Heavy ion collisions at high energies can be used as an interesting way to recreate and study the medium of the quark-gluon plasma (QGP). We particularly investigate the jets produced in hard binary collisions and their interactions with a tentative medium. These jets were obtained numerically from the Monte-Carlo simulations of hard collisions using the KATIE-algorithm [1], where parton momenta within the colliding nucleons were describe by means of unintegrated parton distribution functions (uPDF). We evolved these jets within a medium that contains both, transverse kicks (yielding a broadening in momentum transvers to the jet-axis) as well as medium induced radiation within the MINCAS-algorithm [2] following the works of [3,4]. We produce qualitative results for the decorrelation of dijets. In particular, we study deviations from a transverse momentum broadening that follows a Gaussian distribution.
[1] A. van Hameren, Comput.Phys.Commun. 224 (2018) 371-380 [2] K. Kutak, W. Płaczek, R. Straka, Eur.Phys.J. C79 (2019) no.4, 317 [3] J.-P. Blaizot, F. Dominguez, E. Iancu, Y. Mehtar-Tani, JHEP 1301 (2013) 143 [4] J.-P. Blaizot, F. Dominguez, E. Iancu, Y. Mehtar-Tani, JHEP 1406 (2014) 075
Broadening is a classic jet observable that probes the transverse momentum structure of jets. Traditionally, broadening has been measured with respect to the thrust axis, which is aligned along the (hemisphere) jet momentum to minimize the vector sum of transverse momentum within a jet. In this paper, we advocate measuring broadening with respect to the "broadening axis", which is the direction that minimizes the scalar sum of transverse momentum within a jet. This approach eliminates many of the calculational complexities arising from recoil of the leading parton, and observables like the jet…
We study, at a qualitative level, production of jet pairs in ultrarelativistic nuclear collisions within a framework combining High Energy Factorisation (HEF) and in-medium propagation of jet particles that takes into account stochastic transverse forces as well as medium-induced radiation. We find that the resulting di-jet observables feature the behaviour deviating from that of jet-pairs which undergo transverse-momentum broadening following the Gaussian distribution.
Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e+e- annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present the first all-order expressions for jet-broadening distributions, which are free of large perturbative logarithms in the two-jet limit. Our formulae reproduce known results at next-to-leading logarithmic order but also extend…
In the framework of the soft-collinear effective theory, we present a gauge invariant definition of the transverse momentum broadening probability of a highly-energetic collinear quark in a medium and consequently of the jet quenching parameter $\hat{q}$.
We calculate in perturbative QCD the transverse momentum broadening of vector bosons in heavy ion collisions at the Large Hadron Collider (LHC). We predict transverse momentum broadening of $W/Z$ bosons constructed from their leptonic decay channels, which should be a clean probe of initial-state medium effect. We also predict the upper limit of transverse momentum broadening of J/$ψ$ and $Υ$ production as a function of N$_{\rm part}$ at the LHC energy.
The resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The anomaly coefficient is extracted from the soft function and expressed in terms of polylogarithmic as well as elliptic functions. With our results, the uncertainty on jet-broadening distributions is reduced significantly, which should allow for a precise determination of the strong coupling constant from the existing experimental data and provide a consistency…
Using the Drell-Yan process in hadron-nucleus collisions and deeply inelastic lepton-nucleus scattering (DIS) as examples, I show that the transverse momentum broadening can be expressed in terms of four-parton correlation functions. I argue that jet broadening in DIS provide an excellent measurement of the four-parton correlation functions and a test of QCD treatment of the multiple scattering.
We study the influence of in-medium transverse momentum broadening on observables of jet pairs produced in nuclear collisions. These dijets were obtained numerically via the Monte-Carlo simulations of nuclear collisions, where the partons within the colliding nuclei were described via unintegrated parton densities, and their subsequent propagation within the medium of a quark-gluon plasma (QGP). For jet-evolution in the QGP both, kicks transverse to the momentum of the incoming particle as well as medium induced radiation were considered. After favorable comparison of our results with experime…
We derive an all-order factorization theorem for the narrow jet broadening event shape, a measure of the transverse momentum in jet events. This is a non-global observable which receives logarithmically enhanced contributions associated with the large rapidity difference between soft and collinear radiation and which is also sensitive to soft recoil effects. Our work is the first factorization analysis of an observable of this type and we show that with regard to the non-global nature, the rapidity logarithms do not constitute an essential complication since they can be tied to the jet functio…
The mean transverse momentum in high energy nuclear collisions is studied. The formation of a Color Glass Condensate results in an increase of the square of the mean transverse momentum with the charged multiplicity per unit rapidity and unit transverse area. This prediction is in agreement with the presently available data, in particular with the heavy-ion data, lending support to the notion that the transverse momentum spectra in ultrarelativistic collisions of heavy nuclei might be controlled by intrinsic transverse momentum broadening and not by hadronic rescattering, i.e. transverse flow.
The jet quenching parameter $\hat{q}$ is analyzed for a quark jet propagating in an anisotropic plasma. The momentum anisotropy is calculated at high temperature of the underlying quark-gluon plasma. $\hat{q}$ is explicitly estimated in leading-logarithmic approximation by the broadening of the massless quark interacting via gluon exchange. A plasma instability is present. Strong indications are found that $\hat{q}$ is increasing with increasing anisotropy. Possible implications for the saturation scale $Q_s$ in $A-A$ collisions are pointed out.
I report on the recent result of comparison of forward-forward dijet correlations in azimuthal angle as measured by the ATLAS collaboration in the proton-proton and proton-lead collisions to calculations within ITMD factorization framework [1]. The comparison shows that the broadening effect due to interplay of both the gluon saturation and the Sudakov resummation is necessary to describe the data.
Highly energetic particles in the medium of a quark gluon plasma undergo processes of coherent medium induced radiation and scatterings off medium particles. We solved the evolution equations for particle fragmentation functions that describe in-medium evolution via these two in-medium processes numerically via Monte-Carlo algorithms. We study the in-medium broadening of the distribution over momentum components transverse to the jet-axis for different cases of jet-medium interactions and different values of average transverse momentum transfer.
We show that taking into account the interplay between perturbative and non-perturbative effects, the power-suppressed shift to the broadening distributions becomes B dependent, and the non-perturbative contribution to the mean values becomes proportional to 1/(Q\sqrt{\as(Q)}). The new theoretical treatment greatly improves the consistency of the phenomenology with the notion of the universality of confinement effects in jet shapes.
The jet shape modification due to partonic energy loss in the dense QCD matter is investigated by the help of the special transverse energy-energy correlator in the vicinity of maximum energy deposition of every event. In the accepted scenario with scattering of jet hard partons off comoving medium constituents this correlator is independent of the pseudorapidity position of a jet axis and becomes considerably broader (symmetrically over the pseudorapidity and the azimuthal angle) in comparison with $pp$-collisions. At scattering off "slow" medium constituents the broadening of correlation fun…
The JEWEL 1.0 Monte Carlo simulates jet evolution in a medium with a microscopic description of splitting and scattering processes. In the framework of this model we investigate the transverse momentum broadening due to medium effects in different scenarios. Depending on assumptions about hadronisation, we observe either a small increase or even a slight decrease of the mean transverse momentum, but no sizeable broadening. This appears to be a natural consequence of a model formulation which conserves energy and momentum microscopically at each splitting and at each scattering.
We present predictions of two event shape distributions, the light hemisphere mass and the narrow jet broadening, to next-to-leading logarithmic order. We apply the coherent branching formalism to resum the leading O(alphas^n L^{2n-1}) and next-to-leading O(alphas^n L^{2n-2}) infrared logarithms to all orders in the coupling constant. We include the recently calculated non-logarithmic next-to-leading order contributions. Applying simple power corrections to the resummed result gives good agreement with the available data from LEP.
We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS-specific procedures for matching to fixed-order calculations and compare our results to data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets fro…
The perturbative all-order analysis of the jet-broadening B-distribution in the small-B region is carried out with single-logarithmic accuracy, which requires the control of both the sum of the moduli and the modulus of the sum of the transverse momenta of soft gluons. We confirm the master equation for the B-distribution derived by Catani, Turnock and Webber (CTW). Proper treatment of quark recoil is necessary at this accuracy. This effect was neglected in the CTW solution. We show that the answer can be expressed in terms of the CTW result but evaluated at a properly rescaled B value.
Data for Drell-Yan (DY) processes on nuclei are currently available from fixed target experiments up to the highest energy of $\sqrt{s}=40\GeV$. The bulk of the data cover the range of short coherence length, where the amplitudes of the DY reaction on different nucleons do not interfere. In this regime, DY processes provide direct information about broadening of the transverse momentum of the projectile parton experiencing initial-state multiple interactions. We revise a previous analysis of data from the E772 experiment and perform a new analysis of broadening including data from the E866 exp…
We study evolution equations describing jet propagation through quark--gluon plasma (QGP). In particular we investigate the contribution of momentum transfer during branching and find that such a contribution is sizeable. Furthermore, we study various approximations, such as the Gaussian approximation and the diffusive approximation to the jet-broadening term. We notice that in order to reproduce the BDIM equation (without the momentum transfer in the branching) the diffusive approximation requires a very large value of the jet-quenching parameter $\hat q$.
In deeply inelastic lepton-nucleus scattering (DIS), the average jet transverse momentum is broadened because of the multiple scattering in the nuclear medium. The size of jet broadening is proportional to the multi-parton correlation functions inside nuclei. We show that at leading order, jet broadening in DIS and nulcear enhancement in di-jet momentum imbalance and Drell-Yan $< q_T^2 > $ share the same four-parton correlation functions. We argue that jet broadening in DIS provide an indenpendent measurement of the four-parton correlation functions and a test of QCD treatment of multiple scat…
The leading order $α_s$ effect in jet quenching corresponds to the broadening of the jet's transverse momentum, due to the multiple interactions with the underlying medium. A complete understanding of momentum broadening is critical for the success of jet quenching phenomenology. In this talk, we introduce a strategy to quantum simulate single particle momentum broadening in a QCD background medium. We argue that it is, in principle, possible to extract the jet quenching parameter $\hat{q}$ from such an algorithm. More importantly, this corresponds to the first step towards simulating full med…
We compute the in-medium jet broadening $\langle p_\perp^2\rangle$ to leading order in energy in the opacity expansion. At leading order in $α_s$ the elastic energy loss gives a jet broadening that grows with $\ln E$. The next-to-leading order in $α_s$ result is a jet narrowing, due to destructive LPM interference effects, that grows with $\ln^2 E$. We find that in the opacity expansion the jet broadening asymptotics are -- unlike for the mean energy loss -- extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momen…
We propose a system of evolution equations that describe in-medium time-evolution of transverse-momentum-dependent quark and gluon fragmentation functions. Furthermore, we solve this system of equations using Monte Carlo methods. We then quantify the obtained solutions in terms of a few characteristic features, namely the average transverse momentum $\langle |k|\rangle$ and energy contained in a cone, which allow us to see different behaviour of quark and gluon initiated final-state radiation. In particular, the later allows us to conclude that in the gluon-initiated processes there is less en…
This article gives the perturbative NNLO results for the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable. In addition the NNLO results for the jet rates corresponding to the Durham, Geneva, Jade-E0 and Cambridge jet algorithms are presented.
We reconsider the problem of transverse momentum broadening of a highly-energetic parton suffering multiple scatterings in dense colored media, such as the thermal Quark-Gluon plasma or large nuclei. In the framework of Molière's theory of multiple scattering we re-derive a simple analytic formula, to be used in jet quenching phenomenology, that accounts for both the multiple soft and hard Rutherford scattering regimes. Further, we discuss the sensitivity of momentum broadening to modeling of the non-perturbative infrared sector by presenting a detailed analytic and numerical comparison betwee…
We studied the evolution of jets within a medium that contains both, transverse kicks as well as medium induced coherent radiation. In this framework parton branching occurs simultaneously to scatterings within the medium, leading to the interference effects that reproduce the well known BDMPS-Z emission rates and sizeable transverse momentum broadening. We examined the relative importances of transverse momentum broadening from the coherent splittings and different types of in-medium scatterings and found a clear hierarchy of the influences from different scattering effects and deflections du…
We analyze $x_F$ dependence of Drell-Yan transverse momentum broadening in hadron-nucleus collisions. In terms of generalized factorization theorem, we show that the $x_F$ dependence of transverse momentum broadening, $ Δ< q_T^2 > (x_F) $, can be calculated in perturbative QCD. We demonstrate that $Δ< q_T^2 > (x_F)$ is a good observable for studying the effects of initial-state multiple scattering and extracting quark-gluon correlation functions.
This article gives the perturbative NNLO results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable.
Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES ener…
The interaction of a jet with the medium created in heavy-ion collisions is not yet fully understood from a QCD perspective. This is mainly due to the non-perturbative nature of this interaction which affects both transverse jet momentum broadening and jet quenching. We discuss how lattice simulations of Electrostatic QCD, can be matched to full, four dimensional QCD, to determine non-perturbative contributions to the momentum broadening kernel. We determine the momentum broadening kernel in impact parameter and momentum space and finally show how these results can be used in phenomenological …
We calculate in perturbative QCD the transverse momentum broadening of vector boson production in high energy nuclear collisions. We evaluate the effect of initial-state parton multiple scattering for the production of the Drell-Yan virtual photon and $W/Z$ bosons. We calculate both the initial- and final-state multiple scattering effect for the production of heavy quarkonia and their transverse momentum broadening in both NRQCD and Color Evaporation model of quarkonium formation. We find that J/$ψ$ and $Υ$ broadening in hadron-nucleus collision is close to $2C_A/C_F$ times the corresponding D…
Unveiling the jet angular broadening with photon-tagged jets in high-energy nuclear collisions
College of Science, China Three Gorges University（三峡大学理学院）；Center for Astronomy and Space Sciences and Institute of Modern Physics, China Three Gorges University（三峡大学天文与空间科学中心暨现代物理研究所）
Using deep inelastic scattering on a large nucleus as an example, we consider the transverse momentum broadening of partons in hard processes in the presence of medium. We find that one can factorize the vacuum radiation contribution and medium related $P_T$ broadening effects into the Sudakov factor and medium dependent distributions, respectively. Our derivations can be generalized to other hard processes, such as dijet productions, which can be used as a probe to measure the medium $P_T$ broadening effects in heavy ion collisions when Sudakov effects are not overwhelming.
Building upon the hybrid strong/weak coupling model for jet quenching, we incorporate and study the effects of transverse momentum broadening and medium response of the plasma to jets on a variety of observables. For inclusive jet observables, we find little sensitivity to the strength of broadening. To constrain those dynamics, we propose new observables constructed from ratios of differential jet shapes, in which particles are binned in momentum, which are sensitive to the in-medium broadening parameter. We also investigate the effect of the back-reaction of the medium on the angular structu…
We present a calculation of the transverse momentum broadening of a high-energy fundamental-representation particle, as calculated nonperturbatively within EQCD using the technique proposed by Caron-Huot and pioneered by Panero, Schäfer, and Rummukainen. Our results are continuum extrapolated and provided at four temperatures: 250 MeV, 500 MeV, 1 GeV, and 100 GeV.
Multiple scattering leads to transverse momentum broadening of the struck quark in semi-inclusive deeply inelastic scatterings (SIDIS). Nuclear broadening of the transverse momentum squared at the leading twist is determined by the twist-four collinear quark-gluon correlation function of the target nucleus that is in turn related to the jet transport parameter inside the nuclear medium. The twist-six contributions to the transverse momentum broadening are calculated as power corrections $\sim 1/Q^2$. Such power corrections are found to have no extra nuclear enhancement beyond the twist-four ma…
The transverse broadening of jets produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. A class of medium enhanced higher twist corrections are re-summed to calculate the transverse momentum distribution of the produced collinear jet. In contrast to previous approaches, resummation of the leading length enhanced higher twist corrections is shown to lead to a two dimensional diffusion equation for the transverse momentum of the propagating jet. Results for the average transverse momentum obtained from this approach are then compared to the broadening…
We study the process dependent nuclear $k_\perp$ broadening effect by employing the transverse momentum dependent(TMD) factorization approach in combination with the Mclerran-Venugopalan(MV) model. More specifically, we investigate how the parton transverse momentum distributions are affected by the process dependent gauge links in cold nuclear matter. In particular, our analysis also applies to the polarized cases including the nuclear quark Boer-Mulders function and the linearly polarized gluon distribution. Our main focus is on the nuclear TMDs at intermediate or large x.
In this work, we obtain the leading corrections to the jet momentum broadening distribution in a QCD medium arising from the transverse flow of the matter. We first derive the single-particle propagator of a highly energetic parton resumming its multiple interactions with the homogeneous flowing matter, explicitly keeping the leading subeikonal flow terms. Then, we use this propagator to obtain the jet broadening distribution and its leading moments. We show that this distribution becomes anisotropic in the presence of transverse flow, since its odd moments are generally non-zero and proportio…
We investigate the effect of PT-broadening on jet substructure observables in heavy-ion collisions at the LHC. As an example, we focus on the opening angle of the two branches that satisfy the soft drop grooming condition in a highly energetic jet. The medium modification of the angular distribution can provide important information on the jet transport properties of hot QCD matter. In addition, we take into account a change of the overall fraction of quark and gluon jets in heavy-ion collisions. We comment on the comparison to a recent measurement from the ALICE Collaboration.
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 Glas…
Recently claimed \cite{dj1,dj2,FC} anomalous nuclear effects in di-jet production are analyzed in view of multiple interaction of projectile/ejectile partons in nuclear matter. We derive model--independent relations between A-dependence of the cross section and nuclear broadening of transverse momentum. Comparison with the data show that initial/final state interaction of partons participating in hard process is hard as well. This is a solid argument in favor of smallness of a color neutralization radius of a hadronizing highly virtual quark.
In this work, we study the jet momentum broadening in an inhomogeneous dense QCD medium. The transverse profile of this nuclear matter is described within a gradient expansion, and we focus on the leading gradient contributions. The leading parton is allowed to interact multiple times with the background through the soft gluon exchanges. We derive the associated final particle distribution using both the GLV opacity series and the BDMPS-Z formalism. We further discuss the modified factorization of the initial and final state effects and its consequences for phenomenological applications in the…
Jet energy loss and single inclusive jet suppression in high-energy heavy-ion collisions are studied within a pQCD parton model that includes both elastic and radiative interactions between jet shower and medium partons as they propagate through the quark-gluon plasma. The collisional energy loss of jets with a given cone-size is found to be relatively small comparing with the radiative energy loss. However the effect of transverse momentum broadening due to elastic scattering is significant in the calculation of radiative energy loss within the higher-twist formalism. The nuclear modification…
We study the asymptotic behaviour of the transverse momentum broadening distribution of an energetic quark or gluon propagating through dense QCD matter, in the large system size $L$ limit, taking into account radiative corrections in the double logarithmic approximation. Thanks to a connection between the evolution of the jet quenching parameter $\hat{q}$ and the formation of traveling wave fronts in nonlinear physics, we obtain a formula for the $L$ dependence of the characteristic transverse momentum scale $Q_s$ of the distribution valid up to terms of order $1/\ln(L)$. We briefly discuss t…
We perform numerical simulations of the QCD Boltzmann-Vlasov equation including both hard elastic particle collisions and soft interactions mediated by classical Yang-Mills fields. We provide an estimate of the coupling of jets to a hot plasma which is independent of infrared cutoffs. For weakly-coupled anisotropic plasmas the local rotational symmetry in momentum space is broken. The fields develop unstable modes, forming configurations where B_t>E_t and E_z>B_z. This provides a possible explanation for the experimental observation that high-energy jets traversing the plasma perpendicular to …
Two effects, jet broadening and gluon bremsstrahlung induced by the propagation of a highly energetic quark in dense QCD matter, are reconsidered from effective theory point of view. We modify the standard Soft Collinear Effective Theory (SCET) Lagrangian to include Glauber modes, which are needed to implement the interactions between the medium and the collinear fields. We derive the Feynman rules for this Lagrangian and show that it is invariant under soft and collinear gauge transformations. We find that the newly constructed theory SCET$_{\rm G}$ recovers exactly the general result for the…
We calculate the broadening of the transverse momentum distribution of a quark propagating through nuclear matter. Colour screening plays a fundamental role in that it cuts off quark-nucleon interactions with soft gluons. The mean transverse momentum of the quark acquired along its trajectory, observed via Drell-Yan pairs, is related to it the ratio of the total inelastic meson-nucleon cross section it to the meson mean squared radius. Parameter-free calculations agree with the data.
