We study the single hadron inclusive production in the forward rapidity region in proton-nucleus collisions. We find the long-standing negative cross section at next-to-leading-order (NLO) is driven by the large negative threshold logarithmic contributions. We established a factorization theorem for resumming these logarithms with systematically improvable accuracy within the color glass condensate formalism. We demonstrate how the threshold leading logarithmic accuracy can be realized by a suitable scale choice in the NLO results. The NLO spectrums with the threshold logarithms resummed remain positive and impressive agreements with experimental data are observed.
We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution ($j_T$) for the single hadron production with the thrust axis in electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit $j_T \ll Q$, and joint transverse momentum and threshold limit $j_T \ll Q(1-z_h) \ll Q$, where $Q$ and $z_h$ are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms $\ln(Q/j_T)$ and $\ln(1-z_h)$ to all orde…
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 point out that a study of event shapes at hadron colliders allows to explore novel aspects of QCD. These studies are today made easier by the development of a program which automates the resummation.
The moments of the single inclusive momentum distribution of hadrons in QCD jets, are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the alpha_s strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully reproduces the spectrum of charged hadrons of jets measured in e+e- collisions. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data m…
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…
This writeup gives an introduction to the theoretical understanding that lies behind automated resummation. It then discusses its applications to hadron-collider event shapes.
We investigate the resummation of large logarithmic perturbative corrections to hadron production in electron-positron annihilation and semi-inclusive deep-inelastic scattering. We find modest, but significant, enhancements of hadron multiplicities in the kinematic regimes accessible in present high-precision experiments. Our results are therefore relevant for the determination of hadron fragmentation functions from data for these processes.
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 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 discuss the heavy quark production cross section near partonic threshold in hadronic collisions, including the resummation of leading and next-to-leading logarithms arising from soft gluon emission. We show how to handle the complications due to the non-universal non-leading logarithms. We give analytical results for the $q {\bar q}$ partonic subprocess and numerical results in the DIS scheme for top quark production at the Fermilab Tevatron where the $q {\bar q}$ channel dominates.
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.
A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.
We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for di-hadron production in hadronic collisions, H1 H2 -> h1 h2 X, at high invariant mass of the produced hadron pair. 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, and show how to incorporate consistently cuts in rapidity and transverse momentum of the observed particles. We present numerical results for fixed-target and ISR regimes and find enhancem…
We perform the first global QCD analysis of pion valence, sea quark, and gluon distributions within a Bayesian Monte Carlo framework with threshold resummation on Drell-Yan cross sections at next-to-leading log accuracy. Exploring various treatments of resummation, we find that the large-$x$ asymptotics of the valence quark distribution $\sim (1-x)^{β_v}$ can differ significantly, with $β_v$ ranging from $\approx 1$ to $> 2.5$ at the input scale. Regardless of the specific implementation, however, the resummation induced redistribution of the momentum between valence quarks and gluons boosts t…
We consider the transverse-momentum ($q_T$) distribution of $Z$ bosons produced in hadronic collisions. At small values of $q_T$, we perform the analytic resummation of the logarithmically enhanced QED contributions up to next-to-leading logarithmic accuracy, including the mixed QCD-QED contributions at leading logarithmic accuracy. Resummed results are consistently matched with the next-to-leading fixed-order results (i.e. $\mathcal{O}(α^2)$) at small, intermediate and large values of $q_T$. We combine the QED corrections with the known QCD results at next-to-next-to-leading order ($\mathcal{…
We consider the transverse-momentum distribution of colourless high-mass systems (lepton pairs, vector bosons, Higgs particles...) produced in hadronic collisions. We briefly review a formalism for the all-order resummation of the logarithmically-enhanced contributions at small transverse momenta, and we present an illustrative selection of numerical results obtained by using our method.
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…
In this paper, using the Higgs production in forward rapidity region in proton-nucleus collisions as an example, we demonstrate that we can construct a systematic formalism for the threshold resummation for forward rapidity particle productions in the saturation formalism. The forward threshold jet function, which satisfies the corresponding renormalization group equation, is introduced into the new factorization formula. This calculation can be easily generalized to other processes, such as single forward hadron productions at forward rapidity region, and have important phenomenological impli…
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 derive a resummation formula for a $k_T$-dependent parton distribution function at threshold, where $k_T$ is a parton transverse momentum. The derivation requires infrared cutoffs for both longitudinal and transverse loop momenta as evaluating soft gluon emissions in the Collins-Soper resummation framework. This unified resummation exhibits suppression at large $b$, $b$ being the conjugate variable of $k_T$, which is similar to the $k_T$ resummation, and exhibits enhancement at small $b$, similar to the threshold resummation.
We demonstrate that both the $k_T$ and threshold resummations can be performed in the Collins-Soper resummation formalism by evaluating soft gluon emissions with infrared cutoffs for the longitudinal and transverse loop momenta, respectively. The reason the $k_T$ resummation for a parton distribution function leads to suppression in the large $b$ region, $b$ being the conjugate variable of parton transverse momentum $k_T$, and the threshold resummation leads to enhancement in the large $N$ limit, $N$ being the moment of a distribution function, is a consequence of opposite directions of double…
We compute the effects of soft gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell--Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important on…
We describe the resummation of singular distributions at partonic threshold in heavy quark production, generalizing results for Drell-Yan and other electroweak hard-scattering processes.
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 present a QCD calculation of the transverse momentum distribution of photon pairs produced at hadron colliders, including all-orders soft-gluon resummation valid at next-to-next-to-leading logarithmic accuracy. We specify the region of phase space in which the calculation is most reliable, compare our results with data from the Fermilab Tevatron, and make predictions for the Large Hadron Collider. The uncertainty of predictions for production of diphotons from fragmentation of final-state quarks is examined.
We study the effects of threshold resummation on the rapidity dependence of single-particle-inclusive cross sections, using the prompt photon cross section as an example. We make use of the full resummation formula at next-to-leading logarithmic accuracy and develop a new technique for treating rapidity in resummation. We compare our phenomenological results with those of previous studies and discuss differences and similarities of the two existing resummation formalisms.
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…
I discuss the motivation for resummation of the effects of initial-state soft gluon radiation, to all orders in the strong coupling strength, for processes in which the near-threshold region in the partonic subenergy is important. I summarize the method of "perturbative resummation" and its application to the calculation of the total cross section for top quark production at hadron colliders. Comments are included on the differences between the treatment of subleading logarithmic terms in this method and in other approaches.
We present a complete analysis of threshold resummation effects on direct light and heavy gaugino pair production at the Tevatron and the LHC. Based on a new perturbative calculation at next-to-leading order of SUSY-QCD, which includes also squark mixing effects, we resum soft gluon radiation in the threshold region at leading and next-to-leading logarithmic accuracy, retaining at the same time the full SUSY-QCD corrections in the finite coefficient function. This allows us to correctly match the resummed to the perturbative cross section. Universal subleading logarithms are resummed in full m…
The distribution of W and Z bosons produced with small transverse momentum (pt) at hadron colliders receives important contributions from large logarithms arising from soft gluon emission. Although conventionally the all-orders resummation of these `Sudakov' logarithms is performed in impact parameter (Fourier transform) space, pt-space resummation is also possible, and offers certain advantages.We present a detailed phenomenological analysis of W and Z production at small pt at the Tevatron $p \bar p$ collider, using pt-space resummation. A good description of the CDF and D0 data can be obtai…
We compute the threshold-resummed cross section for pseudo-scalar MSSM Higgs boson production by gluon fusion at hadron colliders. The calculation is performed at next-to-next-to leading logarithmic accuracy. We present results for both the LHC and Tevatron Run II. We analyze the factorization and renormalization scale dependence of the results, finding that after performing the resummation the corresponding cross section can be computed with an accuracy better than 10%.
We investigate the resummation of large logarithmic perturbative corrections to the partonic cross sections for single-inclusive high-p_T hadron production in collisions of transversely polarized hadrons. We perform the resummation to next-to-leading logarithmic accuracy. Phenomenological results are given for pbar-p collisions at center-of-mass energy of 14.5 GeV and for p-p collisions at 62.4 GeV and at 10 GeV, which are relevant for possible experiments at the GSI-FAIR, RHIC and J-PARC facilities, respectively. We find significant enhancements of the spin-dependent and spin-averaged cross s…
We describe some recent refinements of the techniques of threshold resummation, with emphasis on the usefulness of dimensional regularization when applied to nonabelian exponentiation. Threshold resummation is now under theoretical control for DIS and electroweak annihilation cross sections all the way to the fourth tower of logarithms and up to corrections suppressed by powers of the threshold variable.
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 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…
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 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 compute the resummed hadronic transverse-energy ($E_T$) distribution due to initial-state QCD radiation in the production of a Standard Model Higgs boson of mass 126 GeV by gluon fusion at the Large Hadron Collider, with matching to next-to-leading order calculations at large $E_T$. Effects of hadronization, underlying event and limited detector acceptance are estimated using aMC@NLO with the Herwig++ and Pythia 8 event generators.
We compute the resummed hadronic transverse energy (E_T) distribution due to initial-state QCD radiation in vector boson and Higgs boson production at hadron colliders. The resummed exponent, parton distributions and coefficient functions are treated consistently to next-to-leading order. The results are matched to fixed-order calculations at large E_T and compared with parton-shower Monte Carlo predictions at Tevatron and LHC energies.
We present a formalism that improves the applicability of perturbative QCD in the current region of semi-inclusive deep inelastic scattering. The formalism is based on all-order resummation of large logarithms arising in the perturbative treatment of hadron multiplicities and energy flows in this region. It is shown that the current region of semi-inclusive DIS is similar to the region of small transverse momenta in vector boson production at hadron colliders. We use this resummation formalism to describe transverse energy flows and charged particle multiplicity measured at the electron-proton…
We show that the conventional threshold resummation calculation cannot describe well the low energy Drell-Yan (DY) data without including the non-perturbative correction terms which are deduced from analyzing the asymptotic behavior of the resummation formalism. It is demonstrated that the non-perturbative correction is generally small for the large invariant mass DY pairs produced at the Tevatron and the LHC.
We investigate the QCD effects in the production of neutral Higgs bosons via bottom quark fusion in both the standard model and the minimal supersymmetric standard model at the CERN Large Hadron Collider. We include the next-to-leading order (NLO) QCD corrections (including supersymmetric QCD) and the threshold resummation effects. We use the soft-collinear effective theory to resum the large logarithms near threshold from soft gluon emission. Our results show that the resummation effects can enhance the total cross sections by about 5% compared with the NLO results.
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 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 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 corrections 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 SU…
The new relativistic Coulomb-like threshold resummation $S$-factor in quantum chromodynamics is obtained. The consideration is given within the framework of quasipotential approach in quantum field theory which is formulated in relativistic configuration representation for two particles of unequal masses.
We review some techniques of resummation applied to heavy quark production in hadronic scattering and electroproduction near partonic threshold, and discuss the reduction of factorization scale dependence in resummed cross sections.
We present calculations of next-to-leading order and resummed QCD corrections for semi-inclusive deep-inelastic scattering and single-inclusive e+e- annihilation. The resummation is performed to next-to-leading logarithmic accuracy. Knowing these QCD corrections is important in order to extract parton distribution functions and fragmentation functions from present and future data for these reactions. We present comparisons of our results to recent data by the COMPASS, HERMES, Belle, and BaBar experiments.
We show that certain general properties of threshold and joint resummations in Drell-Yan cross sections hold as well for their crossed analogs in semi-inclusive deep-inelastic scattering and double-inclusive leptonic annihilation. We show that all plus-distribution corrections near threshold show the same structure, and are determined to all logarithmic order by two anomalous dimensions, one of which is a generalization of the D-term previously derived in Drell-Yan. We also discuss the possibility of universality in power corrections implied by the resummation.
We construct a set of parton distribution functions (PDFs) in which fixed-order NLO and NNLO calculations are supplemented with soft-gluon (threshold) resummation up to NLL and NNLL accuracy respectively, suitable for use in conjunction with any QCD calculation in which threshold resummation is included at the level of partonic cross sections. These resummed PDF sets, based on the NNPDF3.0 analysis, are extracted from deep-inelastic scattering, Drell-Yan, and top quark pair production data, for which resummed calculations can be consistently used. We find that, close to threshold, the inclusio…
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 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 study the resummation of large logarithmic QCD corrections for the process pp ->H+ X when the Higgs boson H is produced at high transverse momentum. The corrections arise near the threshold for partonic reaction and originate from soft gluon emission. We perform the all-order resummation at next-to-leading logarithmic accuracy and match the resummed result with the next-to-leading order perturbative predictions. The effect of resummation on the Higgs transverse momentum distribution at the LHC is discussed.
Threshold resummation for gluon fusion $ZH$ production at the LHC
RWTH Aachen University（亚琛工业大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Guwahati（古瓦哈提印度理工学院）；Durham University（杜伦大学）
We study the cross section for the photoproduction process $γN\rightarrow h X$ where the incident photon and nucleon are longitudinally polarized and a hadron $h$ is observed at high transverse momentum. Specifically, we address the "direct" part of the cross section, for which the photon interacts in a pointlike way. For this contribution we perform an all-order resummation of logarithmic threshold corrections generated by soft or collinear gluon emission to next-to-leading logarithmic accuracy. We present phenomenological results relevant for the COMPASS experiment and compare to recent COMP…
We examine the soft-gluon resummation effects, including the exact spin correlations among the final state particles, in the search of the Standard Model Higgs boson, via the process $gg\to H\to WW/ZZ \to 4 leptons, at the Tevatron and the LHC. A comparison between the resummation and the Next-to-Leading order (NLO) calculation is performed after imposing various kinematics cuts suggested in the literature for the Higgs boson search. For the $H\to ZZ$ mode, the resummation effects increase the acceptance of the signal events by about 25%, as compared to the NLO prediction, and dramatically alt…
We develop a framework for a systematic resummation of the transverse momentum distribution of top-quark pairs produced at hadron colliders based on effective field theory. Compared to Drell-Yan and Higgs production, a novel soft function matrix is required to account for the soft gluon emissions from the final states. We calculate this soft function at the next-to-leading order, and perform the resummation at the next-to-next-to-leading logarithmic accuracy. We compare our results with parton shower programs and with the experimental data at the Tevatron and the LHC. We also discuss the impli…
