We present results relevant for the extension of threshold resummation beyond the next-to-leading logarithmic (NLL) order for QCD hard-scattering processes. As an example, we consider di-hadron production $H_1 H_2\to h_1 h_2 X$, where the produced pair has a large invariant mass. Taking into account the non-trivial color structure of the partonic hard-scattering process, we determine the hard and soft matrices in color space. In our numerical studies we find a significant improvement compared to previous results at NLL accuracy. In particular, the scale dependence of the resummed cross section is greatly reduced. In addition, we comment on the extension of the techniques developed in this work to other observables relevant for hadronic collisions.
We present new results for W-boson production at large transverse momentum at the LHC and the Tevatron. The contribution of soft-gluon corrections is derived from NNLL resummation and added to the exact NLO result. Numerical results and their uncertainties for the approximate NNLO W-boson transverse momentum distributions are derived and compared to recent data from the LHC.
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.
In the following we present our recent results on the resummation of soft gluon corrections to the $pp\rightarrow t\bar{t}H$ cross section at the LHC. The resummation was carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the Mellin space technique. Obtained results were matched to the NLO cross section. We show that the resummation leads to reduction of scale-variation uncertainty of the total $pp\rightarrow t\bar{t}H$ cross section.
The production of supersymmetric stop-antistop pairs at the Large Hadron Collider (LHC) is studied including corrections from soft-gluon resummation up to next-to-next-to-leading logarithmic (NNLL) accuracy in the Mellin-space approach. Additionally, corrections to the hard-matching coefficient at one-loop and Coulomb contributions at two-loop order are considered. The NNLL corrections enhance the cross section for all stop masses at centre-of-mass energies of 8 and 13 TeV compared to the previously calculated predictions at next-to-leading logarithmic (NLL) accuracy. Furthermore, a slight inc…
We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Higgs boson at the Large Hadron Collider. Starting from a soft-gluon resummation formula derived in previous work, we develop a bespoke parton-level Monte Carlo program which can be used to calculate the total cross section along with differential distributions. We use this tool to study the phenomenological impact of the resummation to next-to-next-to-leading logarithmic (NNLL) accuracy, finding that these corrections increase the total cross section and the differential d…
We perform the resummation of soft-gluon emissions for squark and gluino production at next- to-next-to-leading-logarithmic (NNLL) accuracy. We include also the one-loop hard matching coefficients as well as Coulomb corrections to second order, using Mellin-moment methods. We study the characteristics of this resummation in detail for a centre-of-mass (CM) energy of 8 TeV at the LHC, and for squark and gluino masses up to 2.5 TeV. We find significant enhancing effects for all four processes of squark- and gluino-pair production. Scale dependence is generally reduced compared to NLL resummation…
In this presentation we review recent results on the resummation of soft gluon emission corrections for the associated production of a top-quark pair with a heavy boson (Higgs/W/Z) at the Large Hadron Collider (LHC). We develop a parton level Monte Carlo based on a soft-gluon resummation formula valid up to next-to-next-to-leading logarithmic (NNLL) accuracy. With this tool we study the impact of the newly computed corrections to the total cross sections and some important differential distributions.
If supersymmetry near the TeV scale is realized in Nature, the pair production of scalar top squarks is expected to be observable at the Large Hadron Collider. Recently, effective field-theory methods were employed to obtain approximate predictions for the cross section for this process, which include soft-gluon emission effects up to next-to-next-to-leading order (NNLO) in perturbation theory. In this work we employ the same techniques to resum soft-gluon emission effects to all orders in perturbation theory and with next-to-next-to-logarithmic (NNLL) accuracy. We analyze the effects of NNLL …
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 report on the resummation of soft-gluon emissions for squark-antisquark production at next-to-next-to-leading-logarithmic (NNLL) accuracy. We will put particular emphasis on the one loop hard matching coefficients required to perform the resummation. Furthermore we will discuss the numerical effect of the different ingredients in the corrections. We find a significant reduction in the scale uncertainty and a considerable increase in the prediction of the total cross section at the central scale. Compared to the next-to-leading order prediction, the corrections increase the cross section by …
We consider the resummation of soft gluon emission for squark-antisquark pair-production at the LHC at next-to-next-to-leading-logarithmic (NNLL) accuracy in the framework of the minimal supersymmetric standard model. We present the analytical ingredients needed for the calculation and provide numerical predictions for the LHC at centre-of-mass energies of 7 and 14 TeV. We find a significant reduction in the scale uncertainty and a considerable increase in the prediction of the total cross section. Compared to the next-to-leading order prediction, the corrections increase the cross section by …
We investigate QCD threshold resummation effects beyond the next-to-leading logarithmic (NLL) order for the process H1 H2->h1 h2 X at high invariant mass of the produced hadron pair. We take into account the color structure of the underlying partonic hard-scattering cross sections and determine the relevant hard and soft matrices in color space that contribute to the resummed cross section at next-to-next-to-leading logarithmic (NNLL) accuracy. We present numerical results for fixed-target and collider regimes. We find a significant improvement compared to previous results at NLL accuracy. In …
We present the hard matching coefficients for squark and gluino hadroproduction. The hard matching coefficients follow from the next-to-leading order cross section near threshold and are an important ingredient for performing threshold resummation at next-to-next-to-leading logarithmic accuracy. We discuss the calculation, list the analytical results and study the numerical impact of these corrections. We find that the impact of the hard matching coefficients can be considerable, with the largest effect observed for final states involving gluinos.
We present predictions for the total top-quark pair production cross section at the Tevatron and the LHC with 7,8 and 14 TeV centre-of-mass energy, including the resummation of threshold logarithms and Coulomb corrections through next-to-next-to-leading logarithmic order, and top-antitop bound-state contributions. The remaining theoretical and PDF uncertainties and prospects for the measurement of the top mass from the total cross section are discussed.
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 present state-of-the art predictions for the production of supersymmetric squarks and gluinos at the Large Hadron Collider (LHC), including soft-gluon resummation up to next-to-next-to-leading logarithmic (NNLL) accuracy, the resummation of Coulomb corrections and the contribution from bound states. The NNLL corrections enhance the cross-section predictions and reduce the scale uncertainty to a level of 5-10%. The NNLL resummed cross-section predictions can be obtained from the computer code NNLL-fast, which also provides the scale uncertainty and the pdf and alpha_s error.
We perform threshold resummation of soft gluon corrections to the total cross section and the invariant mass distribution for the process $pp \to t\bar{t}H$. The resummation is carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the direct QCD Mellin space technique in the three-particle invariant mass kinematics. After presenting analytical expressions we discuss the impact of resummation on the numerical predictions for the associated Higgs boson production with top quarks at the LHC. We find that NLO+NNLL resummation leads to predictions for which the central values are…
I discuss threshold resummation at NNLL accuracy in the standard moment-space approach in perturbative QCD for top-pair and single-top production. For top quark pair production I present new approximate NNLO results for the total cross section and for the top quark transverse momentum and rapidity distributions at 8 TeV LHC energy. I discuss the accuracy of the soft-gluon approximation and show that the NLO and NNLO approximate results from resummation are practically indistinguishable from exact NLO and partial NNLO results. For single top production I present new approximate NNLO results for…
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…
We present a general framework that allows to compute the resummed transverse-momentum distribution of a system of colorless particles. The implementation is fully differential in the degrees of freedom of the final-state system. As a first application, we consider the transverse-momentum spectrum of ZZ and WW boson pairs produced in hadron collisions, where we resum the logarithmically enhanced contributions due to multiple soft-gluon emission at small transverse momenta to all orders in perturbation theory. We exploit the most advanced perturbative information for the ZZ and WW production pr…
The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL …
We update the theoretical precision of the total cross section for direct top quark production at the LHC by extending the threshold resummation to the next-to-next-to-leading logarithmic accuracy.
We perform threshold resummation of soft gluon corrections to the total cross sections and the invariant mass distributions for production of a top-antitop quark pair associated with a heavy electroweak boson $V = W^+$, $W^-$ or $Z$ in $pp$ collisions at the Large Hadron Collider. The resummation is carried out at next-to-next-to-leading-logarithmic (NNLL) accuracy using the direct QCD Mellin space technique in the three-particle invariant mass kinematics. It is found that for the $t\bar t Z$ process the soft gluon resummation introduces significant corrections to the next-to-leading order (NL…
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…
I present the next-to-next-to-leading-logarithm (NNLL) resummation of soft and collinear gluon corrections to single top quark production in the s channel. Attaining NNLL accuracy involves the calculation of the two-loop soft anomalous dimension for the partonic subprocesses. Finite-order expansions of the resummed cross section are calculated through next-to-next-to-leading order (NNLO). Numerical results are presented for s-channel single top quark production at the Tevatron and the LHC, including the dependence of the cross sections on the top quark mass and the uncertainties in the theoret…
We develop threshold resummation for single-particle inclusive cross sections in hadron-hadron collisions to the level of next-to-next-to-leading logarithm, up to full matching with two-loop hard functions. We define and calculate all one-loop soft functions for all partonic channels. This enables us to separate the hard and soft functions at one loop. Along with these results, the one-loop finite parts of jet functions are used to check that the full soft, collinear and virtual corrections are reproduced to one loop for all partonic reactions. We exhibit these NLO results explicitly. NLO expa…
In this talk we report on the recent progresses on IR logarithms resummation for the Thrust distribution in e^{+}e^{-} collisions. Using renormalisation group (RG) evolution in Laplace space, the resummation of logarithmically enhanced corrections is performed to next-to-next-to-leading logarithmic (NNLL) accuracy. To combine the resummed expressions with the fixed-order results, we derive the log(R)-matching and R-matching of the NNLL approximation to the fixed-order NNLO distribution.
Transverse-momentum resummation at mixed QCD$\otimes$QED NNLL accuracy for Z boson production at hadron colliders
Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所（IFIC），西班牙瓦伦西亚大学）；CERN（欧洲核子研究中心）；Tif Lab, Dipartimento di Fisica, Universitá di Milano and INFN, Sezione di Milano（米兰大学物理系及意大利国家核物理研究院米兰分部）；Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca（萨拉曼卡大学基础物理系）
The Wilson Coefficients for all 4-parton operators which arise in matching QCD to Soft-Collinear Effective Theory (SCET) are computed at 1-loop. Any dijet observable calculated in SCET beyond leading order will require these results. The Wilson coefficients are separated by spin and color, although most applications will involve only the spin-averaged hard functions. The anomalous dimensions for the Wilson coefficients are given to 2-loop order, and the renormalization group equations are solved explicitly. This will allow for analytical resummation of dijet observables to next-to-next-to-lead…
We present results for the total top-pair production cross section at the Tevatron and the LHC. Our predictions supplement fixed-order results with resummation of soft logarithms and Coulomb singularities to next-to-next-to-leading (NNLL) logarithmic accuracy and include top-antitop bound-state effects. The effects of resummation, the dependence on the PDF set used, the residual sources of theoretical uncertainty and their implication for measurements of the top-quark mass are discussed.
We present predictions for the total cross sections for pair production of squarks and gluinos at the LHC including a combined NNLL resummation of soft and Coulomb gluon effects. We derive all terms in the NNLO cross section that are enhanced near the production threshold, which include contributions from spin-dependent potentials and so-called annihilation corrections. The NNLL corrections at $\sqrt{s}=13$ TeV range from up to $20\%$ for squark-squark production to $90\%$ for gluino pair production relative to the NLO results and reduce the theoretical uncertainties of the perturbative calcul…
We consider the production of pairs of lepton through the Drell-Yan process at the LHC and present the most accurate prediction on their rapidity distribution. While the fixed order prediction is already known to next-to-next-to-leading order in perturbative QCD, the resummed contribution coming from threshold region of phase space up to next-to-next-to-leading logarithmic (NNLL) accuracy has been computed in this article. The formalism developed in [1-3] has been used to resum large threshold logarithms in the two dimensional Mellin space to all orders in perturbation theory. We have done a d…
We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Z boson at the Large Hadron Collider to next-to-next-to-leading logarithmic accuracy. By means of an in-house parton level Monte Carlo code we evaluate the resummation formula for the total cross section and several differential distributions at a center-of-mass energy of 13 TeV, and we match these calculations to next-to-leading order results.
We compute the total top-quark pair production cross section at the Tevatron and LHC based on approximate NNLO results, and on the summation of threshold logarithms and Coulomb enhancements to all orders with next-to-next-to-leading logarithmic (NNLL) accuracy, including bound-state effects. We find σ_{t\bar t} = 7.22^{+0.31+0.71}_{-0.47-0.55} pb at Tevatron and σ_{t\bar t} = 162.6^{+7.4+15.4}_{-7.6-14.7} pb at LHC with 7 TeV c.o.m. energy, for m_t=173.3 GeV. The implementation of joint soft and Coulomb resummation, its ambiguities, and the present theoretical uncertainty are discussed in deta…
We propose a new approach to the resummation of the transverse-momentum distribution of a high-mass colour-singlet system in hadronic collisions. The resummation is performed in momentum space and is free of kinematic singularities at small transverse momentum. We derive a formula accurate at the next-to-next-to-leading-logarithmic level, and present the first matched predictions to next-to-next-to-leading order for Higgs-boson production in gluon fusion at the LHC. This method can be adapted to all observables featuring kinematic cancellations in the infrared region.
We present new results for the jet-veto efficiency and zero-jet cross section in Higgs production through gluon fusion. We incorporate the N$^3$LO corrections to the total cross section, the NNLO corrections to the 1-jet rate, NNLL resummation for the jet $p_t$ and LL resummation for the jet radius dependence. Our results include known finite-mass corrections and are obtained using the jet-veto efficiency method, updated relative to earlier work to take into account what has been learnt from the new precision calculations that we include. For 13 TeV collisions and using our default choice for …
We investigate threshold resummation effects in the production of a color sextet (antitriplet) scalar at next-to-next-to-leading logarithmic (NNLL) order at the LHC in the frame of soft-collinear effective theory. We show the total cross section and the rapidity distribution with NLO+NNLL accuracy, and we compare them with the NLO results. Besides, we use recent dijet data at the LHC to give the constraints on the couplings between the colored scalars and quarks.
We study the resummation of the $0$-jettiness resolution variable $\mathcal{T}_0$ for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $\mathcal{T}_0\to 0$ limit. We then calculate the $\mathcal{O}(α_s)$ corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic ($\mathrm{NNLL}$) accuracy. …
We present an update to the NNLL RG-improved QCD prediction of top-antitop production in electron-positron annihilation at threshold. It includes for the first time a complete NNLL resummation of ultrasoft logarithms, which are dominant at this order and give a sizable correction. The renormalization scale dependence of the total resonance cross section decreases substantially compared to earlier predictions, where the ultrasoft logarithms were included only partially.
I present results for two-loop soft anomalous dimensions for heavy quark production which control soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. I derive an explicit expression for the exact result and study it numerically for top quark production via e+ e- -> t tbar, and I construct a surprisingly simple but very accurate approximation. I show that the two-loop soft anomalous dimensions with massive quarks display a simple proportionality relation to the one-loop result only in the limit of vanishing quark mass. I also discuss the extension of the calculation to …
We examine the impact of threshold resummation for the inclusive hadronic production cross section of gluino pairs at next-to-next-to-leading-logarithmic accuracy, compared to the exact next-to-leading-order cross section and the next-to-next-to-leading-order approximation. Here, we apply formulas derived recently in the classical Mellin-space formalism. Moreover, we give the analytic input for the alternative momentum-space formalism and discuss the crucial points of the numeric implementation. We find that soft resummation keeps the hadronic cross section close to the fixed next-to-leading-o…
We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL' accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL' accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the M_{tt} and top-quark p_T distributions in the boosted regime where fixed order calculations may become str…
We consider the transverse-momentum ($p_T$) distribution of $ZZ$ and $W^+W^-$ boson pairs produced in hadron collisions. At small $p_T$, the logarithmically enhanced contributions due to multiple soft-gluon emission are resummed to all orders in QCD perturbation theory. At intermediate and large values of $p_T$, we consistently combine resummation with the known fixed-order results. We exploit the most advanced perturbative information that is available at present: next-to-next-to-leading logarithmic resummation combined with the next-to-next-to-leading fixed-order calculation. After integrati…
We present first results on the resummation of Next-to-Soft Virtual (NSV) logarithms for the threshold production of pseudoscalar Higgs boson through gluon fusion at the LHC. These results are presented after resumming the NSV logarithms of the kind ${\log}^{i}(1-z)$ to $\overline{\text{NNLL}}$ accuracy and matching them systematically to the fixed order NNLO cross-sections. These results are obtained using collinear factorization, renormalization group invariance and recent developments in the NSV resummation techniques. The phenomenological implications of these NSV resummed results for 13 T…
We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve this by exploiting the factorization properties and K+G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-l…
In this talk we present results of our recent calculations of cross sections and distributions for the associate production of top-antitop quark pairs with a heavy boson (Higgs, W, Z) at the LHC, obtained using threshold resummation in direct QCD, i.e. in the Mellin-space approach.
We are interested in the transverse-momentum ($q_T$) distribution of a diphoton pair produced in hadron collisions. We resum the logarithmically-enhanced perturbative QCD contributions at small values of $q_T$ up to next-to-next-to-leading logarithmic accuracy. We consistently combine resummation with the known next-to-leading order perturbative result at intermediate and large values of $q_T$ . We include all perturbative terms up to order $α_S^2$ in our computation which, after integration over $q_T$ , reproduces the known next-to-next-to-leading order result for the diphoton pair production…
We present new results for QCD corrections to the top-pair invariant mass and top-quark $p_T$ distributions in boosted top-quark pair production at hadron colliders. They are derived from a formalism which allows the joint resummation of soft and small-mass logarithms at NNLL$'$ order, thus taking into account all potentially large corrections in the boosted regime, where the partonic center-of-mass energy is parameterically much larger than the mass of the top quark. We match these results with those from standard soft-gluon resummation away from the small-mass limit to NNLL order and also wi…
We present predictions for Higgs production via gluon fusion with a p_T veto on jets and with the resummation of jet-veto logarithms at NNLL'+$NNLO order. These results incorporate explicit O(alphas^2) calculations of soft and beam functions, which include the dominant dependence on the jet radius R. In particular the NNLL' order accounts for the correct boundary conditions for the N3LL resummation, for which the only unknown ingredients are higher-order anomalous dimensions. We use scale variations in a factorization theorem in both rapidity and virtuality space to estimate the perturbative u…
We present studies of QCD corrections to dilepton production in transversely polarized pp and \bar{p}p scattering. In particular we briefly discuss the effects of NNLL threshold resummation on the rapidity distribution of the lepton pair.
We present results for the Higgsstrahlung process within the GENEVA Monte Carlo framework. We combine the fully differential NNLO calculation with the higher-order resummation in the 0-jettiness resolution variable (beam-thrust). The resulting parton-level events are further showered and hadronised by Pythia8. The beam-thrust resummation is carried out to NNLL$'$ accuracy, which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment …
The $q_{\mathrm{T}}$ and $Δϕ_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities
