Resummation Of Logarithms Research Articles

Renormalization-group improved resummation of super-leading logarithms

A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

A partitioned dipole-antenna shower with improved transverse recoil

The implementation of a new final-state parton-shower algorithm in the Pythia event generator is described. The shower algorithm, dubbed Apollo, combines central aspects of the Vincia antenna shower with the global transverse-recoil scheme of the Alaric framework in order to achieve formal consistency with next-to-leading logarithmic (NLL) resummation. The shower algorithm is constructed in such a way that it facilitates a straightforward combination with fixed-order calculations. As an explicit proof of concept, a general scheme for matrix-element corrections (MECs) and two separate multiplicative next-to-leading order (NLO) matching schemes are outlined. It is argued that both matching schemes retain the logarithmic accuracy of the shower. The improved modelling of radiation is examined by contrasting the new algorithm with existing leading-logarithmic parton showers in Pythia.

Automated resummation of electroweak Sudakov logarithms in diboson production at future colliders

At energies that are large with respect to the electroweak scale, the electroweak corrections to scattering processes involve large logarithms that have to be resummed to obtain decent predictions. Soft-collinear effective theory (SCET) has been proposed as a suitable framework to allow for this resummation, while retaining non-logarithmic corrections in a consistent way. In this paper, we investigate the approximations needed to use this approach for the calculation of electroweak corrections to off-shell diboson production at high-energy colliders. Upon implementing the method into a Monte-Carlo integration code, we provide resummed predictions for cross sections and distributions at a 3TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3\\,\ ext {TeV} $$\\end{document} lepton collider and a 100TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100\\,\ ext {TeV} $$\\end{document} proton collider.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Resummation of Next-to-Leading Nonglobal Logarithms at the LHC.

In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as nonglobal logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading nonglobal logarithms remained a challenge that we solve in this Letter using renormalization group methods in effective field theory. To achieve next-to-leading logarithmic accuracy, we implement the two-loop anomalous dimension governing the resummation of nonglobal logarithms into a large-N_{c} parton shower framework, together with one-loop matching corrections. As a first application, we study the interjet energy flow in e^{+}e^{-} annihilation into two jets. We then present, for the first time, resummed predictions at next-to-leading logarithmic accuracy for a gap-between-jets observable at hadron colliders.

Factorization of non-global LHC observables and resummation of super-leading logarithms

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy ŝ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\hat{s}} $$\\end{document}, and low-energy matrix elements, which are sensitive to the low scale Q0 ≪ ŝ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\hat{s}} $$\\end{document} characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary 2 → M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called “super-leading logarithms” discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp → 2 jets processes, but suppressed in H/Z and H/Z + jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.

A high-energy QCD portal to exotic matter: Heavy-light tetraquarks at the HL-LHC

By taking advantage of the natural stability of the high-energy resummation, recently discovered in the context of heavy-flavor studies, we investigate the inclusive hadroproduction of a neutral heavy-light, hidden-flavored tetraquark (Xcuc¯u¯ or Xbsb¯s¯ state), in association with a heavy (single c- or b-flavored) hadron or a light jet at the (HL-)LHC. We make use of the JETHAD multi-modular working package to provide predictions for rapidity, azimuthal-angle and transverse-momentum distributions calculated via the hybrid high-energy and collinear factorization, where the Balitsky–Fadin–Kuraev–Lipatov resummation of energy logarithms is supplemented by collinear parton densities and fragmentation functions. We rely upon the single-parton fragmentation mechanism, valid in the large transverse-momentum regime, to describe the tetraquark production. Our study represents a first attempt at bridging the gap between all-order calculations of high-energy QCD and the exotics.

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.

NNLL resummation of Sudakov shoulder logarithms in the heavy jet mass distribution

The heavy jet mass event shape has large perturbative logarithms near the leading order kinematic threshold at ρ=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\rho =\\frac{1}{3} $$\\end{document}. Catani and Webber named these logarithms Sudakov shoulders and resummed them at double-logarithmic level. A resummation to next-to-leading logarithmic level was achieved recently. Here, we extend the resummation using an effective field theory framework to next-to-next-to-leading logarithmic order and show how to combine it with the resummation of dijet logarithms. We also solve the open problem of an unphysical singularity in the resummed momentum space distribution, in a way similar to how it is resolved in the Drell-Yan qT spectrum: through a careful analysis of the kinematics and scale-setting in position space. The heavy jet mass Sudakov shoulder is the first observable that does not involve transverse momentum for which position space resummation is critical. These advances may lead to a more precise extraction of the strong coupling constant from e+e− data.

Small-x factorization from effective field theory

We derive a factorization theorem that allows for resummation of small-x logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor Wμν in deep inelastic scattering, and leads to the definition of a new gauge invariant soft function Sμν that describes quark and gluon emission in the central region. This soft function provides a new framework for extending resummed calculations for coefficient functions to higher logarithmic orders. Our factorization also defines impact factors by universal collinear functions that are process independent, for instance being identical in small-x DIS and Drell-Yan.

Explaining large electromagnetic logarithms from loops of inflationary gravitons

Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of ln(a). We speculate that the factor of ln(Hr) in the Coulomb potential should not be considered as a leading logarithm effect.

Radiative B to tensor meson decays at NLO in SCET

The radiative B to tensor meson decays are studied at next-to-leading order in soft-collinear effective theory (SCET). The SCET allows the systematic treatment of factorizable and non-factorizable contributions along with the resummation of large perturbative logarithms. We performed a two-step matching and determined the soft-overlap function and branching ratios for these B to tensor meson decays. In the case of , the numerical value of the branching ratio lies close to its experimental measurements. The estimated values of the branching ratios of Cabibbo–Kobayashi–Maskawa suppressed decays are significantly small compared to that of , but still could be measured in some ongoing and future B physics experiments.

Threshold resummation for computing large-x parton distribution through large-momentum effective theory

Parton distribution functions (PDFs) at large x are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-x through large-momentum Pz expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale Pz|1 − y| and a pair of heavy-light Sudakov form factors at scale Pz. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-x PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes.

Double Higgs production at NNLO interfaced to parton showers in GENEVA

In this work, we study the production of Higgs boson pairs at next-to-next-to-leading order in QCD matched to parton showers, using the Geneva framework and working in the heavy-top-limit approximation. This includes the resummation of large logarithms of the zero-jettiness mathcal{T} 0 up to the next-to-next-to-next-to-leading-log accuracy. This process features an extremely large momentum transfer, which makes its study particularly relevant for matching schemes such as that employed in Geneva, where the resummation of a variable different from that used in the ordering of the parton shower is used. To further study this effect, we extend the original shower interface designed for Pythia8 to include other parton showers, such as Dire and Sherpa.

Precision control in lattice calculation of x-dependent pion distribution amplitude

We present a new Bjorken x-dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing a=0.06,0.09,0.12 fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum xPz and the antiquark momentum (1−x)Pz inside a meson of boost momentum Pz up to 1.72 GeV along the z direction, allowing us to have more accurate determination of the x-dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions x∼0,1, thus obtaining the full-range x-dependence of the amplitude.

Measurements of the groomed jet radius and momentum splitting fraction with the soft drop and dynamical grooming algorithms in pp collisions at sqrt{s} = 5.02 TeV

This article presents measurements of the groomed jet radius and momentum splitting fraction in pp collisions at sqrt{s} = 5.02 TeV with the ALICE detector at the Large Hadron Collider. Inclusive charged-particle jets are reconstructed at midrapidity using the anti-kT algorithm for transverse momentum 60<{p}_{textrm{T}}^{textrm{ch};textrm{jet}}<80 GeV/c. We report results using two different grooming algorithms: soft drop and, for the first time, dynamical grooming. For each grooming algorithm, a variety of grooming settings are used in order to explore the impact of collinear radiation on these jet substructure observables. These results are compared to perturbative calculations that include resummation of large logarithms at all orders in the strong coupling constant. We find good agreement of the theoretical predictions with the data for all grooming settings considered.

Dead-cone searches in heavy-ion collisions using the jet tree

We explore the possibility of using the dead cone of heavy quarks as a region of the Lund plane where medium-induced gluon radiation can be isolated and characterised. The filling of the dead cone by medium-induced gluons is expected to be the result of the interplay between the minimum angle of such radiation due to transverse momentum broadening and the dead-cone angle. Since the measurement of a fully corrected Lund plane in heavy-ion collisions is currently challenging, we propose to use jet grooming techniques to identify a particular splitting in the jet tree that is both perturbative and sensitive to the dead-cone effect. To that end, we propose a new jet substructure groomer, dubbed Late-$k_t$, that selects the most collinear splitting in a QCD jet above a certain transverse momentum cutoff $k_{t,\rm{cut}}$. The role of $k_{t,\rm{cut}}$ is to guarantee perturbative splittings, while selecting the most collinear splitting enhances the sensitivity to mass effects. As a proof of concept, we study the angular distribution of the splitting tagged by Late-$k_t$ both analytically and with Monte Carlo simulations. First, we derive the logarithmic resummation structure in vacuum and demonstrate its capability to distinguish between inclusive and heavy-flavoured jets. Next, we extend the calculation for in-medium jets and show that medium-induced emissions lead to an enhancement of collinear emissions below the dead cone angle. Numerically, we demonstrate an excellent resilience of Late-$k_t$ against uncorrelated thermal background, thus confirming this observable as a potential candidate to unveil medium dynamics around the dead cone regime.

Emergence of high-energy dynamics from cascade-baryon detections at the LHC

We propose the inclusive detection at the LHC of a cascade Xi ^-/bar{Xi }^+ baryon in association with a jet, as a novel probe channel for the QCD dynamics at high energies. We investigate the behavior of a selection of distributions, differential in rapidity, azimuthal angle and/or transverse momenta, calculated via the hybrid high-energy/collinear factorization encoding the full next-to-leading BFKL resummation of energy logarithms. We come out with the conclusion that the fragmentation mechanism underlying the production of Xi ^-/bar{Xi }^+ baryon states leads to stabilization effects of the resummation, similar to those recently observed in the context of heavy-flavor studies within the same formalism.

Resummation of threshold logarithms in deeply-virtual Compton scattering

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to frac{alpha_s^n}{xpm xi } log {left(frac{xi pm x}{2xi}right)}^k in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the x → ±ξ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.

Azimuthal decorrelation for photon induced dijet production in ultra-peripheral collisions of heavy ions

We study the azimuthal angular decorrelation of the dijet production via photon fusion in ultra-peripheral heavy ion collisions. The impact parameter dependent cross section of quark-antiquark pairs production is derived using the equivalent photon approximation, and the contribution from final-state QCD radiations to the azimuthal angular distribution are calculated within Soft-Collinear Effective Theory. We carry out the QCD resummation of large logarithms of the azimuthal angle as well as the jet radius at next-to-leading logarithmic accuracy. In the end we present the normalized differential cross section for azimuthal decorrelation of the dijet pair and find that our results are consistent with the measurements reported by the ATLAS collaboration.