We discuss corrections from the elastic limit (partonic threshold) in hadronic hard-scattering cross sections. We show why these corrections can be large at all orders in perturbation theory, and describe their resummation to arbitrary logarithmic accuracy. In particular, we discuss the role of color exchange in the hard scattering. This enables us to generalize the resummation of the Drell-Yan cross section to QCD reactions.
As an example, we give the explicit resummed hard-scattering cross section for heavy-quark production through light quark annihilation, which takes into account next-to-leading logarithms to all orders.
We present a master formula, with applicability conditions, which allows us to automate the resummation of infrared and collinear logarithms appearing in distributions of jet observables in QCD at next-to-leading logarithmic accuracy.
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 build a computer code that fully automates the resummation of jet-observable distributions at next-to-leading logarithmic accuracy. As an application we present results for a jet shape in hadronic dijet production.
We investigate the resummation effects for the SM Higgs and vector boson associated production at the LHC with a jet veto in soft-collinear effective theory using "collinear anomalous" formalism. We calculate the jet vetoed invariant mass distribution and the cross section for this process at Next-to-Next-to-Leading-Logarithmic level, which are matched to the QCD Next-to-Leading Order results, and compare the differences of the resummation effects with different jet veto $p_{T}^{\rm veto}$ and jet radius $R$. Our results show that both resummation enhancement effects and the scale uncertaintie…
I discuss the resummation of soft gluon contributions to direct photon and W + jet production and I present some results for the next-to-next-to-leading order expansions of the resummed cross sections for these processes near threshold.
We investigate the QCD resummation for the Higgs boson plus a high $P_T$ jet production with large rapidity separations in proton-proton collisions at the LHC. The relevant Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Sudakov logs are identified and resummed. In particular, we apply recent developments of the transverse momentum dependent factorization formalism in the impact factors, which provides a systematic framework to incorporate both the BFKL and Sudakov resummations.
The resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The anomaly coefficient is extracted from the soft function and expressed in terms of polylogarithmic as well as elliptic functions. With our results, the uncertainty on jet-broadening distributions is reduced significantly, which should allow for a precise determination of the strong coupling constant from the existing experimental data and provide a consistency…
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…
For many observables, the most difficult part of a single logarithmic resummation is the analytical treatment of the observable's dependence on multiple emissions. We present a general numerical method, which allows the resummation specifically of these single logarithms. Some first applications and new results for the thrust major, the oblateness and the two-jet rate in the Durham algorithm are also presented.
We study the effect of multiple parton radiation to Higgs boson plus jet production at the LHC, by applying the transverse momentum dependent (TMD) factorization formalism to resum large logarithmic contributions to all orders in the expansion of the strong interaction coupling. We show that the appropriate resummation scale should be the jet transverse momentum, rather than the partonic center of mass energy which has been normally used in the TMD resummation formalism. Furthermore, the transverse momentum distribution of the Higgs boson, particularly near the lower cut-off applied on the jet…
We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton dis…
We investigate the resummation effects with a jet veto, for WZ and ZZ productions at the LHC in soft-collinear effective theory. We present the invariant mass distributions and the total cross section with different jet veto and jet radius for these process at Next-to-Next-to-Leading-Logarithmic level. Our results show that the jet-veto resummation can increase the jet-veto cross section and decrease the scale uncertainties, especially in the large center-of-mass energy. We find that for pt_veto>30 GeV and R=0.4, the resummation results can increase POWHEG+PYTHIA predictions by about 19% for W…
Using methods of effective field theory, we derive the first all-order factorization theorem for the Higgs-boson production cross section with a jet veto, imposed by means of a standard sequential recombination jet algorithm. Like in the case of small-q_T resummation in Drell-Yan and Higgs production, the factorization is affected by a collinear anomaly. Our analysis provides the basis for a systematic resummation of large logarithms log(m_H/p_T^veto) beyond leading-logarithmic order. Specifically, we present predictions for the resummed jet-veto cross section and efficiency at next-to-next-to…
We study the effect of soft gluon resummation on the gaps-between-jets cross-section at the LHC. We review the theoretical framework that enables one to sum logarithms of the hard scale over the veto scale to all orders in perturbation theory. We then present a study of the phenomenological impact of Coulomb gluon contributions and super-leading logarithms on the gaps between jets cross-section at the LHC.
We argue that the production of forward jets in polarised deep inelastic scattering can be a useful tool for probing the double $ln^2(1/x)$ resummation effects which control the polarised deep inelastic scattering for small values of the Bjorken parameter $x$. We solve the corresponding integral equations generating the double $ln^2(1/x)$ resummation and calculate the differential structure function describing the forward jet production in the small $x$ regime which can possibly be probed by the polarised HERA measurements. We show that these structure functions should exhibit the characterist…
We consider the quark beam function that describes collinear initial-state radiation that is constrained by a veto on reconstructed jets. As the veto is imposed on the transverse momenta of the jets, the beam function is subject to rapidity divergences, and we use the collinear-anomaly framework to extract the perturbative matching kernels to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on a novel framework that automates the computation of beam functions in Mellin space and it provides the ingredients to extend jet-veto resummations for quark…
Starting from a factorization theorem in effective field theory, we present resummed results for two non-global observables: the invariant-mass distribution of jets and the energy distribution outside jets. Our results include the full next-to-leading-order corrections to the hard, jet and soft functions and are implemented in a parton-shower framework which generates the renormalization-group running in the effective theory. The inclusion of these matching corrections leads to an improved description of the data and reduced theoretical uncertainties. They will have to be combined with two-loo…
Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e+e- annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present the first all-order expressions for jet-broadening distributions, which are free of large perturbative logarithms in the two-jet limit. Our formulae reproduce known results at next-to-leading logarithmic order but also extend…
In this paper, the soft gluon resummation effect in the Higgs boson plus two-jet production at the LHC is studied. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of the Higgs boson plus two-jet final state system, are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm. We also compare our result with the prediction of the Monte Carlo event generator Pythia8, and found noticeable difference in the distributions of the total transvers…
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 wit…
We calculate several differential cross sections for Z0 and high-pT jet production in the forward rapidity region at the LHC using the hybrid High Energy Factorization. We test various unintegrated gluon distributions involving subleading BFKL effects (such as kinematic constraint, running strong coupling and DGLAP correction) and compare the results with experimental data obtained by the LHCb experiment. We find that the hard scale dependence of unintegrated gluon distributions, which effectively resums the Sudakov-type logarithms on the top of the resummation of the small x logarithms, is es…
We compute the resummed on-shell $W^+ W^-$ production cross section under a jet-veto at the LHC to partial N$^3$LL order matched to the fixed order NNLO result. Differential NNLO cross sections are obtained from an implementation of $q_T$ subtraction in Sherpa. The two-loop virtual corrections to the $q \bar q \rightarrow W^+ W^-$ amplitude, used in both fixed order and resummation predictions, are extracted from the public code {\tt qqvvamp}. We perform resummation using soft collinear effective theory (SCET), with approximate beam functions where only the logarithmic terms are included at tw…
We compute in the heavy quark effective theory the soft coefficient D_2 entering the resummation of next-to-next-to-leading threshold logarithms for jets initiated by a quark with a small mass compared to the hard scale of the process. We find complete agreement with a previous computation in full QCD. Contrary to our previous guess, this coefficient turns out to be different from that one entering heavy flavor decay or heavy flavor fragmentation.
Jet vetoes are widely used in experimental analyses at the LHC to distinguish different hard-interaction processes. Experimental jet selections require a cut on the (pseudo)rapidity of reconstructed jets, $|η_{\rm jet}| \leq η_{\rm cut}$. We extend the standard jet-$p_T$ (jet-veto) resummation, which implicitly works in the limit $η_{\rm cut}\to\infty$, by incorporating a finite jet rapidity cut. We also consider the case of a step in the required $p_T^{\rm cut}$ at an intermediate value of $|η| \simeq 2.5$, which is of experimental relevance to avoid the increased pile-up contamination beyond…
Threshold resummation for factorizable cross sections in hadron-hadron collisions has a number of applications and extensions. We discuss factorization scale dependence, resummation at nonleading power in the moment variable, and the implications of resummation for power corrections in the hard momentum scale.
We construct an evolution equation for the invariant-mass distribution of light-quark and gluon jets in the framework of QCD resummation. The solution of the evolution equation exhibits a behavior consistent with Tevatron CDF data: the jet distribution vanishes in the small invariant-mass limit, and its peak moves toward the high invariant-mass region with the jet energy. We also construct an evolution equation for the energy profile of the light-quark and gluon jets in the similar framework. The solution shows that the energy accumulates faster within a light-quark jet cone than within a gluo…
A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level (NLL), …
From a detailed analysis of cone-jet cross sections in effective field theory, we obtain novel factorization theorems which separate the physics associated with different energy scales present in such processes. The relevant low-energy physics is encoded in Wilson lines along the directions of the energetic particles inside the jets. This multi-Wilson-line structure is present even for narrow-cone jets due to the relevance of small-angle soft radiation. We discuss the renormalization-group equations satisfied by these operators. Their solution resums all logarithmically enhanced contributions …
We study the multiple soft gluon radiation effects in $Z$ boson plus jet production at the LHC. By applying the transverse momentum dependent factorization formalism, the large logarithms introduced by the small total transverse momentum of the $Z$ boson plus jet final state system, are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of Next-to-Leading Logarithm(NLL). We also compare the prediction of our resummation calculation to the CMS data by employing a reweighting procedure to estimate the effect from imposing kinematic cuts on the leptons from…
In this paper we investigate the extension of high energy resummation at LLx accuracy to jet observables. In particular, we present the high energy resummed expression of the transverse momentum distribution of the outgoing parton in the general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach this result, several new ideas are introduced and exploited. First we prove that LLx resummation is achieved by dressing with hard radiation an off-shell gluon initiated LO process even if its on-shell limit is vanishing or trivial. Then we present a gauge-invariant framework where these ca…
We derive threshold resummations for single-particle and single-jet inclusive cross sections, thus generalizing previous results at fixed invariant mass to a wider class of cross sections with phenomenological interest. We confirm the structure of our resummed expressions by comparison with explicit one-loop calculations for direct photons and heavy quarks.
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 discuss the simultaneous resummation of threshold and recoil enhancements to partonic cross sections due to soft radiation. Our method is based on a refactorization of the parton cross section near its partonic threshold. It avoids double counting, conserves the flow of partonic energy, and reproduces either threshold or recoil resummation when the other enhancements are neglected.
We discuss a model for total hadronic and photonic cross-sections which includes hard parton-parton scattering to drive the rise and soft gluon resummation to tame it. Unitarity is ensured by embedding the cross-section in the eikonal formalism. Predictions for LHC and ILC are presented.
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.
We investigate the effect of QCD resummation to kinematical correlations in the Higgs boson plus high transverse momentum (Pt) jet events produced at hadron colliders. We show that at the complete one-loop order, the Collins-Soper-Sterman resummation formalism can be applied to derive the Sudakov form factor, which is found to be independent of jet-finding algorithm. We compare the singular behavior of resummation calculation to fixed order prediction in the case that Higgs boson and high Pt jet are produced nearly back-to-back in their transverse momenta, and find a perfect agreement. The phe…
Using the standard Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach, with partial inclusion of next-to-leading order effects, we propose the inclusive hadroproduction of a Higgs boson and of a jet, featuring large transverse momenta and well separated in rapidity, as a new channel to probe the BFKL dynamics. Predictions are presented for cross-sections and azimuthal angle correlations in different kinematics configurations for the final-state transverse momenta. We find that the large energy scales provided by the emission of a Higgs boson stabilize the BFKL series.
I present results for the resummation of soft-gluon contributions to QCD hard-scattering cross sections at next-to-next-to-leading logarithm accuracy. A key ingredient is the calculation of two-loop soft anomalous dimensions for the partonic processes. Explicit expressions and applications are provided for processes that involve massless partons and/or massive quarks.
The 1-Jettiness (tau_1) event shape for Deep Inelastic Scattering (DIS), allows for a quantitative and global description of the pattern of QCD radiation for single jet (J) production in electron-nucleus (N_A) collisions e^- + N_A \to e^- + J + X. It allows for precision studies of QCD and is a sensitive probe of nuclear structure and dynamics. The large transverse momentum (P_{J_T}) of the final state jet $J$, characterizes the hard scale in the problem. The region of phase space where tau_1 << P_{J_T}, corresponds to configurations where energetic radiation (E~ P_{J_T}) is only along either …
Inclusion of down to zero-momentum gluons and their k_t resummation is shown to quench the too fast rise of the mini jet cross section and thereby obtain realistic total cross-sections.
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for the process pp->h X at high transverse momentum of the hadron h. These corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy. We present numerical results for the fixed-target regime and find enhancements over the next-to-leading order cross section, which significantly improve the agreement between theoretical predictions and data. We also apply the resummation…
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 compare the high energy behaviour of hadronic photon-photon cross-sections in different models. We find that the photon-photon cross-section appears to rise faster than the purely hadronic ones (proton-proton and proton-antiproton).
The production of vector bosons in association with jets contains at least two unrelated scales. The first is the mass of the vector boson m_V and the second is the hard interaction scale giving rise to large transverse momenta of the produced jets. The production cross sections depend logarithmically on the ratio of these scales, which can lead to a poor convergence in fixed order perturbation theory. We illustrate how to resum all leading logarithmic terms using effective theory methods, and show that they can be resummed by a simple choice of the factorization scale. Implementing this scale…
We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS-specific procedures for matching to fixed-order calculations and compare our results to data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets fro…
A model for total cross-sections incorporating QCD jet cross-sections and soft gluon resummation is described and compared with present data on $pp$ and ${\bar p}p$ cross-sections. Predictions for LHC are presented for different parameter sets. It is shown that they differ according to the small x-behaviour of available parton density functions.
Calculating the distribution of jet masses in high-energy collisions is challenging because fixed-order perturbation theory breaks down near the peak region, and because multiple scales complicate the resummation. To avoid using a jet veto, one can consider inclusive observables, in which every particle is in a jet. We demonstrate that calculating the mass of the hardest jet in multijet events can be problematic, and we give an example of an inclusive observable, asymmetric thrust, which can be resummed to next-to-next-to-leading logarithmic accuracy. Exclusive observables with out-of-jet regi…
The physics underlying the fall and eventual rise in various total cross-sections at high energies has been investigated over a decade using a model based on the Bloch-Nordsieck resummation in QCD. Here a brief review of our latest results is presented and comparison made with experimental data on $pp$, $γproton$ and $γγ$ total cross-sections.
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…
We reconsider the high energy resummation of photoproduction, electroproduction and hadroproduction cross-sections, in the light of recent progress in the resummation of perturbative parton evolution to NLO in logarithms of Q^2 and x. We show in particular that the when the coupling runs the dramatic enhancements seen at fixed coupling, due to infrared singularities in the partonic cross-sections, are substantially reduced, to the extent that they are largely accounted for by the usual NLO and NNLO perturbative corrections. This leads to a novel explanation of the large K-factors commonly foun…
A quantity that promises to reveal important information on perturbative and non-perturbative QCD dynamics is the azimuthal decorrelation between jets in different hard processes. In order to access this information fixed-order NLO predictions need to be supplemented by resummation of logarithmic terms which are large in the region where the jets are nearly back-to-back in azimuth. In the present letter we carry out this resummation to next-to--leading logarithmic accuracy explaining the important role played by the recombination scheme in general resummations for such jet observables.
In this paper we demonstrate the agreement of jet-veto resummation and pT resummation for explaining the WW cross sections at Run 1 of the LHC, and in the future. These two resummation techniques resum different logarithms, however via reweighting methods they can be compared for various differential or exclusive cross sections. We find excellent agreement between the two resummation methods for predicting the zero-jet cross section, and propose a new reweighting method for jet-veto resummation that can be used to compare other differential distributions. We advocate a cross-channel comparison…
We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sud…
The region of small transverse momentum in q qbar- and gg-initiated processes must be studied in the framework of resummation to account for the large, logarithmically-enhanced contributions to physical observables. In this paper, we will calculate the fixed order next-to-leading order (NLO) perturbative total and differential cross-sections for both a Standard Model (SM) scalar Higgs boson and the Minimal Supersymmetric Standard Model's (MSSM) pseudoscalar Higgs boson in the Heavy Quark Effective Theory (HQET) where the mass of the top quark is taken to be infinite. Resummation coefficients B…
We discuss the resummation of threshold logarithms for heavy quark and dijet cross sections in hadronic collisions. The resummed cross sections are presented at next-to-leading logarithmic accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We apply our formalism to the calculation of the top quark production cross section at the Fermilab Tevatron.
In electroweak-boson production processes with a jet veto, higher-order corrections are enhanced by logarithms of the veto scale over the invariant mass of the boson system. In this paper, we resum these Sudakov logarithms at next-to-next-to-leading logarithmic (NNLL) accuracy and match our predictions to next-to-leading order (NLO) fixed-order results. We perform the calculation in an automated way, for arbitrary electroweak final states and in the presence of kinematic cuts on the leptons produced in the decays of the electroweak bosons. The resummation is based on a factorization theorem fo…
