Leading-logarithmic Accuracy Research Articles

A fragmentation approach to jet flavor

An intuitive definition of the partonic flavor of a jet in quantum chromodynamics is often only well-defined in the deep ultraviolet, where the strong force becomes a free theory and a jet consists of a single parton. However, measurements are performed in the infrared, where a jet consists of numerous particles and requires an algorithmic procedure to define their phase space boundaries. To connect these two regimes, we introduce a novel and simple partonic jet flavor definition in the infrared. We define the jet flavor to be the net flavor of the partons that lie exactly along the direction of the Winner-Take-All recombination scheme axis of the jet, which is safe to all orders under emissions of soft particles, but is not collinear safe. Collinear divergences can be absorbed into a perturbative fragmentation function that describes the evolution of the jet flavor from the ultraviolet to the infrared. The evolution equations are linear and a small modification to traditional DGLAP and we solve them to leading-logarithmic accuracy. The evolution equations exhibit fixed points in the deep infrared, we demonstrate quantitative agreement with parton shower simulations, and we present various infrared and collinear safe observables that are sensitive to this flavor definition.

The soft drop momentum sharing fraction zg beyond leading-logarithmic accuracy

Grooming techniques, such as soft drop, play a central role in reducing sensitivity of jets to e.g. underlying event and hadronization at current collider experiments. The momentum sharing fraction zg, of the two branches in a jet that pass the soft drop condition, is one of the most important observables characterizing a collinear splitting inside the jet, and directly probes the QCD splitting functions. In this work, we present a factorization framework that enables a systematic calculation of the corresponding cross section beyond modified leading-logarithmic (MLL) accuracy, showing that this measurement is not only sensitive to the QCD charge but also the spin of the parton that initiates the jet. Our results at next-to-leading logarithmic (NLL′) accuracy include non-global logarithms, and provide a first meaningful assessment of the perturbative uncertainty. We present a comparison to the available experimental data from ALICE, ATLAS, and STAR and find excellent agreement.

Leading jets and energy loss

The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL′) accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.

Measurement of hadronic event shapes in high-pT multijet final states at sqrt{s} = 13 TeV with the ATLAS detector

A measurement of event-shape variables in proton-proton collisions at large momentum transfer is presented using data collected at sqrt{s} = 13 TeV with the ATLAS detector at the Large Hadron Collider. Six event-shape variables calculated using hadronic jets are studied in inclusive multijet events using data corresponding to an integrated luminosity of 139 fb−1. Measurements are performed in bins of jet multiplicity and in different ranges of the scalar sum of the transverse momenta of the two leading jets, reaching scales beyond 2 TeV. These measurements are compared with predictions from Monte Carlo event generators containing leading-order or next-to-leading order matrix elements matched to parton showers simulated to leading-logarithm accuracy. At low jet multiplicities, shape discrepancies between the measurements and the Monte Carlo predictions are observed. At high jet multiplicities, the shapes are better described but discrepancies in the normalisation are observed.

Parton Showers beyond Leading Logarithmic Accuracy.

Parton showers are among the most widely used tools in collider physics. Despite their key importance, none so far have been able to demonstrate accuracy beyond a basic level known as leading logarithmic order, with ensuing limitations across a broad spectrum of physics applications. In this Letter, we propose criteria for showers to be considered next-to-leading logarithmic accurate. We then introduce new classes of shower, for final-state radiation, that satisfy the main elements of these criteria in the widely used large-N_{C} limit. As a proof of concept, we demonstrate these showers' agreement with all-order analytical next-to-leading logarithmic calculations for a range of observables, something never so far achieved for any parton shower.

Threshold factorization of the Drell-Yan process at next-to-leading power

We present a factorization theorem valid near the kinematic threshold z={Q}^2/hat{s}to 1 of the partonic Drell-Yan process qoverline{q}to {gamma}^{ast }+X for general subleading powers in the (1 − z) expansion. We then consider the specific case of next-to-leading power. We discuss the emergence of collinear functions, which are a key ingredient to factorization starting at next-to-leading power. We calculate the relevant collinear functions at mathcal{O}left({alpha}_sright) by employing an operator matching equation and we compare our results to the expansion-by- regions computation up to the next-to-next-to-leading order, finding agreement. Factorization holds only before the dimensional regulator is removed, due to a divergent convolution when the collinear and soft functions are first expanded around d = 4 before the convolution is performed. This demonstrates an issue for threshold resummation beyond the leading-logarithmic accuracy at next-to-leading power.

Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power

Perturbative cross-sections in QCD are beset by logarithms of kinematic invariants, whose arguments vanish when heavy particles are produced near threshold. Contributions of this type often need to be summed to all orders in the coupling, in order to improve the behaviour of the perturbative expansion, and it has long been known how to do this at leading power in the threshold variable, using a variety of approaches. Recently, the problem of extending this resummation to logarithms suppressed by a single power of the threshold variable has received considerable attention. In this paper, we show that such next-to-leading power (NLP) contributions can indeed be resummed, to leading logarithmic (LL) accuracy, for any QCD process with a colour-singlet final state, using a direct generalisation of the diagrammatic methods available at leading power. We compare our results with other approaches, and comment on the implications for further generalisations beyond leading-logarithmic accuracy.

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.

Sea quark Sivers distribution

We compute sea quark Sivers distribution within color glass condensate (CGC) framework. It has been found that up to the leading logarithm accuracy, the collinear twist-3 approach and the CGC calculation yield the same result for sea quark Sivers distribution in the dilute limit. We further verify that transverse momentum dependent factorization is consistent with CGC treatment at small x for the case of transverse single spin asymmetry in open charm quark production in semi-inclusive deeply inelastic scattering process in an overlap kinematical region.

Jet Topics: Disentangling Quarks and Gluons at Colliders.

We introduce jet topics: a framework to identify underlying classes of jets from collider data. Because of a close mathematical relationship between distributions of observables in jets and emergent themes in sets of documents, we can apply recent techniques in "topic modeling" to extract jet topics from the data with minimal or no input from simulation or theory. As a proof of concept with parton shower samples, we apply jet topics to determine separate quark and gluon jet distributions for constituent multiplicity. We also determine separate quark and gluon rapidity spectra from a mixed Z-plus-jet sample. While jet topics are defined directly from hadron-level multidifferential cross sections, one can also predict jet topics from first-principles theoretical calculations, with potential implications for how to define quark and gluon jets beyond leading-logarithmic accuracy. These investigations suggest that jet topics will be useful for extracting underlying jet distributions and fractions in a wide range of contexts at the Large Hadron Collider.

Jet substructure studies with CMS open data

We use public data from the CMS experiment to study the 2-prong substructure of jets. The CMS Open Data is based on 31.8/pb of 7 TeV proton-proton collisions recorded at the Large Hadron Collider in 2010, yielding a sample of 768,687 events containing a high-quality central jet with transverse momentum larger than 85 GeV. Using CMS's particle flow reconstruction algorithm to obtain jet constituents, we extract the 2-prong substructure of the leading jet using soft drop declustering. We find good agreement between results obtained from the CMS Open Data and those obtained from parton shower generators, and we also compare to analytic jet substructure calculations performed to modified leading-logarithmic accuracy. Although the 2010 CMS Open Data does not include simulated data to help estimate systematic uncertainties, we use track-only observables to validate these substructure studies.

Casimir meets Poisson: improved quark/gluon discrimination with counting observables

Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a “soft drop multiplicity” which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.

Saturation in inclusive production beyond leading logarithm accuracy

We review the recent progress on the calculations on the inclusive forward hadron production within the saturation formalism. After introducing the concept of perturbative parton saturation and nonlinear evolution we discuss the formalism for the forward hadron production at high energy in the leading and next-to-leading order. Numerical results are presented and compared with the experimental data on forward hadron production in [Formula: see text] and [Formula: see text]. We discuss the problem of the negativity of the NLO cross-section at high transverse momenta, study its origin in detail and present possible improvements which include the corrected kinematics and the suitable choice of the rapidity cutoff.

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

Gluon saturation beyond (naive) leading logs

Abstract An improved version of the Balitsky–Kovchegov equation is presented, with a consistent treatment of kinematics. That improvement allows to resum the most severe of the large higher order corrections which plague the conventional versions of high-energy evolution equations, with approximate kinematics. This result represents a further step towards having high-energy QCD scattering processes under control beyond strict Leading Logarithmic accuracy and with gluon saturation effects.

A QCD description of the ATLAS jet veto measurement

We present a new QCD description of the ATLAS jet veto measurement, using the Banfi-Marchesini-Smye equation to constrain the inter-jet QCD radiation. This equation resums emissions of soft gluons at large angles, at leading-logarithmic accuracy, and accounts for both the so-called Sudakov and non-global logarithms. We show that this approach is able to reproduce, with no fitting parameters, the fraction of high-pT forward/backward di-jet events which do not contain additional hard emissions in the inter-jet rapidity range. We also compute the gap fraction in fixed-order perturbation theory to O(alpha_s^2) and show that the perturbative series is unstable at large rapidity intervals.

Determination ofαsfrom the QCD static energy

We compare lattice data for the short-distance part of the static energy in $2+1$ flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale ${r}_{0}$ with the QCD scale ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$. With the input of the value of ${r}_{0}$, this provides a determination of the strong coupling ${\ensuremath{\alpha}}_{s}$ at the typical distance scale of the lattice data. We obtain ${\ensuremath{\alpha}}_{s}(1.5\text{ }\text{ }\mathrm{GeV})=0.326\ifmmode\pm\else\textpm\fi{}0.019$, which provides a novel determination of ${\ensuremath{\alpha}}_{s}$ with three-loop accuracy (including resummation of the leading ultrasoft logarithms), and constitutes one of the few low-energy determinations of ${\ensuremath{\alpha}}_{s}$ available. When this value is evolved to the $Z$-mass scale ${M}_{Z}$, it corresponds to ${\ensuremath{\alpha}}_{s}({M}_{Z})={0.1156}_{\ensuremath{-}0.0022}^{+0.0021}$.

Precision Determination ofr0ΛMS¯from the QCD Static Energy

We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r₀ΛMS by comparison with available lattice data, where r₀ is the lattice scale and ΛMS is the QCD scale. We obtain r₀ΛMS=0.637(+0.032)(-0.030) [corrected] for the zero-flavor case. The procedure we describe can be directly used to obtain r₀ΛMS in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling α(s) as an input, the unquenched result would provide a determination of the lattice scale r₀.

NJettiness: An Inclusive Event Shape to Veto Jets

Jet vetoes are essential in many analyses at the LHC and Tevatron. Typical signals have a specific number of hard jets or leptons, while backgrounds have additional jets. Vetoing undesired jets efficiently discriminates signal and background. For a sample with ≥N jets, the veto to give N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space and causes large double logarithms in perturbation theory that must be summed. Jet vetoes are typically implemented using jet algorithms, yielding complicated phase-space restrictions, and reliance on leading-log parton-shower Monte Carlo simulations. We introduce a global event shape "N jettiness" τN, which is defined for events with N signal jets. Requiring τN≪1 constrains radiation between the signal jets and provides a theoretically well-controlled jet veto. N jettiness yields a factorization formula with inclusive jet and beam functions.

QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy

We compute the static energy of QCD at short distances at next-to-next-to-next-to-leading logarithmic accuracy in terms of the three-loop singlet potential. By comparing our results with lattice data we extract the value of the unknown piece of the three-loop singlet potential.