QCD Parton 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.

Five-parton scattering in QCD at two loops

We compute all helicity amplitudes for the scattering of five partons in two-loop QCD in all the relevant flavor configurations, retaining all contributing color structures. We employ tensor projection to obtain helicity amplitudes in the ’t Hooft-Veltman scheme starting from a set of primitive amplitudes. Our analytic results are expressed in terms of massless pentagon functions, and are easy to evaluate numerically. These amplitudes provide important input to investigations of soft-collinear factorization and to studies of the high-energy limit. Published by the American Physical Society 2024

Correcting for cutoff dependence in backward evolution of QCD parton showers

Monte Carlo event generators for hard hadronic collisions depend on the evolution of parton showers backwards from a high-scale subprocess to the hadronization scale. The evolution is treated as a branching process with a sequence of resolvable parton emissions. The criterion of resolvability involves cutoffs that determine the no-emission probability (NEP) for a given range of the evolution scale. Existing event generators neglect cutoff-dependent terms in the NEP that, although formally power-suppressed, can have significant phenomenological effects. We compute such terms and study their consequences. One important result is that it is not possible for the backward shower to faithfully reproduce the cutoff-independent parton distribution functions (PDFs) used to generate it. We show that the computed NEP corrections mitigate but do not eliminate this problem. An alternative approach is to use cutoff-dependent PDFs that are consistent with the uncorrected NEP. Then one must apply cutoff-dependent corrections to hard subprocess matrix elements. We compute those corrections to the first nontrivial order for the Drell-Yan process and for Higgs production by gluon fusion.

Wee partons in QCD and gravity: Double copy and universality

We discuss a quantitative “double copy” between radiation from shockwave collisions in Einstein gravity and in QCD. The correspondence extends to 2 → N amplitudes in Regge asymptotics. The classicalization and unitarization of these amplitudes at maximal occupancy, corresponding to black hole and Color Glass Condensate (CGC) states respectively, are described by the emergent Goldstone dynamics of wee partons. We outline some consequences of the universal dynamics on both sides of the correspondence.

Extracting the jet transport coefficient from hadron suppressions by confronting current NLO parton fragmentation functions

Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ( $$p_{\mathrm{T}}$$ ) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $$A+A$$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $$\hat{q}$$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $$p_{\mathrm{T}}$$ hadron productions, we extract $$\hat{q}$$ quantitatively via a global fit to data for both single hadron and dihadron suppressions and obtain $$\hat{q}/T^3 = 4.74 - 6.72$$ at $$T = 370$$ MeV in central $$Au+Au$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=200$$ GeV, and $$\hat{q}/T^3 = 3.07 - 3.98$$ at $$T = 480$$ MeV in central $$Pb+Pb$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=2.76$$ TeV. The numerical results show that the uncertainties for $$\hat{q}$$ extraction are brought by the different contributions of gluon-to-hadron in the six sets of FFs due to gluon energy loss being 9/4 times of quark energy loss.

Multi-jet merging with TMD parton branching

One of the main theoretical systematic uncertainties in studies of final states with large jet multiplicities at high-energy hadron colliders is associated with the merging of QCD parton showers and hard-scattering matrix elements. We present a method to incorporate the physics of transverse momentum recoils due to initial-state shower evolution into multi-jet merging algorithms by using the concept of transverse momentum dependent (TMD) distributions and the associated parton branching. We investigate the dependence on the merging scale and illustrate the impact of the new method at the level of both exclusive and inclusive final-state observables by studying differential jet rates, transverse momentum spectra and multiplicity distributions, using vector boson + jets events at the LHC as a case study.

Single photon production at hadron colliders at NNLO QCD with realistic photon isolation

Isolated photons at hadron colliders are defined by permitting only a limited amount of hadronic energy inside a fixed-size cone around the candidate photon direction. This isolation criterion admits contributions from collinear photon radiation off QCD partons and from parton-to-photon fragmentation processes. We compute the NNLO QCD corrections to isolated photon and photon-plus-jet production, including these two contributions. Our newly derived results allow us to reproduce the isolation prescription used in the experimental measurements, performing detailed comparisons with data from the LHC experiments. We quantify the impact of different photon isolation prescriptions, including no isolation at all, on photon-plus-jet cross sections and discuss possible measurements of the photon fragmentation functions at hadron colliders.

Disentangling soft and collinear effects in QCD parton showers

We introduce a method for the separation of soft and collinear logarithms in QCD parton evolution at $\mathcal{O}(\alpha_s^2)$ and at leading color. Using an implementation of the technique in the Dire parton shower, we analyze the numerical impact of genuine triple-collinear corrections from quark pair emission in $e^+e^-\to$ hadrons.

Influence of QCD parton showers in deep learning invisible Higgs bosons through vector boson fusion

Vector boson fusion established itself as a highly reliable channel to probe the Higgs boson and an avenue to uncover new physics at the Large Hadron Collider. This channel provides the most stringent bound on Higgs' invisible decay branching ratio, where the current upper limits are significantly higher than the one expected in the Standard Model. It is remarkable that merely low-level calorimeter data from this characteristically simple process can improve this limit substantially by employing sophisticated deep-learning techniques. The construction of such neural networks seems to comprehend the event kinematics and radiation pattern exceptionally well. However, the full potential of this outstanding capability also warrants a precise theoretical projection of QCD parton showering and corresponding radiation pattern. This work demonstrates the relation using different recoil schemes in the parton shower with leading order and higher-order computation.

Classicalization and unitarization of wee partons in QCD and gravity: The CGC-black hole correspondence

We discuss a remarkable correspondence between the description of Black Holes as highly occupied condensates of $N$ weakly interacting gravitons and that of Color Glass Condensates (CGCs) as highly occupied gluon states. In both cases, the dynamics of "wee partons" in Regge asymptotics is controlled by emergent semi-hard scales that lead to perturbative unitarization and classicalization of $2\rightarrow N$ particle amplitudes at weak coupling. In particular, they attain a maximal entropy permitted by unitarity, bounded by the inverse coupling $\alpha$ of the respective constituents. Strikingly, this entropy is equal to the area measured in units of the Goldstone constant corresponding to the spontaneous breaking of Poincar{\'{e}} symmetry by the corresponding graviton or gluon condensate. In gravity, the Goldstone constant is the Planck scale, and gives rise to the Bekenstein-Hawking entropy. Likewise, in the CGC, the corresponding Goldstone scale is determined by the onset of gluon screening. We point to further similarities in Black Hole formation, thermalization and decay, to that of the Glasma matter formed from colliding CGCs in ultrarelativistic nuclear collisions, which decays into a Quark-Gluon Plasma.

The diffractive contribution to deep inelastic lepton-proton scattering: Implications for QCD momentum sum rules and parton distributions

The cross section for deep inelastic lepton-proton scattering (DIS) ℓp→ℓ′X includes a diffractive deep inelastic (DDIS) contribution ℓp→ℓ′p′X, in which the proton remains intact with a large longitudinal momentum fraction xF greater than 0.9 and small transverse momentum. The DDIS events, which can be identified with Pomeron exchange in the t-channel, account for approximately 10% of all of the DIS events. Thus, when one measures DIS, one automatically includes the leading-twist Bjorken-scaling DDIS events as a contribution to the DIS cross section, whether or not the final-state proton p′ is detected. In such events, the missing momentum fraction xp′∼0.9 carried by the final-state proton p′ in the DDIS events could be misidentified with the light-front momentum fraction carried by sea quarks or gluons in the protons' Fock structure. As we shall show in this article, the underlying QCD Pomeron-exchange amplitude which produces the DDIS events does not obey the operator product expansion nor satisfy momentum sum rules. Thus we conclude that the quark and gluon distributions measured in DIS experiments will be misidentified, unless the measurements explicitly exclude the DDIS events and that a correct determination of the parton distribution functions (PDFs) derived from the DIS data requires the explicit subtraction of the DDIS contribution from the full DIS cross section.

γ -hadron spectra in p+Pb collisions at sNN=5.02 TeV

Under the assumption that a quark-gluon plasma droplet is produced and its evolution can be described by hydrodynamics in p + A collisions, $\gamma$-triggered hadron spectra are studied within a next-to-leading-order perturbative QCD parton model with the medium-modified parton fragmentation functions. The initial conditions and space-time evolution of the small QGP droplet are provided by the superSONIC hydrodynamic model simulations and parton energy loss in such a medium is described by the high-twist (HT) approach. The scaled jet transport coefficient $\hat{q}/T^3$ in this HT approach is extracted from single hadron suppression in central A + A collisions at the same colliding energy. Numerical results for this scenario show that $\gamma$-hadron spectra at $p_{\rm T}^\gamma=12-40$ GeV/$c$ are suppressed by 5\% $\sim$ 10\% in the most central 0 - 10\% p + Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. The suppression becomes weaker at higher transverse momentum of the $\gamma$ trigger. As a comparison, $\gamma$-hadron suppression in Pb + Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ and 5.02 TeV is also predicted.

Parton energy loss: new theoretical progress

The physics of jet quenching combines the dynamics of the QCD parton shower with bremsstrahlung radiation and decoherence processes induced by interactions with an underlying medium. Here we present a brief overview of the established features of medium-induced bremsstrahlung spectrum in a deconfined QCD plasma, highlight the aspect of rapid jet showering inside the medium and compute the resulting energy lost out of the jet cone in heavy-ion collisions.

Mixed QCD-electroweak corrections to on-shell Z production at the LHC

We present the first complete calculation of mixed QCD-electroweak corrections to the production of on-shell Z bosons in hadron collisions and their decays to massless charged leptons. Our computation is fully differential with respect to final state QCD partons and resolved photons, allowing us to compute any infra-red safe observable pertinent to the pp→Z→l+l− process in the approximation that the Z boson is on shell. Although mixed QCD-electroweak corrections are small, at about the per mill level, we observe that the interplay between QCD-QED and QCD-weak contributions is subtle and observable-dependent. It is therefore not possible to avoid computing one or the other if O(αEWαs) precision is desired.

Seebeck effect in a thermal QCD medium in the presence of strong magnetic field

The strongly interacting partonic medium created post ultrarelativistic heavy ion collision experiments exhibits a significant temperature-gradient between the central and peripheral regions of the collisions, which in turn, is capable of inducing an electric field in the medium; a phenomenon known as Seebeck effect. The effect is quantified by the magnitude of the induced electric field per unit temperature-gradient - the Seebeck coefficient ($S$). We study the coefficient, $S$ in the relativistic Boltzmann transport equation in relaxation-time approximation, as a function of temperature ($T$) and chemical potential ($\mu$), wherein we find that with current quark masses, the magnitude of $S$ for individual flavours as well as that for the medium as a whole decreases with $T$ and increases with $\mu$, with the electric charge of the flavour deciding the sign of $S$. The emergence of a strong magnetic field ($B$) in the non-central collisions at heavy-ion collider experiments motivates us to study the effect of $B$ on Seebeck effect. The strong $B$ affects $S$ in multifold ways, via : a) modification of phase-space due to the dimensional reduction, b) dispersion relation in lowest Landau level (occupation probability), and c) relaxation-time. We find that a strong $B$ not only decreases the magnitudes of $S$'s of individual species, it also flips their signs. This leads to a faster reduction of the magnitude of $S$ of the medium than its counterpart at $B=0$. We then explore how the interactions among partons in perturbative thermal QCD in the quasiparticle framework affect Seebeck effect, where we find that even in strong B, there is no more a flip of the sign of $S$ for individual species and an enhancement of the magnitudes of $S$ of individual species as well as that of the medium, compared to current quark mass description at either $B=0$ or $B \neq 0$.

Cosmological analogies in the search for new physics in high-energy collisions

In this paper, analogies between multiparticle production in high-energy collisions and the time evolution of the early universe are discussed. A common explanation is put forward under the assumption of an unconventional early state: a rapidly expanding universe before recombination (last scattering surface), followed by the CMB, later evolving up to present days, versus the formation of hidden/dark states in hadronic collisions followed by a conventional QCD parton shower yielding final-state particles. In particular, long-range angular correlations are considered pointing out deep connections between the two physical cases potentially useful for the discovery of new physics.

Soft diffraction within the QCD color dipole picture

In this work we consider the QCD parton saturation models to describe soft interactions at the high energy limit. The total and elastic cross sections as well as the elastic slope parameter are obtained for proton-proton and pion-proton collisions and compared to recent experimental results. The analyses are done within the color dipole formalism taking into account saturation models which have been tested against DIS data. The main point is that the match between soft and hard interaction occurs in the saturation region which can be described by high density QCD approaches. Discussion is performed on the main theoretical uncertainties associated with calculations.

Numerical solutions to Giovannini’s QCD parton branching processes

In 1979, Giovannini [1] formulated multiparticle production as a manifestation of four QCD processes: A: g → gg (gluon bremsstrahlung), A-: q → qg (quark bremsstrahlung), B: g → qq (quark pair creation) and C: g → ggg (four-gluon vertex). At present, only approximate solutions exist, such as the Generalized Multiplicity Distribution (GMD) which excludes pro- cesses B and C [2, 3]. These approximate solutions have been very successful in describing charged particle multiplicities at lower energies, at least until the appearance of a shoulder-like structure at √s ≈ 200 GeV and 900 GeV first reported by the UA5 collaboration [4], also known as “KNO-scaling violation”. Here, we extend the work of Sakai [5] and attempt a numerical solution that incorporates all four QCD processes, and see if the addition of processes B and C can explain the shoulder-like structure.

Relating amplitude and PDF factorisation through Wilson-line geometries

We study long-distance singularities governing different physical quantities involving massless partons in perturbative QCD by using factorisation in terms of Wilson-line correlators. By isolating the process-independent hard-collinear singularities from quark and gluon form factors, and identifying these with the ones governing the elastic limit of the perturbative Parton Distribution Functions (PDFs) — δ(1 − x) in the large-x limit of DGLAP splitting functions — we extract the anomalous dimension controlling soft sin- gularities of the PDFs, verifying that it admits Casimir scaling. We then perform an independent diagrammatic computation of the latter using its definition in terms of Wil- son lines, confirming explicitly the above result through two loops. By comparing our eikonal PDF calculation to that of the eikonal form factor by Erdogan and Sterman and the classical computation of the closed parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges whereby all singularities emerge in diagrammatic configurations localised at the cusps or along lightlike lines, but where distinct contributions to the anomalous dimensions are associated with finite (closed) lightlike segments as compared to infinite (open) ones. Both are relevant for resumming large logarithms in physical quantities, notably the anomalous dimension controlling Drell-Yan or Higgs production near threshold on the one hand, and the gluon Regge trajectory controlling the high-energy limit of partonic scattering on the other.

Investigating the Soft Processes within the QCD Color Dipole Picture

We consider the QCD parton saturation models to describe the soft interactions at the high-energy limit. The total and elastic cross-sections, as well as the elastic slope parameter, are obtained for proton-proton and pion-proton collisions and compared to recent experimental results.