Parton Splitting Research Articles

Precise description of medium-induced emissions

We study jet fragmentation via final-state parton splittings in the medium. These processes are usually calculated theoretically by invoking the large-Nc limit. In this paper we perform the first computation of a 1 → 2 parton splitting in a thermal medium at finite numbers of colors Nc, for arbitrary momentum-sharing fraction z and with full transverse dynamics. We show how the problem can be transformed into a system of coupled Schrödinger equations, that we solve numerically. The novel numerical results are used to estimate the accuracy of several widely used approximations. We check the error introduced while going from finite Nc (i.e. Nc = 3) to the large-Nc limit, which we find to be small. For unbalanced splittings, e.g. when z → 0, only one of the partons is affected by transverse momentum exchanges with the medium. The emission process then separates into a term responsible for the 1 → 2 splitting and the subsequent independent broadening of the daughter partons. This is also referred to as the factorizable term. For finite z, further contributions arise that are responsible for the coherent color dynamics of the two-parton system, and these are referred to as non-factorizable terms. These were argued to be small for soft (unbalanced) splittings and for large media. In this work we therefore determine the accuracy of keeping only the factorizable term of the large-Nc solution. We find that the error is insignificant at a small splitting fraction z ~ 0, but can be sizable in a more balanced splitting with z ~ 0.5. Finally, we also examine the eikonal approximation, which amounts to approximating the partons’ paths through the medium as straight lines. We find that it is associated with a substantial error for the parameter values we explored in this work.

Yangian symmetry applied to quantum chromodynamics

We review applications of Yangian symmetry to high-energy Quantum chromodynamics (QCD) phenomenology. Some basic facts about high-energy QCD are recalled, in particular the spinor-helicity form of scattering amplitudes, the scale evolution equations of deep-inelastic scattering structure functions and the high-energy asymptotics of scattering. As the working tool the Yangian symmetric correlators are introduced and constructed in the framework of the Yangian algebra of [Formula: see text] type. We present the application to the tree scattering amplitudes and their iterative relation, to the parton splitting amplitudes and the kernels of the scale evolution equations of structure functions and to the equations describing the high-energy asymptotics of scattering.

The medium-modified gto coverline{c} splitting function in the BDMPS-Z formalism

The formalism of Baier-Dokshitzer-Mueller-Peigné-Schiff and Zakharov determines the modifications of parton splittings in the QCD plasma that arise from medium-induced gluon radiation. Here, we study medium-modifications of the gluon splitting into a quark-anti-quark pair in this BDMPS-Z formalism. We derive a compact path-integral formulation that resums effects from an arbitrary number of interactions with the medium to leading order in the 1/{N}_c^2 expansion. Analyses in the N = 1 opacity and the saddle point approximations reveal two phenomena: a medium-induced momentum broadening of the relative quark-anti-quark pair momentum that increases the invariant mass of quark-anti-quark pairs, and a medium-enhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium is comparable to the quark mass. In ultra-relativistic heavy-ion collisions, this condition is satisfied for charm quarks. We therefore focus our numerical analysis on the medium modification of gto coverline{c} , although our derivation applies equally well to gto boverline{b} and to gluons splitting into light-flavoured quark-anti-quark pairs.

Multivariable evolution in parton showers with initial state partons

One can use more than one scale variable to define the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. In an earlier paper, we developed this idea for electron-positron annihilation. Here, we use multiple scale variables for a parton shower with initial state partons. Then we need a more sophisticated analysis because the evolution of parton distribution functions must be coordinated with the parton shower evolution. We make the needed connections more precise than in our earlier work, even for the case of just one scale variable. Then we develop an example with three scale variables, which leads to advantages compared to the usual shower formulation with only one scale variable. We provide results for Drell-Yan muon pair production.

Parton splitting scales of reclustered large-radius jets in high-energy nuclear collisions

We carry out the first theoretical investigation on yields and the hardest parton splitting of large-radius jets reclustered from small radius (R=0.2) anti-k_t jets in Pb + Pb collisions, and confront them with the recent ATLAS measurements. The Linear Boltzmann Transport (LBT) model is employed for jet propagation and jet-induced medium excitation in the hot-dense medium. We demonstrate that, with their complex structures, the medium suppression of the reclustered large radius jets at R=1 is larger than that of inclusive R=0.4 jets defined conventionally. The large radius jet constituents are reclustered with the k_t algorithm to obtain the splitting scale sqrt{d_{12}}, which characterizes the transverse momentum scale for the hardest splitting in the jet. The large-radius jet production as a function of the splitting scale sqrt{d_{12}} of the hardest parton splitting is overall suppressed in Pb + Pb relative to p + p collisions due to the reduction of jets yields. A detailed analyses show that the alterations of jet substructures in Pb + Pb also make significant contribution to the splitting scale sqrt{d_{12}} dependence of the nuclear modification factor R_{AA}. Numerical results for the medium modifications of the jet splitting angle Delta R_{12} and the splitting fraction z are also presented.

Multivariable evolution in final state parton shower algorithms

One can use more than one scale variable to specify the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. Considering $e^+e^-$ annihilation, we use two variables, with shower evolution following a special path in this two dimensional space. In addition, we treat in a special way the part of the splitting function that has a soft emission singularity but no collinear singularity. This leads to certain advantages compared to the usual shower formulation with only one scale variable.

Measurement of the Groomed Jet Radius and Momentum Splitting Fraction in pp and Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

This article presents groomed jet substructure measurements in pp and Pb-Pb collisions at sqrt[s_{NN}]=5.02 TeV with the ALICE detector. The soft drop grooming algorithm provides access to the hard parton splittings inside a jet by removing soft wide-angle radiation. We report the groomed jet momentum splitting fraction, z_{g}, and the (scaled) groomed jet radius, θ_{g}. Charged-particle jets are reconstructed at midrapidity using the anti-k_{T} algorithm with resolution parameters R=0.2 and R=0.4. In heavy-ion collisions, the large underlying event poses a challenge for the reconstruction of groomed jet observables, since fluctuations in the background can cause groomed parton splittings to be misidentified. By using strong grooming conditions to reduce this background, we report these observables fully corrected for detector effects and background fluctuations for the first time. A narrowing of the θ_{g} distribution in Pb-Pb collisions compared to pp collisions is seen, which provides direct evidence of the modification of the angular structure of jets in the quark-gluon plasma. No significant modification of the z_{g} distribution in Pb-Pb collisions compared to pp collisions is observed. These results are compared with a variety of theoretical models of jet quenching, and provide constraints on jet energy-loss mechanisms and coherence effects in the quark-gluon plasma.

Wilson line correlators beyond the large-Nc

We study hard 1 → 2 final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an effect that is encapsulated in a Wilson line along their trajectory. When calculating observables, one typically has to calculate traces of two or more medium-averaged Wilson lines. These are usually dealt with in the literature by invoking the large-Nc limit, but exact calculations have been lacking in many cases. In our work, we show how correlators of multiple Wilson lines appear, and develop a method to calculate them numerically to all orders in Nc. Initially, we focus on the trace of four Wilson lines, which we develop a differential equation for. We will then generalize this calculation to a product of an arbitrary number of Wilson lines, and show how to do the exact calculation numerically, and even analytically in the large-Nc limit. Color sub-leading corrections, that are suppressed with a factor {N}_c^{-2} relative to the leading scaling, are calculated explicitly for the four-point correlator and we discuss how to extend this method to the general case. These results are relevant for high-pT jet processes and initial stage physics at the LHC.

A quantum strategy to compute the jet quenching parameter hat{q}

Jet quenching, the modification of the properties of a QCD jet when the parton cascade takes place inside a medium, is an intrinsically quantum process, where color coherence effects play an essential role. Despite a very significant progress in the last years, the simulation of a full quantum medium induced cascade remains inaccessible to classical Monte Carlo parton showers. In this situation, alternative formulations are worth being tried and the fast developments in quantum computing provide a very promising direction. The goal of this paper is to introduce a strategy to quantum simulate single particle momentum broadening, the simplest building block of jet quenching. Momentum broadening is the modification of the quark or gluon transverse momentum due interactions with the underlying medium, modeled as a QCD background field. At the lowest order in alpha _s that we consider here, momentum broadening does not involve parton splittings and particle number is conserved, greatly simplifying the quantum algorithmic implementation. This quantity is, however, very relevant for the phenomenology of RHIC, LHC or the future EIC.

An analysis of parton distribution functions of the pion and the kaon with the maximum entropy input

We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton–parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale Q_0^2, there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in the kaon. The obtained valence quark and sea quark distributions at high Q^{2} (Q^2>5 GeV^2) are compatible with the existed experimental measurements. Furthermore, the asymptotic behaviours of parton distribution functions at small and large x have been studied for both the pion and the kaon. Lastly, the first three moments of parton distributions at high Q^{2} scale are calculated, which are consistent with other theoretical predictions.

Jet substructure and parton splitting: an experimental overview

It has been established that experimental jets in heavy ion collisions have less energy as compared to pp collisions on average, where the lost energy is manifested as soft particles at large angles with respect to the jet axis. It is known as jet quenching. Various experiments have reported new measurements of jet nuclear modification factor extending to large radius and low momentum, which provide unique information on how the energy is redistributed. Substructure measurements aim to study this phenomenon in a greater detail, and one can hope to unravel the underlying mechanisms from which the parton interacts with the hot QCD matter created in the collisions. In this talk, most recent results on jet substructures and jet nuclear modification factors from experiments in LHC and RHIC are summarized.

Improved opacity expansion for medium-induced parton splitting

We revisit the calculation of the medium-induced gluon radiative spectrum and propose a novel expansion scheme that encompasses the two known analytic limits: i) the high frequency regime dominated by a single hard scattering that corresponds to the leading order in the standard opacity expansion, ii) the low frequency regime that is dominated by multiple soft scatterings. Our approach is based on expanding around the harmonic oscillator instead of vacuum in the leading logarithmic approximation. We compute the first two orders in this improved opacity expansion and show that they account for the aforementioned limits.

Jet momentum broadening in the pre-equilibrium Glasma

Jets are important probes of heavy ion collisions as they can provide information on the interaction of a highly energetic parton with the medium it traverses. In the hydrodynamic stage of dense, strongly interacting matter, these interactions can be explained in terms of scattering processes, soft gluon emission and collinear parton splittings. However, jets originate even before the hydrodynamic stage. Here we report on the first numerical simulation of transverse momentum broadening of jets stemming from the interaction of partons with boost-invariantly expanding Glasma flux tubes. The Glasma stage is a pre-hydrodynamic stage based on the Color Glass Condensate framework. Our calculation shows strong time-dependence and an intrinsic anisotropy of momentum broadening in the directions transverse to the jet propagation direction.

Improved opacity expansion for medium-induced parton splitting

We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This provides the tools to go beyond the leading logarithmic approximation and compare to the full numerical solution to the corresponding Schrödinger equation across a wide range of gluon frequencies. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.

Novel tools and observables for jet physics in heavy-ion collisions

Studies of fully-reconstructed jets in heavy-ion collisions aim at extracting thermodynamical and transport properties of hot and dense QCD matter. Recently, a plethora of new jet substructure observables have been theoretically and experimentally developed that provide novel precise insights on the modifications of the parton radiation pattern induced by a QCD medium. This report, summarizing the main lines of discussion at the 5th Heavy Ion Jet Workshop and CERN TH institute ‘Novel tools and observables for jet physics in heavy-ion collisions’ in 2017, presents a first attempt at outlining a strategy for isolating and identifying the relevant physical processes that are responsible for the observed medium-induced jet modifications. These studies combine theory insights, based on the Lund parton splitting map, with sophisticated jet reconstruction techniques, including grooming and background subtraction algorithms.

Nuclear modification of leading hadrons and jets within a virtuality ordered parton shower

The event generator based on the higher-twist energy loss formalism -- Modular All Twist Transverse-scattering Elastic-drag and Radiation (MATTER) -- is further developed and coupled to a hydrodynamic model for studying jet modification in relativistic nuclear collisions. The probability of parton splitting is calculated using the Sudakov form factor that is constructed by a combination of vacuum and medium-induced splitting functions; and the full parton showers are simulated, including both energy-momentum and space-time evolutions of all jet partons. With the assumption that partons below a virtual scale of 1 GeV is absorbed by the medium, this framework is able to provide a reasonable description of the nuclear modification of both leading hadrons and jets at high transverse momentum at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.

Mapping collinear in-medium parton splittings

We map the spectrum of 1rightarrow 2 parton splittings inside a medium characterized by a transport coefficient {hat{q}} onto the kinematical Lund plane, taking into account the finite formation time of the process. We discuss the distinct regimes arising in this map for in-medium splittings, pointing out the close correspondence to a semi-classical description in the limit of hard, collinear radiation with short formation times. Although we disregard any modifications of the original parton kinematics in course of the propagation through the medium, subtle modifications to the radiation pattern compared to the vacuum baseline can be traced back to the physics of color decoherence and accumulated interactions in the medium. We provide theoretical support to vacuum-like emissions inside the medium by delimiting the regions of phase space where it is dominant, identifying also the relevant time-scales involved. The observed modifications are shown to be quite general for any dipole created in the medium.

Modified Boltzmann approach for modeling the splitting vertices induced by the hot QCD medium in the deep Landau-Pomeranchuk-Migdal region

Hard probes produced in perturbative processes are excellent probes for the study of the hot and dense QCD matter created in relativistic heavy-ion collisions. Transport theory, allowing for coupling to an evolving medium with fluctuating initial conditions, has become a powerful tool in this endeavor. However, the implementation of the Landau-Pomeranchuk-Migdal (LPM) effect for medium-induced parton bremsstrahlung and pair production, poses a challenge to semi-classical transport models based on Boltzmann-type transport equations. In this work, we investigate a possible solution to approximate the LPM effect in a "modified Boltzmann transport" approach, including a prescription for the running coupling constant. By fixing a numerical parameter, this approach quantitatively reproduces the rates of medium-induced parton splitting predicted by the next-to-lead-log solution of the AMY equation which is valid in the deep-LPM regime of an infinite medium. We also find qualitative agreement of our implementation with calculations in a finite and expanding medium, but future improvements are needed for added precision at small path length. This work benefits transport model-based studies and the usage of these models in the phenomenological extraction of the jet transport coefficient.

Two-loop splitting in double parton distributions

Double parton distributions (DPDs) receive a short-distance contribution from a single parton splitting to yield the two observed partons. We investigate this mechanism at next-to-leading order (NLO) in perturbation theory. Technically, we compute the two-loop matching of both the position and momentum space DPDs onto ordinary PDFs. This also yields the 1 \to 21→2 splitting functions appearing in the evolution of momentum-space DPDs at NLO. We give results for the unpolarised, colour-singlet DPDs in all partonic channels. These quantities are required for calculations of double parton scattering at full NLO. We discuss various kinematic limits of our results, and we verify that the 1 \to 21→2 splitting functions are consistent with the number and momentum sum rules for DPDs.

Deep learning as a parton shower

We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, which also preserves existing parton splittings by using layer-skipping connections. By applying a shower merging procedure, the network can be evaluated on unshowered events produced by a matrix element calculation. The trained network behaves as a parton shower that qualitatively reproduces jet-based observables.