Fixed-order Predictions Research Articles

Measurement of the 1-jettiness event shape observable in deep-inelastic electron-proton scattering at HERA

The H1 Collaboration reports the first measurement of the 1-jettiness event shape observable τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document} in neutral-current deep-inelastic electron-proton scattering (DIS). The observable τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document} is equivalent to a thrust observable defined in the Breit frame. The data sample was collected at the HERA ep collider in the years 2003–2007 with center-of-mass energy of s=319GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=319\\,\ extrm{GeV} $$\\end{document}, corresponding to an integrated luminosity of 351.1 pb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{pb}^{-1}$$\\end{document}. Triple differential cross sections are provided as a function of τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document}, event virtuality Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^{2}$$\\end{document}, and inelasticity y, in the kinematic region Q2>150GeV2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^{2} >150\\,\ extrm{GeV}^2 $$\\end{document}. Single differential cross sections are provided as a function of τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document} in a limited kinematic range. Double differential cross sections are measured, in contrast, integrated over τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document} and represent the inclusive neutral-current DIS cross section measured as a function of Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^{2}$$\\end{document} and y. The data are compared to a variety of predictions and include long-standing and more recent Monte Carlo event generators, predictions in fixed-order perturbative QCD where calculations up to O(αs3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(\\alpha _\ extrm{s} ^3)$$\\end{document} are available for τ1b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _1^b$$\\end{document} or inclusive DIS, and resummed predictions at next-to-leading logarithmic accuracy matched to fixed order predictions at O(αs2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(\\alpha _\ extrm{s} ^2)$$\\end{document}. These comparisons reveal sensitivity of the 1-jettiness observable to QCD parton shower and resummation effects, as well as the modeling of hadronization and fragmentation. Within their range of validity, the fixed-order predictions provide a good description of the data. Monte Carlo event generators are predictive over the full measured range and hence their underlying models and parameters can be constrained by comparing to the presented data.

NNLO+PS predictions for Higgs production through bottom-quark annihilation with MINNLOPS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{_{\ ext {PS}}}$$\\end{document}

We consider Higgs production through bottom-quark annihilation at hadron colliders and we calculate next-to-next-to-leading-order (NNLO) corrections in QCD perturbation theory matched to parton showers (NNLO+PS). To this end, we have adapted the MINNLOPS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{_{\ ext {PS}}}$$\\end{document} method to account for the extra scale dependence induced by an overall Yukawa coupling that is MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{\ extrm{MS}}$$\\end{document} renormalized. We compare our results against state-of-the-art fixed-order predictions at NNLO as well as resummed predictions at next-to-next-to-leading-logarithmic (NNLL) accuracy.

N3LL resummation of one-jettiness for Z -boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the color-singlet plus jet production process pp→(γ*/Z→ℓ+ℓ−)+jet at hadron colliders up to the fourth logarithmic order (N3LL). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the framework. Published by the American Physical Society 2024

NNLO QCD predictions of the asymmetry probe of the Z γ pair-production process

The paper presents for the first time a novel idea of exploiting asymmetry between differential cross sections of the off-shell Z γ pair-production in proton-proton (pp) collisions for the final states of a charged-lepton pair plus a photon pp → Z γ → l + l − γ (leptonic decay) and of a neutrino pair plus a photon (invisible decay). Asymmetry between the leptonic and invisible decays of the Z γ process is investigated by using fixed-order predictions through inclusion of next-to-next-to-leading (NNLO) radiative corrections in quantum chromodynamics (QCD) perturbation theory. NNLO QCD predictions are presented at various pp-collision energies as functions of several key observables including transverse momenta and azimuthal-angle separation, regarding the Z γ decay products. The predicted distributions for the Z γ asymmetry are provided based on realistic fiducial phase-space requirements in line with the related hadron-collider measurements. The predicted distributions are assessed at various pp-collision energies and in different phase-space regions such as with higher lepton-pair invariant mass or higher neutrino-pair transverse momentum requirements. The Z γ asymmetry is shown to be significantly sensitive in different regions of phase space including high- and high- regions. The Z γ asymmetry can therefore be translated into an important quantity for probing deviation from the Standard Model (SM) predictions. In this regard, the asymmetry probe is proposed as a sensitive indicator for indirect searches for physics beyond the SM encompassing high-mass resonances and dark-matter sector.

Detailed comparison of renormalization scale-setting procedures based on the principle of maximum conformality

The {\it Principle of Maximum Conformality} (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC$_\infty$). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities $R_{e^+e^-}$, $R_{\tau}$, and $\Gamma(H \to b \bar{b})$ up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling $\alpha_s(Q)$ by the recursive use of the renormalization group equation, whose argument $Q$ represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

New determination of |Vcb| using the three-loop QCD corrections for the B → D⁎ semi-leptonic decays

We present a new determination of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb| by using the three-loop perturbative QCD corrections for the B→D⁎ semi-leptonic decay. The decay width of B→D⁎ semi-leptonic decay can be factorized as perturbatively calculable short-distance part and the non-perturbative but universal long-distance part. We adopt the principle of maximum conformality (PMC) single-scale setting approach to deal with the perturbative series so as to achieve a precise fixed-order prediction for the short-distance parameter ηA. By applying the PMC, an overall effective αs value is achieved by recursively using the renormalization group equation, which inversely results in a precise scale-invariant pQCD series. Such scale-invariant series also provides a reliable basis for predicting the contributions from uncalculated perturbative terms. We then obtain ηA=0.9225−0.0168+0.0117, where the error is the squared average of those from Δαs(MZ)=±0.0010 and the uncertainties caused by the uncalculated higher-order perturbative terms. By using the data of B→D⁎ℓν¯ℓ, we finally obtain |Vcb|PMC=(40.60−0.57+0.53)×10−3, which is consistent with the PDG value within errors.

Soft gluon resummation for associated squark-electroweakino production at the LHC

We perform a threshold resummation calculation for the associated production of squarks and electroweakinos at the LHC to the next-to-leading logarithmic (NLL) accuracy. Analytical results for the process-dependent soft anomalous dimension and the hard matching coefficient are presented. The resummed results are matched to fixed-order predictions at next-to-leading order (NLO) in QCD, which are generalised to scenarios with non-universal squark masses and mixings. Numerically, the NLL contributions increase the total NLO cross section by 2% to 6% for squark masses ranging from 1 TeV to 3 TeV, respectively, and they reduce the dependence of the predictions on the factorisation and renormalisation scales from typically ±10% to below ±5%. Our NLO and NLO+NLL calculations have been implemented in the publicly available program Resummino.

Drell–Yan lepton-pair production: qT resummation at N3LL accuracy and fiducial cross sections at N3LO

We present high-accuracy QCD predictions for the transverse-momentum (${q}_{T}$) distribution and fiducial cross sections of Drell--Yan lepton pairs produced in hadronic collisions. At small values of ${q}_{T}$ we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (${\mathrm{N}}^{3}\mathrm{LL}$) accuracy, including all the next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$) [i.e., $\mathcal{O}({\ensuremath{\alpha}}_{S}^{3})$] terms. Our resummed calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state lepton kinematics. We consistently combine our resummed results with the known $\mathcal{O}({\ensuremath{\alpha}}_{S}^{3})$ fixed-order predictions at large values of ${q}_{T}$ thus also obtaining full ${\mathrm{N}}^{3}\mathrm{LO}$ accuracy for fiducial cross sections. We show numerical results at LHC energies discussing the reduction of the perturbative uncertainty with respect to lower-order calculations.

A comparative study of Higgs boson production from vector-boson fusion

The data taken in Run II at the Large Hadron Collider have started to probe Higgs boson production at high transverse momentum. Future data will provide a large sample of events with boosted Higgs boson topologies, allowing for a detailed understanding of electroweak Higgs boson plus two-jet production, and in particular the vector-boson fusion mode (VBF). We perform a detailed comparison of precision calculations for Higgs boson production in this channel, with particular emphasis on large Higgs boson transverse momenta, and on the jet radius dependence of the cross section. We study fixed-order predictions at next-to-leading order and next-to-next-to-leading order QCD, and compare the results to NLO plus parton shower (NLOPS) matched calculations. The impact of the NNLO corrections on the central predictions is mild, with inclusive scale uncertainties of the order of a few percent, which can increase with the imposition of kinematic cuts. We find good agreement between the fixed-order and matched calculations in non-Sudakov regions, and the various NLOPS predictions also agree well in the Sudakov regime. We analyze backgrounds to VBF Higgs boson production stemming from associated production, and from gluon-gluon fusion. At high Higgs boson transverse momenta, the ∆yjj and/or mjj cuts typically used to enhance the VBF signal over background lead to a reduced efficiency. We examine this effect as a function of the jet radius and using different definitions of the tagging jets. QCD radiative corrections increase for all Higgs production modes with increasing Higgs boson pT, but the proportionately larger increase in the gluon fusion channel results in a decrease of the gluon-gluon fusion background to electroweak Higgs plus two jet production upon requiring exclusive two-jet topologies. We study this effect in detail and contrast in particular a central jet veto with a global jet multiplicity requirement.

A novel determination of non-perturbative contributions to Bjorken sum rule

Based on the operator product expansion, the perturbative and nonperturbative contributions to the polarized Bjorken sum rule (BSR) can be separated conveniently, and the nonperturbative one can be fitted via a proper comparison with the experimental data. In the paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Basing on the accurate pQCD prediction of BSR, we then give a novel fit of the non-perturbative high-twist contributions by comparing with JLab data. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic and strict way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate alpha _s-running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low Q^2-region, the effective momentum of the process is small and in order to derive a reliable prediction, we adopt four low-energy alpha _s models to do the analysis, i.e. the model based on the analytic perturbative theory (APT), the Webber model (WEB), the massive pQCD model (MPT) and the model under continuum QCD theory (CON). Our predictions show that even though the high-twist terms are generally power suppressed in high Q^2-region, they shall have sizable contributions in low and intermediate Q^2 domain. Based on the more accurate scheme-and-scale independent pQCD prediction, our newly fitted results for the high-twist corrections at Q^2=1;mathrm{GeV}^2 are, f_2^{p-n}|_{mathrm{APT}}=-0.120pm 0.013, f_2^{p-n}|_mathrm{WEB}=-0.081pm 0.013, f_2^{p-n}|_{mathrm{MPT}}=-0.128pm 0.013 and f_2^{p-n}|_{mathrm{CON}}=-0.139pm 0.013; mu _6|_mathrm{APT}=0.003pm 0.000, mu _6|_{mathrm{WEB}}=0.001pm 0.000, mu _6|_mathrm{MPT}=0.003pm 0.000 and mu _6|_{mathrm{CON}}=0.002pm 0.000, respectively, where the errors are squared averages of those from the statistical and systematic errors from the measured data.

Precision studies for Drell\u2013Yan processes at NNLO

We present a detailed comparison of the fixed-order predictions computed by four publicly available computer codes for Drell–Yan processes at the LHC and Tevatron colliders. We point out that while there is agreement among the predictions at the next-to-leading order accuracy, the predictions at the next-to-next-to-leading order (NNLO) differ, whose extent depends on the observable. The sizes of the differences in general are at least similar, sometimes larger than the sizes of the NNLO corrections themselves. We demonstrate that the neglected power corrections by the codes that use global slicing methods for the regularization of double real emissions can be the source of the differences. Depending on the fiducial cuts, those power corrections become linear, hence enhanced as compared to quadratic ones that are considered standard.

Fiducial qT resummation of color-singlet processes at N3LL+NNLO

We present a framework for qT resummation at N3LL+NNLO accuracy for arbitrary color-singlet processes based on a factorization theorem in SCET. Our implementation CuTe-MCFM is fully differential in the Born kinematics and matches to large-qT fixed-order predictions at relative order {alpha}_s^2 . It provides an efficient way to estimate uncertainties from fixed-order truncation, resummation, and parton distribution functions. In addition to W±, Z and H production, also the diboson processes γγ, Zγ, ZH and W±H are available, including decays. We discuss and exemplify the framework with several direct comparisons to experimental measurements as well as inclusive benchmark results. In particular, we present novel results for γγ and Zγ at N3LL+NNLO and discuss in detail the power corrections induced by photon isolation requirements.

MiNNLO_{text {PS}}: optimizing 2rightarrow 1 hadronic processes

We consider the MiNNLO_mathrm{PS} method to consistently combine next-to-next-to-leading order (NNLO) QCD calculations with parton-shower simulations. We identify the main sources of differences between MiNNLO_mathrm{PS} and fixed-order NNLO predictions for inclusive observables due to corrections beyond NNLO accuracy and present simple prescriptions to either reduce or remove them. Refined predictions are presented for Higgs, charged- and neutral-current Drell Yan production. The agreement with fixed-order NNLO calculations is considerably improved for inclusive observables and scale uncertainties are reduced. The codes are released within the POWHEG-BOX.

Defiducialization: providing experimental measurements for accurate fixed-order predictions

An experimental procedure is proposed to perform measurements of differential cross sections for vector boson production which can be compared to fixed-order QCD predictions with improved accuracy. The procedure relies on applying theoretical acceptance corrections computed as a function of the transverse momentum of the W/Z boson, p_T, to the experimental measurement, rather than comparing data directly against fiducial fixed-order predictions. It is demonstrated that, contrary to standard fiducial computations, these acceptance factors vary little at low p_T, so they can be reliably computed using fixed-order perturbation theory. An example analysis is performed using the ATLAS measurement of the Z-boson production cross section at center-of-mass energy of 8 TeV. The resulting full phase space measurement of the cross section differential in the boson rapidity is compared to theoretical predictions computed with next-to-next-to leading-order accuracy in QCD. Further extensions of the approach which include different types of measurements and improved theoretical predictions are discussed.

The Zγ transverse-momentum spectrum at NNLO+N3LL

We consider the transverse-momentum (pT) distribution of Zγ pairs produced in hadronic collisions. Logarithmically enhanced contributions at small pT are resummed to all orders in QCD perturbation theory and combined with the fixed-order prediction. We achieve the most advanced prediction for the ZγpT spectrum by matching next-to-next-to-next-to-leading logarithmic (N3LL) resummation to the integrated cross section at next-to-next-to-leading order (NNLO). By considering ℓ+ℓ−γ production at the fully differential level, including spin correlations, interferences and off-shell effects, arbitrary cuts can be applied to the leptons and the photon. We present results at the LHC in presence of fiducial cuts and find agreement with the 13TeV ATLAS data at the few-percent level.

W+W− production at the LHC: NLO QCD corrections to the loop-induced gluon fusion channel

We compute the NLO QCD corrections to the loop-induced gluon fusion contribution in W+W− production at the LHC. We consider the full leptonic process pp→ℓ+ℓ′−νℓν¯ℓ′+X, by including resonant and non-resonant diagrams, spin correlations and off-shell effects. Quark–gluon partonic channels are included for the first time in the calculation, and our results are combined with NNLO predictions to the quark annihilation channel at the fully differential level. The computed corrections, which are formally of O(αS3), increase the NNLO cross section by only about 2%, but have an impact on the shapes of kinematical distributions, in part due to the jet veto, which is usually applied to reduce the top-quark background. Our results, supplemented with NLO EW effects, provide the most advanced fixed-order predictions available to date for this process, and are compared with differential ATLAS data at s=13TeV.

Jet cross sections at the LHC and the quest for higher precision

We perform a phenomenological study of Z plus jet, Higgs plus jet and di-jet production at the Large Hadron Collider. We investigate in particular the dependence of the leading jet cross section on the jet radius as a function of the jet transverse momentum. Theoretical predictions are obtained using perturbative QCD calculations at the next-to and next-to-next-to-leading order, using a range of renormalization and factorization scales. The fixed order predictions are compared to results obtained from matching next-to-leading order calculations to parton showers. A study of the scale dependence as a function of the jet radius is used to provide a better estimate of the scale uncertainty for small jet sizes. The non-perturbative corrections as a function of jet radius are estimated from different generators.

Pseudoscalar quarkonium+\u03b3 production at NLL+NLO accuracy

We consider the exclusive pseudoscalar heavy-quarkonium (ηb, c) production in association with a photon at future lepton colliders where the collider energies of O(102) GeV are far greater than the quarkonium mass. At these energies, the logarithm of mass to collision energy becomes increasingly large hence its resummation becomes particularly important. By making use of the light-cone-distribution factorization formula, we resum the logarithms up to next-to-leading-logarithmic accuracy (NLL) that corresponds to order-αs accuracy. We combine the resummed result with a known fixed-order result at next-to-leading order (NLO) such that both resummed-logarithmic terms and non-logarithmic terms are included at the same order in αs. This allowed us to provide reliable predictions at accuracies of order αs ranging from relatively low energies near quarkonium mass to the collider energies of O(102) GeV. We also include the leading relativistic corrections resummed at leading-logarithmic accuracy. Our prediction at the Belle energy is comparable with fixed-order predictions in literatures while it shows a large deviation from a recent Belle’s upper limit by about 4 σ. Finally, we make predictions for the energies of future Z - and Higgs factories.

Erratum to: NNLO QCD corrections for Drell-Yan p T Z and ϕ η * observables at the LHC

We correct an error in the implementation of the NNLO corrections, which modifies the numerical predictions. In the light of these modifications, we re-assess the kinematical range of applicability of the fixed-order NNLO predictions.

Threshold resummation of the rapidity distribution for Drell-Yan production at NNLO+NNLL

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 detailed numerical comparison against other approaches that resum certain threshold logarithms in Mellin-Fourier space. Our predictions at NNLL level are close to theirs even though at leading logarithmic and next-to-leading logarithmic level we differ. We have also investigated the impact of these threshold logarithms on the stability of perturbation theory against factorisation and renormalisation scales. While the dependence on these scales does not get better with resummed results, the convergence of the perturbative series shows a better trend compared to the fixed order predictions. This is evident from the reduction in the K-factor for the resummed case compared to fixed order. We also present the uncertainties on the predictions resulting from parton distribution functions.