Soft-gluon Resummation Research Articles

Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders

We consider extensions of the soft-gluon effective coupling that generalize the Catani-Marchesini-Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD β function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling αS. In d = 4 dimensions we obtain the explicit relation between the soft couplings at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αS3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_{\ extrm{S}}^3 $$\\end{document}). Finally, we study the structure of the soft coupling in the large-nF limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-nF results agree with the known result of the cusp anomalous dimension.

A consistent resummation of mass and soft logarithms in processes with heavy flavours

Perturbative calculations for processes that involve heavy flavours can be performed in two approaches: the massive scheme and the massless one. The former enables one to fully account for the heavy-quark kinematics, while the latter allows one to resum potentially-large mass logarithms. Furthermore, the two schemes can be combined to take advantage of the virtues of each of them. Both massive and massless calculations can be supplemented by soft-gluon resummation. However matching between massive and massless resummed calculations is difficult, essentially because of the non-commutativity of the soft and massless limits. In this paper, we develop a formalism to combine resummed massive and massless calculations. We obtain an all-order expression that consistently resums both mass and soft logarithms to next-to-leading logarithmic accuracy. We perform detailed calculations for the decay of the Higgs into a heavy-quark pair, and discuss the applications of this formalism to different processes.

Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell–Yan production in proton–proton collisions at sqrt{s} = 13,text {Tehspace{-.08em}V}

The double differential cross sections of the Drell–Yan lepton pair (ell ^+ell ^-, dielectron or dimuon) production are measured as functions of the invariant mass m_{ell ell }, transverse momentum p_{textrm{T}} (ell ell ), and varphi ^{*}_{eta }. The varphi ^{*}_{eta } observable, derived from angular measurements of the leptons and highly correlated with p_{textrm{T}} (ell ell ), is used to probe the low-p_{textrm{T}} (ell ell ) region in a complementary way. Dilepton masses up to 1,text {Tehspace{-.08em}V} are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various m_{ell ell } ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3,text {fb}^{-1} of proton–proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13,text {Tehspace{-.08em}V}. Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

NNLO B-fragmentation fits and their application to toverline{t} production and decay at the LHC

In this work we derive three sets of non-perturbative fragmentation functions, with uncertainties, for B-hadrons, J/ψ’s and muons resulting from semileptonic B decays. All three sets are with next-to-next-to leading order accuracy and include next-to-next-to leading logarithmic soft gluon resummation. The novel feature of these new sets is that they are fully consistent with our formalism for next-to-next-to leading order (NNLO) calculations for final states with identified B, J/ψ or a μ. We employ the fragmentation functions derived in this work to make state of the art predictions for such final states in toverline{t} events at the LHC. A special emphasis is placed on observables sensitive to the top quark mass. The present work opens the door for many LHC applications, like, open B production or B production in association with bosons.

On soft gluon resummation for associated single top production with a Higgs boson at the LHC

We investigate threshold resummation of soft gluon corrections for the s-channel process of a single top quark production in association with a Higgs boson in the Standard Model. We choose to work in the three-particle invariant mass kinematics in direct QCD, i.e. in the space of Mellin moments. Our results take into account terms of up to next-to-leading logarithmic (NLL) precision, as well as {mathcal {O}} (alpha _{textrm{s}}) non-logarithmic terms which do not vanish at threshold. After presenting analytical expressions, we discuss the corresponding numerical results for the total cross section and the invariant mass distribution at the LHC.

N3LO+N3LL QCD improved Higgs pair cross sections

We report a new calculation of the soft-gluon threshold resummation for the Higgs boson pair production in the dominant production mode — gluon-gluon fusion — up to the next-to-next-to-next-to-leading logarithmic (N3LL) accuracy. After matching N3LL to the next-to-next-to-next-to-leading order (N3LO) QCD calculation in the infinite top quark mass approximation, we show that the central values of the inclusive cross sections are quite stable with respect to N3LO, while the conventional renormalisation and factorisation scale uncertainties are reduced by a factor of two, reaching to the subpercent level. Our study further consolidates the good asymptotic perturbative convergence. After combining with the full top-quark mass dependent next-to-leading order QCD results, our most advanced predictions are presented for both the inclusive total cross sections and the differential invariant mass distributions of the Higgs pair.

Soft photon bremsstrahlung at next-to-leading power

The emission of soft radiation provides a fundamental probe of the consistency of the underlying quantum field theory. Correspondingly, the measurement of the soft photon bremsstrahlung, such as the one proposed with the planned future upgrade of the ALICE experiment at the LHC, is of great interest. In this letter we explore the possibility to implement analytic techniques that have been recently developed for soft gluon resummation at Next-to-Leading-Power (NLP) in the context of the soft photon spectrum. We provide a formula for the differential cross-section with shifted kinematics that is particularly suitable for numerical implementations. We also discuss the impact of loop corrections to Low's theorem due to radiative jet functions.

Drell-Yan $p_{\bot}$ with NLO-matched Parton Branching TMDs at energies from fixed-target to LHC

The description of the Drell-Yan (DY) transverse momentum spectrum requires matching of fixed order QCD calculations with soft gluon resummation up to all orders in the QCD coupling. It has been noticed in the literature that a consistent description of DY data in a wide kinematic regime from fixed-target to LHC energies is problematic. In this work the predictions for transverse momentum spectrum of DY data coming from experiments in very different kinematic ranges (NuSea, R209, Phenix, LHC 8 TeV and 13 TeV center-of-mass energies \sqrt{s}s) are calculated by applying transverse momentum dependent (TMD) parton distributions obtained from the Parton Branching (PB) method, combined with the next-to-leading-order (NLO) calculation of the hard process in the MCatNLO method. We discuss the problems involved in matching of the fixed order calculation and resummation, especially in the moderate to low mass and p_{\bot}p⊥ region accessible at fixed target experiments. We find that at low DY mass and low \sqrt{s}s even in the region of p_{\bot}/Q\sim 1p⊥/Q∼1 the contribution of multiple soft gluon emissions (included in the PB-TMDs) is essential to describe the measurements, while at larger masses and LHC energies the contribution from soft gluons in the region of p_{\bot}/Q\sim 1p⊥/Q∼1 is small.

Resummation for $tqH$ production

We present results with soft-gluon resummation for the associated production of a single top quark and a Higgs boson. We present analytical results for the higher-order soft-gluon corrections and numerical results for the total cross section and top-quark transverse momentum and rapidity distributions at LHC energies.

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.

Scalar-pseudoscalar pair production at the Large Hadron Collider at NLO+NLL accuracy in QCD * *Supported in part by the National Natural Science Foundation of China (11775211, 12061141005, 11805001, 11935001) and the CAS Center for Excellence in Particle Physics (CCEPP)

We thoroughly investigate both transverse momentum and threshold resummation effects on scalar-pseudoscalar pair production via quark-antiquark annihilation at the Large Hadron Collider at QCD NLO+NLL accuracy. A factorization method is introduced to properly supplement the soft-gluon (threshold) resummation contribution from parton distribution functions to the resummed results obtained by the Collins-Soper-Sterman resummation approach. We find that the impact of the threshold-resummation improved PDFs is comparable to the resummation effect of the partonic matrix element and can even predominate in high invariant mass regions. Moreover, the loop-induced gluon-gluon fusion channel in the type-I two-Higgs-doublet model is considered in our calculations. The numerical results show that the electroweak production via quark-antiquark annihilation dominates over the gluon-initiated QCD production by orders of magnitude.

Azimuthal angular asymmetry of soft gluon radiation in jet production

We investigate the impact of soft gluon resummation on the azimuthal angle correlation between the total and relative momenta of two energetic final state particles (jets). We show that the initial and final state radiations induce sizable $\cos(\phi)$ and $\cos (2\phi)$ asymmetries in single jet and dijet events, respectively. We numerically evaluate the magnitude of these asymmetries for a number of processes in collider experiments, including diffractive dijet and dilepton production in ultraperipheral $pA$ and $AA$ collisions, inclusive and diffractive dijet production at the EIC and inclusive dijet production in $pp$ collisions at the LHC. In particular, the $\cos (2\phi)$ asymmetry of perturbative origin can dominate over the primordial asymmetry due to the linearly polarized gluon distribution.

Soft-gluon corrections for the associated production of a single top quark and a Higgs boson

We discuss soft-gluon resummation for the associated production of a single top quark and a Higgs boson ($tqH$ production) in single-particle-inclusive (1PI) kinematics. We present analytical results for the higher-order corrections and numerical results for the cross sections at LHC energies. We calculate approximate NNLO total rates, including scale dependence and uncertainties from parton distributions, as well as top-quark transverse-momentum and rapidity distributions. In all cases we find that the soft-gluon corrections are dominant and provide important contributions to the total and differential cross sections.

Numerical resummation at subleading color in the strongly ordered soft gluon limit

We present a Monte Carlo approach to soft-gluon resummation at subleading color which can be used to improve existing parton shower algorithms. At the single-emission level, soft-collinear enhancements of the splitting functions are explicitly linked to quadratic Casimir operators, while wide angle single-soft enhancements are connected to nontrivial color correlators. We focus on a numerically stable implementation of color matrix element corrections to all orders and approximate the virtual corrections by requiring unitarity at the single-emission level. We provide a proof-of-concept implementation to compute nonglobal event shapes at lepton colliders.

The role of the threshold variable in soft-gluon resummation of the toverline{t}h production process

We study the role of the scale of the threshold variable in soft-gluon threshold resummation. We focus on the computation of the resummed total cross section, the final-state invariant-mass distribution, and transverse-momentum distribution of the Higgs boson when produced in association with a top-anti-top quark pair for the Large Hadron Collider operating at 13 TeV. We show that different choices for the scale of the threshold variable result in differences at next-to-leading power, i.e. contributions that are down by one power of the threshold variable. These contributions are noticeable numerically, although their effect on the resummed observables lies within the scale uncertainty of those observables. The average central results, obtained after combining several central- scale choices, agree remarkably well for different choices of the threshold variable. However, different threshold choices do affect the resulting scale uncertainty. To compute our results, we introduce a novel numerical method that we call the deformation method, which aids the stabilization of the inverse Mellin transform in cases where the analytical Mellin transform of the partonic cross section is unknown. We show that this method leads to a factor of 10 less function evaluations, while gaining a factor of 4 − 5 in numerical precision when compared to the standard method.

Soft Anomalous Dimensions and Resummation in QCD

I discuss and review soft anomalous dimensions in QCD that describe soft-gluon threshold resummation for a wide range of hard-scattering processes. The factorization properties of the cross section in moment space and renormalization-group evolution are implemented to derive a general form for differential resummed cross sections. Detailed expressions are given for the soft anomalous dimensions at one, two, and three loops, including some new results, for a large number of partonic processes involving top quarks, electroweak bosons, Higgs bosons, and other particles in the standard model and beyond.

Resummation for 2→n processes in single-particle-inclusive kinematics

We present a formalism and detailed analytical results for soft-gluon resummation for $2\rightarrow n$ processes in single-particle-inclusive (1PI) kinematics. This generalizes previous work on resummation for $2 \rightarrow 2$ processes in 1PI kinematics. We also present soft anomalous dimensions at one and two loops for certain $2 \rightarrow 3$ processes involving top quarks and Higgs or $Z$ bosons, and we provide some brief numerical results.

Measurement of hbox {t}{bar{hbox {t}}} normalised multi-differential cross sections in {text {p}}{text {p}} collisions at sqrt{s}=13,{text {TeV}} , and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Normalised multi-differential cross sections for top quark pair (hbox {t}{bar{hbox {t}}}) production are measured in proton-proton collisions at a centre-of-mass energy of 13,{text {TeV}} using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of 35.9{,{text {fb}}^{-1}} . The double-differential hbox {t}{bar{hbox {t}}} cross section is measured as a function of the kinematic properties of the top quark and of the hbox {t}{bar{hbox {t}}} system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the hbox {t}{bar{hbox {t}}} system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength alpha _{S} and the top quark pole mass (m_{{text {t}}}^{{text {pole}}}) using several sets of parton distribution functions (PDFs). The measurement of m_{{text {t}}}^{{text {pole}}} exploits the sensitivity of the hbox {t}{bar{hbox {t}}} invariant mass distribution to m_{{text {t}}}^{{text {pole}}} near the production threshold. Furthermore, a simultaneous fit of the PDFs, alpha _{S}, and m_{{text {t}}}^{{text {pole}}} is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of alpha _{S} and m_{{text {t}}}^{{text {pole}}}. The values alpha _{S}(m_{{text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017} and m_{{text {t}}}^{{text {pole}}} = 170.5 pm 0.8 ,{text {GeV}} are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the hbox {t}{bar{hbox {t}}} production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of m_{{text {t}}}^{{text {pole}}} of the order of +1 ,{text {GeV}} , which can be regarded as additional theoretical uncertainty in the current m_{{text {t}}}^{{text {pole}}} extraction.

Drell\u2013Yan production with the CCFM-K evolution

We discuss the Drell–Yan dilepton production using the transverse momentum dependent parton distributions evolved with the Catani–Ciafaloni–Fiorani–Marchesini–Kwieciński (CCFM-K) equations in the single loop approximation. Such equations are obtained assuming angular ordering of emitted partons (coherence) for xsim 1 and transverse momentum ordering for x ll 1. This evolution scheme also contains the Collins–Soper–Sterman (CSS) soft gluon resummation. We make a comparison with a broad class of data on transverse momentum spectra of low mass Drell–Yan dileptons.

TZ' production at hadron colliders

We study the production of a single top quark in association with a heavy extra Z' at hadron colliders in new physics models with and without flavor-changing neutral-current (FCNC) couplings. We use QCD soft-gluon resummation and threshold expansions to calculate higher-order corrections for the total cross section and transverse-momentum distributions for t Z' production. The impact of the uncertainties due to the structure of the proton and scale dependence is also analyzed.