_a$ and $α_b$. We discuss possible strategies for solving the system of evolution equations that arises. As an example, we obtain the complete three-loop (NNLL) QCD$\otimes$QED Sudakov evolution factor. Our results also readily apply to the joint higher-order resummation of el…
We improve the theoretical predictions for the production of extra neutral gauge bosons at hadron colliders by implementing the Z' bosons in the MC@NLO generator and by computing their differential and total cross sections in joint p_T and threshold resummation. The two improved predictions are found to be in excellent agreement with each other for mass spectra, p_T spectra, and total cross sections, while the PYTHIA parton and ``power'' shower predictions usually employed for experimental analyses show significant shortcomings both in normalization and shape. The theoretical uncertainties fro…
We consider the associated production of a vector or Higgs boson with a jet in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet system is much smaller than its invariant mass $Q$, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all orders. We discuss the all-order resummation structure of the logarithmically enhanced contributions up to next-to-leading logarithmic accuracy. Resummation is performed at the differential level with respect to the kinematical variables of the boson-jet system. Soft-parton radiation produces azi…
We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in $e^+e^-$ collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effec…
We numerically analyse the evolution of the flavor non-singlet $g_{1}$ structure function taking into account the all-order resummation of $α_{s} ln^{2}x$ terms which is expected to have much stronger effects than the DGLAP evolution in the small x region. We include a part of the next-to-leading logarithmic corrections coming from the resummed ``coefficient function'' which are not considered in the calculation of Blümlein and Vogt to respect the factorization scheme independence. It is pointed out that the resummed coefficient function gives unexpectedly large suppression factor over the exp…
We study a class of nonperturbative corrections to single-inclusive photon cross sections at measured transverse momentum p_T, in the large-x_T limit. We develop an extension of the joint (threshold and transverse momentum) resummation formalism, appropriate for large x_T, in which there are no kinematic singularities associated with recoil, and for which matching to fixed order and to threshold resummation at next-to-leading logarithm (NLL) is straightforward. Beyond NLL, we find contributions that can be attributed to recoil from initial state radiation. Associated power corrections occur as…
We present state of the art resummation predictions for differential cross sections in top-quark pair production at the LHC. They are derived from a formalism which allows the simultaneous resummation of both soft and small-mass logarithms, which endanger the convergence of fixed-order perturbative series in the boosted regime, where the partonic center-of-mass energy is much larger than the mass to the top quark. We combine such a double resummation at NNLL$'$ accuracy with standard soft-gluon resummation at NNLL accuracy and with NLO calculations, so that our results are applicable throughou…
Multivariate analyses are emerging as important tools to understand properties of hadronic jets which play a key role in the LHC experimental program. We take a first step towards precise and differential theory predictions by calculating the cross section for $e^+ e^- \to$ 2 jets differential in the angularities $e_α$ and $e_β$. The logarithms of $e_α$ and $e_β$ in the cross section are jointly resummed to next-to-next-to-leading logarithmic accuracy, using the SCET+ framework we developed, and are matched to the next-to-leading order cross section. We perform analytic one-loop calculations t…
Double logarithms resummation has been much studied in inclusive as well as exclusive processes. The Sudakov mechanism has often be the crucial tool to exponentiate potentially large contributions to amplitudes or cross-sections near phase-space boundaries. We report on a recent work where a very different pattern emerges : the DVCS quark coefficient function C(x,ξ) develops, near the particular point x=ξ, a non-alternate series in α_s^n log^{2n}(x-ξ) which may be resummed in a cosh[K sqrt α_s log(x-ξ)] factor. This result is at odds with the known result for the corresponding coefficient func…
The jet shape is a simple measure of how widely a jet's energy is spread. At present jet shape distributions have only been calculated to leading order in perturbative QCD. In this paper we consider how much these predictions should be affected by higher order perturbative corrections, by resummation of enhanced corrections to all orders, and by (power-suppressed) non-perturbative corrections. We also show that current cone-type jet definitions are not infrared safe for final states with more than three partons. Unless this situation is rectified by using improved definitions, hadron collider …
We first review the general framework which enables one to resum high-energy logarithms in hadronic processes, both in the evolution of parton densities and in the coefficient functions. We then present an all-order calculation in perturbative QCD of the inclusive Drell Yan and vector boson production in hadron-hadron collisions, in the limit where centre of mass energy is much bigger than the invariant mass of the final state. Our calculation resums leading non-trivial logarithms in the ratio of these two scales. We also study the phenomenological relevance of the high-energy corrections for …
We present the combination of fully differential cross sections for colour-singlet production processes at next-to-next-to-leading order (NNLO) QCD obtained with MATRIX and all-order resummation through RadISH. This interface allows us to achieve unprecedented accuracy for various transverse observables in $2 \rightarrow 2$ production processes. As an important application we consider $W^+ W^-$ production at the LHC, more precisely the full leptonic process $pp\to \ell^+\ell^{\prime\, -}ν_{\ell}{\barν}_{\ell^\prime}+X$ with $\ell'\neq\ell$, and we present resummed predictions for differential …
We consider the production of a pair of heavy quarks ($Q{\bar Q}$) in hadronic collisions. When the transverse momentum $q_T$ of the heavy-quark pair is much smaller than its invariant mass, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all-orders. This behavior is well known from the simpler case of hadroproduction of colourless high-mass systems, such as vector or Higgs boson(s). In the case of $Q{\bar Q}$ production, the final-state heavy quarks carry colour charge and are responsible for additional soft radiation (through direct emission and…
We construct an evolution equation for the $B$ meson wave functions in the $k_T$ factorization theorem, whose solutions sum the double logarithms associated with the light-cone singularities, namely, the rapidity logarithms. The derivation is subtler than that of the Sudakov resummation for an energetic light hadron, due to the involvement of the effective heavy-quark field. The renormalization-group evolution in the factorization scale needs to be included in order to derive an ultraviolet-finite and scale-invariant kernel for resumming the rapidity logarithms. It is observed that this kernel…
We discuss different resummations of large logarithms that arise in hard-scattering cross sections of quarks and gluons in regions of large and small x. The large-x logarithms are typically dominant near threshold for the production of a specified final state. These soft and collinear gluon corrections produce large enhancements of the cross section for many processes, notably top quark and Higgs production, and typically the higher-order corrections reduce the factorization and renormalization scale dependence of the cross section. The small-x logarithms are dominant in the regime where the m…
We consider the $HZ$ associated production at the $14~{\rm TeV}$ LHC in the littlest Higgs model (LHM) and study the corrections of the transverse momentum resummation and threshold resummation at the next-to-leading logarithmic (NLL) accuracy and the fixed-order prediction at the QCD next-to-leading order (NLO) including the contribution from the one-loop-induced $gg$-fusion channel. The QCD NLO+NLL effects on the integrated cross section and the distributions of transverse momentum and invariant mass of the $HZ$ system for the $HZ$ production in the LHM are discussed. The distributions of tr…
Clustering logs have been the subject of much study in recent literature. They are a class of large logs which arise for non-global jet-shape observables where final-state particles are clustered by a non-cone--like jet algorithm. Their resummation to all orders is highly non--trivial due to the non-trivial role of clustering amongst soft gluons which results in the phase-space being non-factorisable. This may therefore significantly impact the accuracy of analytical estimations of many of such observables. Nonetheless, in this paper we address this very issue for jet shapes defined using the …
Gluon-induced processes such as Higgs production typically exhibit large perturbative corrections. These partially arise from large virtual corrections to the gluon form factor, which at timelike momentum transfer contains Sudakov logarithms evaluated at negative arguments $\ln^2(-1) = -π^2$. It has been observed that resumming these terms in the timelike form factor leads to a much improved perturbative convergence for the total cross section. We discuss how to consistently incorporate the resummed form factor into the perturbative predictions for generic cross sections differential in the Bo…
An unresolved problem in J/psi phenomenology is a systematic understanding of the differential photoproduction cross section, dsigma/dz [gamma + p -> J/psi + X], where z= E_psi/E_gamma in the proton rest frame. In the non-relativistic QCD (NRQCD) factorization formalism, fixed-order perturbative calculations of color-octet mechanisms suffer from large perturbative and nonperturbative corrections that grow rapidly in the endpoint region, z -> 1. In this paper, NRQCD and soft collinear effective theory are combined to resum these large corrections to the color-octet photoproduction cross section…
Partonic cross sections for the production of massive objects in hadronic collisions receive large corrections when the invariant mass of the initial-state partons is just above the production threshold. Since typically the center-of-mass energy of the hadronic collision is much higher than the mass of the heavy objects, it is not obvious that these contributions translate into large corrections to the hadronic cross section. Using a recent approach to threshold resummation based on effective field theory, we quantify to which extent the fall-off of the parton densities at high x leads to a dy…
Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called non-global logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. This effect was discovered a long time ago, but not much is known about the higher-order behavior of these terms and their process dependence. We derive, for the first time, t…
We present predictions of the total cross sections for pair production of squarks and gluinos at the LHC, including the stop-antistop production process. Our calculation supplements full fixed-order NLO predictions with resummation of threshold logarithms and Coulomb singularities at next-to-leading logarithmic (NLL) accuracy, including bound-state effects. The numerical effect of higher-order Coulomb terms can be as big or larger than that of soft-gluon corrections. For a selection of benchmark points accessible with data from the 2010-2012 LHC runs, resummation leads to an enhancement of the…
Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approa…
We reexamine the top quark production cross section at the Tevatron and LHC, in the light of recent progress on the resummation of logarithmic soft gluon corrections. We find that resummation effects are much smaller than previously thought. We also compute Coulombic threshold effects, and find them negligible. We update the discussion of uncertainties due to scale dependence, the value of the strong coupling constant, and the parton density parametrization. Our current best estimate of the top production cross section at the Tevatron and its error is $σ(\mt=175\,{\rm GeV})=4.75{+0.73\atop-0.6…
We present accurate predictions for the inclusive production of a Higgs boson in proton-proton collisions, via gluon-gluon fusion. Our calculation includes next-to-next-to-leading order (NNLO) corrections in perturbative QCD, as well as the resummation of threshold-enhanced contributions to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy, with the inclusion of the recently-determined three-loop constant coefficient (sometimes referred to as N$^3$LL' accuracy). Our result correctly accounts for finite top, bottom and charm masses at leading order (LO) and next-to-leading order (N…
We extend next-to-leading logarithmic threshold and joint resummation for prompt photon production to include leading collinear effects. The impact of these effects is assessed for both fixed-target and collider kinematics. We find them in general to be small, but noticeable.
We consider the longitudinal momentum distribution of hadrons inside jets in proton-proton collisions. At partonic threshold large double logarithmic corrections arise which need to be resummed to all orders. We develop a factorization formalism within SCET that allows for the joint resummation of threshold and jet radius logarithms. We achieve next-to-leading logarithmic NLL$'$ accuracy by including non-global logarithms in the leading-color approximation. Overall, we find that the threshold resummation leads to a sizable enhancement of the cross section and a reduced QCD scale dependence, su…
We study the fragmentation of (light) quarks and gluons to hadrons inside a jet of cone size R. This allows for a more exclusive analysis of fragmentation than is currently the case. The shape of semi-inclusive cross sections in the hadron energy fraction z is described by fragmenting jet functions (FJFs), which we calculate in terms of R and the jet energy E. We introduce a new joint resummation to sum the double logarithms of R and 1-z in the FJFs, which may similarly be applied to initial-state radiation at hadron colliders. Our results at next-to-leading logarithmic order indicate that the…
We develop the framework to perform all-orders resummation of electroweak logarithms of Q/M for inclusive scattering processes at energies Q much above the electroweak scale M. We calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 $\to$ 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov double logarithms, is computed. If only the invariant mass of the final state is measured, all electroweak logarithms can be resummed by the PDF evolution, at least to LL. However, simply identifying…
This document emerged from work that started in January 2012 as a joint effort by the ATLAS, CMS and LPCC supersymmetry (SUSY) working groups to compile state-of-the-art cross section predictions for SUSY particle production at the LHC. We present cross sections for various SUSY processes in pp collisions at $\sqrt{s} =7$ TeV, including an estimate of the theoretical uncertainty due to scale variation and the parton distribution functions. Further results for higher LHC centre-of-mass energies will be collected at https://twiki.cern.ch/twiki/bin/view/LHCPhysics/SUSYCrossSections. For squark an…
We have updated predictions for high energy neutrino and antineutrino charged current cross-sections within the conventional DGLAP formalism of NLO QCD using a modern PDF fit to HERA data, which also accounts in a systematic way for PDF uncertainties deriving from both model uncertainties and from the experimental uncertainties of the input data sets. Furthermore the PDFs are determined using an improved treatment of heavy quark thresholds. A measurement of the neutrino cross-section much below these predictions would signal the need for extension of the conventional formalism as in BFKL resum…
We derive a new factorization formula in perturbative quantum chromodynamics for the Drell-Yan massive lepton-pair cross section as a function of the transverse momentum $Q_T$ of the pair. When $Q_T$ is much larger than the pair's invariant mass $Q$, this factorization formula systematically resums the logarithmic contributions of the type $α_s^m \ln^m(Q_T^2/Q^2)$ to all orders in the strong coupling $α_s$. When $Q_T\sim Q$, our formula yields the same Drell-Yan cross section as conventional fixed order QCD perturbation theory. We show that resummation is important when the collision energy $\…
