We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences, and which contains all relevant time scales, like production, coherence, formation, etc. The cross section includes the probability of pre-hadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the pre-hadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one of the reasons of a too large gluon density, reported by such analyzes.
We discuss preliminary results on medium-modified fragmentation functions obtained in a combined NLO fit to data on semi-inclusive deep inelastic scattering off nuclei and hadroproduction in deuteron-gold collisions.
A new analysis of the modification of the hadronization process in the nuclear medium for pions is presented. The effective description is condensed in a set of medium modified fragmentation functions (nFFs) obtained at next-to-leading order (NLO) accuracy. The study was made using the open-source tool xFitter, conveniently modified to incorporate semi-inclusive processes. Theoretical uncertainties for the nFFs are also provided.
The possibility to observe the medium-modified fragmentation of hard b-quarks tagged by a leading muon in ultrarelativistic heavy ion collisions is analyzed. We have found that reasonable statistics, ~20000 events per 1 month of LHC run with lead beams, can be expected for the realistic geometrical acceptance and kinematic cuts. The numerical estimates on the effect of the medium-induced softening b-jet fragmentation function are given.
In nucleus-nucleus collisions at RHIC and LHC, partons produced at high transverse momentum can undergo multiple scattering within the collision region prior to fragmenting into hadrons. We have studied the resulting medium-modified fragmentation function based on a calculation of the BDMPS-Z medium-induced gluon radiation for a dense, expanding medium of small finite extension. Here we explain how the BDMPS transport coefficient which measures the energy density attained in the collision, can be extracted from the observed modification of high-pt hadroproduction. We also comment on the signif…
The unified description of fragmentation function evolution from large to small x which was developed for the vacuum in previous publications is now generalized to the medium, and is studied for the case in which the complete contribution from the largest class of soft gluon logarithms, the double logarithms, are accounted for and with the fixed order part calculated to leading order. In this approach it proves possible to choose the remaining degrees of freedom related to the medium such that the distribution of produced hadrons is suppressed at large momenta while the production of soft radi…
The hydrodynamic (hydro) model applied to data from the relativistic heavy ion collider (RHIC) suggests that a dense QCD medium opaque to partons is formed in more-central Au-Au collisions. However, two-component spectrum analysis reveals a hard component, consistent with parton fragmentation described by pQCD, which can masquerade as "radial flow." Minimum-bias angular correlations reveal that most scattered partons survive as "minijets" even in central Au-Au collisions. Such alternative methods quantitatively describe spectrum and correlation structure via pQCD calculations. RHIC collisions …
We present the mini-proceedings of the workshop on ``Parton fragmentation in the vacuum and in the medium'' held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*, Trento) in February 2008. The workshop gathered both theorists and experimentalists to discuss the current status of investigations of quark and gluon fragmentation into hadrons at different accelerator facilities (LEP, B-factories, JLab, HERA, RHIC, and Tevatron) as well as preparations for extension of these studies at the LHC. The main physics topics covered were: (i) light-quark and gluon …
Medium-induced gluon radiation is usually identified as the dominant dynamical mechanism underling the {\it jet quenching} phenomenon observed in heavy-ion collisions. In its actual implementation, multiple medium-induced gluon emissions are assumed to be independent, leading, in the eikonal approximation, to a Poisson distribution. Here, we introduce a medium term in the splitting probabilities so that both medium and vacuum contributions are included on the same footing in a DGLAP approach. The improvements include energy-momentum conservation at each individual splitting, medium-modified vi…
Within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross section of deeply inelastic scattering off a large nucleus, multiple parton scattering leads to an effective medium-modified fragmentation function and the corresponding medium-modified DGLAP evolution equations. We extend the study to include gluon multiple scattering and induced quark-antiquark production via gluon fusion . We numerically solve these medium-modified DGLAP (mDGLAP) evolution equations and study the scale ($Q^2$), energy ($E$), length ($L$) and jet transport parameter ($\hat…
We study the fragmentation of a jet propagating in a dense quark-gluon plasma. Using a leading, double-logarithmic approximation in perturbative QCD, we compute for the first time the effects of the medium on the vacuum-like emissions. We show that, due to the scatterings off the plasma, the in-medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside the medium can violate angular ordering. We compute the jet fragmentation function and find results in qualitative agreement with measurements at the LHC.
We study the fragmentation of a jet propagating in a dense quark-gluon plasma. Using a leading, double-logarithmic approximation in perturbative QCD, we compute for the first time the effects of the medium on the vacuum-like emissions. We show that, due to the scatterings off the plasma, the in-medium parton showers differ from the vacuum ones in two crucial aspects: their phase-space is reduced and the first emission outside the medium can violate angular ordering. We compute the jet fragmentation function and find results in qualitative agreement with measurements at the LHC.
We discuss the modification of a jet fragmentation function due to medium-induced partonic energy loss in context of leading particle observables in ultrarelativistic nucleus-nucleus interactions. We also analyze the relation between in-medium softening jet fragmentation function and suppression of the jet rates due to energy loss outside the jet cone. The predicted anti-correlation between two effects allows to probe a fraction of partonic energy loss carried out of the jet cone and truly lost to the jet.
The parton-to-hadron fragmentation functions (FFs) obtained from the YaJEM and PYTHIA6 Monte Carlo event generators, are studied for jets produced in a strongly-interacting medium and in the QCD "vacuum" respectively. The medium modifications are studied with the YaJEM code in two different scenarios by (i) accounting for the medium induced virtuality DeltaQ^2 transferred to the leading parton from the medium, and (ii) by altering the infrared sector in the Borghini-Wiedemann approach. The results of our simulations are compared to experimental jet data measured by the CMS experiment in PbPb a…
It is the central goal of our studies to describe parton fragmentation in the hot and dense medium of a quark gluon plasma (QGP). Under the assumption that the medium is not static and homogeneous, knowledge about the temporal evolution of the processes involved can be of essential importance. Therefore, parton fragmentation has been studied with a Monte-Carlo algorithm that approximates the DGLAP-evolution of fragmentation functions via a set of parton cascades. The presented work consists mainly of implementations of this kind of algorithm and the application of a simple approximation, which…
We calculate the evolution of a jet shower due to medium induced splittings in the deep LPM regime. Due to the characteristic energy dependence of the formation time $t_{\rm form}(ω)= \sqrt{ω/\hat{\bar{q}}}$, the radiative break-up process exhibits turbulent characteristics, allowing for analytic predictions of various inclusive properties of the medium induced cascade in an inertial range of energies $T \ll ω\ll E$, where $E$ is the energy of the jet and $T$ is the temperature of the medium.
In this short review paper, we discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron production data in e+e-, deep inelastic scattering and hadronic collisions are presented, together with global analyses of fragmentation functions into light and heavy hadrons and developments on parton fragmentation in perturbative QCD at small momentum fraction. Motivated by the recent RHIC data indicating a significant suppression of large-pT hadron production in heavy-ion collisions, several recent attemp…
Initial conditions are required to solve medium modified DGLAP (mDGLAP) evolution equations for modified fragmentation functions due to multiple scatterings and parton energy loss. Such initial conditions should in principle include energy loss for partons at scale $Q_0$ above which mDGLAP evolution equations can be applied. Several models for the initial condition motivated by induced gluon bremsstrahlung in perturbative QCD are used to calculate the modified fragmentation functions in nuclear medium and to extract the jet transport parameter $\hat q$ from fits to experimental data in deeply …
Within the framework of generalized factorization of higher-twist contributions, including modification to splitting functions of both quark and gluon, we get and numerically resolve the medium-modified DGLAP (mDGLAP) evolution equations. With Woods-Saxon nuclear geometry and Hirano 3D ideal hydrodynamic simulations of hot medium, we study the medium modified fragmentation functions (mFF) in DIS and Au+Au collisions in RHIC. Our calculation imply that the parton density in hot medium produced in RHIC is about 30 times larger than cold nucleon.
We investigate the energy loss and equilibration of highly energetic particles/jets inside a QCD medium. Based on an effective kinetic description of QCD, including $2\leftrightarrow 2$ elastic processes, radiative $1\leftrightarrow 2$ processes, as well as the back-reaction of jet constituents onto the thermal medium, we describe the in-medium evolution of jets from the energy scale of the jet $\sim E$ all the way to the medium scale $\sim T $. While elastic processes and back-reaction are important to describe the equilibration of soft fragments of the jet, we find that the energy loss is do…
Coupled linear Boltzmann transport and hydrodynamic (CoLBT-hydro) model has been developed for simultaneous simulations of jet propagation and jet-induced medium excitation in heavy-ion collisions. Within this coupled approach, the final reconstructed jets in heavy-ion collisions include not only hadrons from the hadronization of medium modified jet shower partons from the linear Boltzmann transport (LBT) but also hadrons from the freeze-out of the jet-induced medium excitation in the hydrodynamic evolution of the bulk medium. Using the CoLBT-hydro model, we study medium modification of the fr…
Based on a multiphase transport model, medium modifications of prompt photon-tagged jet fragmentation function are investigated by comparing prompt photon-tagged hadron azimuthal correlation in Au+Au collisions (0-40\%) with that in p+p collisions at $\sqrt{s_{_{\rm NN}}}$ = 200 GeV. The measured modification factor, $I_{AA}$, increases with the increasing integration range of the away side, which reveals a medium-modified jet shape in which the medium enhancement of soft particles is preferentially located far away from the jet axis. The $I_{AA}$ largely results from strong interactions betwe…
Based on a pQCD inspired dynamical model of jet-medium interactions, Jewel, we have studied possible modifications to inclusive jet yields and a set of jet shape observables, namely, the fragmentation functions and radial momentum distributions when jets propagate through a deconfined partonic medium created in collisions of heavy nuclei at Large Hadron Collider (LHC) energies. Jets are reconstructed with anti-k T algorithm in the pseudorapidity range $|η_{\rm jet} | < 2.1$ for resolution parameter R= 0.2, 0.3 and 0.4. For background subtraction, a Jewel-compatible 4-Momenta subtraction techni…
A study of several observables characterising fragment distributions of medium-modified parton showers using the JEWEL and Q-PYTHIA models is presented, with emphasis on the relation between the different observables.
Recent LHC results indicate a suppression of jet fragmentation functions in Pb-Pb collisions at intermediate values of $ξ=\ln(1/z)$. This seems to contradict the picture of energy loss based on the induced QCD radiation that is expected to lead to the enhancement of in-medium fragmentation functions. We use an effective 1+1 dimensional quasi-Abelian model to describe the dynamical modification of jet fragmentation in the medium. We find that this approach describes the data, and argue that there is no contradiction between the LHC results and the picture of QCD radiation induced by the in-medi…
We study the time structure of vacuum jet evolution via a simple uncertainty principle estimate in the kinematic range explored by current heavy ion collisions at the LHC. We observe that a large fraction of the partonic splittings occur at large times, of the order of several fm. We compare the time distribution of vacuum splittings with the distribution of path lengths traversed by jets in a heavy ion collision. We find that if no medium induced modification of the jet dynamics were present, a very large fraction (larger than 80% for inclusive jets) of the jet splittings would occur outside …
The first order correction to the parton fragmentation functions in a thermal medium is derived in the leading logarithmic approximation in the framework of thermal field theory. The medium-modified evolution equations of the parton fragmentation functions are also derived. It is shown that all infrared divergences, both linear and logarithmic, in the real processes are canceled among themselves and by corresponding virtual corrections. The evolution of the quark number and the energy loss (or gain) induced by the thermal medium are investigated.
The medium modification of dihadron fragmentation functions in the deeply inelastic scattering (DIS) off a large nucleus is studied within the framework of the higher-twist expansion in the collinear factorization formalism. It is demonstrated that the modification due to multiple parton scattering in the nuclear medium is similar to that of the single hadron fragmentation function. However, the conditional distribution of the associated hadron given by the ratio of dihadron to single hadron fragmentation function shows only slight modification. The final results depend modestly on the nuclear…
The recently developed quantum mechanical string+${}^3P_0$ model of polarized quark fragmentation with pseudoscalar and vector meson production has been implemented in a stand alone Monte Carlo program. The simulation enables the detailed study of the quark spin dependent effects in the fragmentation process such as the transverse spin asymmetries. In particular, it allows to investigate the effects of the production and decay of vector mesons on the Collins and dihadron asymmetries of the observed hadrons, and to study the still unknown Collins effect for vector mesons. The main results of th…
Medium modifications of parton fragmentation provide a novel tomographic tool for the study of the hot and dense matter created in ultrarelativistic nucleus-nucleus collisions. Their quantitative analysis, however, is complicated by the strong dynamical expansion of the collision region. Here, we establish for the multiple scattering induced gluon radiation spectrum a scaling law which relates medium effects in a collision of arbitrary dynamical expansion to that in an equivalent static scenario. Based on this scaling, we calculate for typical kinematical values of the RHIC and LHC heavy ion p…
Using a simple quark-diquark model, we extract a set of unpolarized and polarized fragmentation functions for the $Λ$ based on the available unpolarized $Λ$ production data in $e^+ e ^- $ annihilation. It is found that there is a strong SU(3) flavor symmetry breaking in the unpolarized $Λ$ fragmentation functions and that the polarized $u$ and $d$ quark contributions to the polarized $Λ$ fragmentation are positive in medium and large $z$ region. The predictions of $Λ$-polarization with the obtained quark fragmentation functions are compatible with the available data on the longitudinally polar…
The in-medium modification of the scale dependence of the fragmentation function in dense matter, brought about by higher twist corrections to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, is derived. A phenomenologically motivated resummation is outlined which incorporates the next-to-leading twist single gluon emission kernel along with the vacuum emission kernel and provides an in-medium virtuality evolution of the final fragmentation function of a hard jet propagating through dense matter. The concept of a fragmentation function is generalized to include a dep…
We present a Monte Carlo simulation of the perturbative Quantum Chromodynamics (pQCD) shower developing after a hard process embedded in a heavy-ion collision. The main assumption is that the cascade of branching partons traverses a medium which (consistent with standard radiative energy loss pictures) is characterized by a local transport coefficient qhat which measures the virtuality per unit length transferred to a parton which propagates in this medium. This increase in parton virtuality alters the development of the shower and in essence leads to extra induced radiation and hence a soften…
We explore a novel method of describing the radiation friction of particles traveling through a mechanically resistive medium. We introduce a particle motion induced matter warping along the path in a manner assuring that charged particle dynamics occurs subject to radiative energy loss described by the Larmor formula. We compare our description with the Landau-Lifshitz-like model for the radiation friction and show that the established model exhibits non-physical behavior. Our approach predicts in the presence of large mechanical friction an upper limit on radiative energy loss being equal to…
In this paper we implement Schwinger-Keldysh closed-time path integral formalism in non-equilibrium QCD to the definition of Collins-Soper fragmentation function. We consider a high p_T parton in QCD medium at initial time t_0 with arbitrary non-equilibrium (non-isotropic) distribution function f(\vec{p}) fragmenting to hadron. We formulate parton to hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final state interactions with the medium via modification of the Wilson lines in this definition of the non-equilibrium fr…
Medium modification of jet fragmentation functions and parton energy loss in cold and hot matter are reviewed. The predicted nuclear modification of the jet fragmentation function agrees well with the recent HERMES data with a resultant energy loss dE/dx approximately 0.5 GeV/fm. From the the recent PHENIX data of high p_T pi_0 spectra in central Au+Au collisions at sqrt(s)=130 GeV, one extracts an energy loss for a 10 GeV parton that is equivalent to dE/dx=7.3 GeV/fm in a static medium with the same gluon density as in the initial stage of the collision at tau_0=0.2 fm/c. Constraints on jet q…
Medium modification of dihadron fragmentation functions due to gluon bremsstrahlung induced by multiple partonic scattering is studied in both deep-inelastic scattering (DIS) off large nuclei and high-energy heavy-ion collisions within the same framework of twist expansion. The modified fragmentation functions for dihadrons are found to follow closely that of single hadrons leading to a weak nuclear suppression of their ratios as measured by HERMES in DIS experiments. Meanwhile, a moderate medium enhancement of the near-side correlation of two high transverse momentum hadrons with increasing c…
The effect of medium-induced parton energy loss on jet fragmentation is studied in high-energy heavy-ion collisions. It is shown that an effective jet fragmentation function can be extracted from the inclusive $p_T$ spectrum of charged particles in the opposite direction of a tagged direct photon with a fixed transverse energy. We study the modification of the effective jet fragmentation function due to parton energy loss in AA as compared to pp collisions, including $E_T$ smearing from initial state radiations for the photon-tagged jets. The effective fragmentation function at $z=p_T/E_T^γ\si…
Both charged hadrons and D mesons are considered to be excellent probes of QCD matter created in ultra relativistic heavy ion collisions. Surprisingly, recent experimental observations at LHC show the same jet suppression for these two probes, which - contrary to pQCD expectations - may suggest similar energy losses for light quarks and gluons in QCD medium. We here use our recently developed energy loss formalism in a finite size dynamical QCD medium to analyze this phenomenon that we denote as the "heavy flavor puzzle at LHC". We show that this puzzle is a consequence of an unusual combinati…
We study the fragmentation of a jet propagating in a dense quark-gluon plasma. We show that the "vacuum-like" emissions triggered by the parton virtualities can be factorized from the medium-induced radiation responsible for the energy loss within a controlled, "double-logarithmic", approximation in perturbative QCD. We show that the collisions with the plasma constituents modify the vacuum-like parton shower already at leading twist, in two ways: the radiation phase-space is reduced and the first emission outside the medium can violate angular ordering. We compute the jet fragmentation functi…
We present the main theoretical aspects of the quantum mechanical string+${}^3P_0$ model of polarized quark fragmentation for pseudoscalar and vector meson production. The model is an extension of the Lund string fragmentation model that systematically includes the quark spin degree of freedom assuming the ${}^3P_0$ mechanism of quark pair production at string breaking. The recently achieved introduction of vector mesons accounts for the spin correlations between the latter and the quark of the fragmentation chain. The string+${}^3P_0$ model reproduces transverse spin effects such as the Colli…
We investigate the medium induced fragmentation of jets in a high-temperature QCD plasma. Based on an effective kinetic theory of QCD, we study the non-equilibrium evolution of the jet shower and the chemical equilibration of jet fragments in the medium. By including radiative emissions as well as elastic interactions, our approach extends all the way from the jet energy scale to the temperature of the medium and includes important effects such as the recoil of the medium. We present results for the in-medium fragmentation, including chemical and kinetic equilibration of the soft fragments and…
We present predictions for b-quark production in photoprodcution and compare with experimental data from HERA. Our theoretical predictions are obtained at next-to-leading-order in the general-mass variable-flavor-number scheme, an approach which takes into account the finite mass of the b quarks. We use realistic evolved nonperturbative fragmentation functions obtained from fits to e+e- data. We find in general good agreement of data with both the GM-VFNS and the FFNS calculations, while the more precise ZEUS data seem to prefer the GM-VFNS predictions.
Modifications to quark and antiquark fragmentation functions due to quark-quark (antiquark) double scattering in nuclear medium are studied systematically up to order \cal{O}(α_{s}^2)$ in deeply inelastic scattering (DIS) off nuclear targets. At the order $\cal{O}(α_s^2)$, twist-four contributions from quark-quark (antiquark) rescattering also exhibit the Landau-Pomeranchuck-Midgal (LPM) interference feature similar to gluon bremsstrahlung induced by multiple parton scattering. Compared to quark-gluon scattering, the modification, which is dominated by $t$-channel quark-quark (antiquark) scatt…
The value of the parton to hadron fragmentation function in QCD in vacuum (for example from proton-proton collisions at high energy colliders) is directly/indirectly used in the literature to study the jet quenching and the hadron production from quark-gluon plasma at RHIC and LHC. In this paper we show that this is not possible because, unlike the perturbative propagator in non-equilibrium QCD, the parton to hadron fragmentation function is a non-perturbative quantity in QCD and hence it is not possible to decompose the fragmentation function in non-equilibrium QCD into the vacuum part and th…
Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the energy loss and hadronization mechanisms of heavy quarks in medium, the evolution profile of pre-equilibrium stage, the flow of medium and the temperature dependence of heavy quark diffusion coefficient influence the suppression and elliptic flow of heavy mesons at RHIC and the LHC. Our result shows that different modeling of initial condition…
The observed strong suppression of heavy flavored hadrons produced with high $p_T$, is caused by final state interactions with the created dense medium. Vacuum radiation of high-pT heavy quarks ceases at a short time scale, as is confirmed by pQCD calculations and by LEP measurements of the fragmentation functions of heavy quarks. Production of a heavy flavored hadrons in a dense medium is considerably delayed due to prompt breakup of the hadrons by the medium. This causes a strong suppression of the heavy quark yield because of the specific shape of the fragmentation function. The parameter-f…
We review recent progress in the study of parton propagation, interaction and fragmentation in both cold and hot strongly interacting matter. Experimental highlights on high-energy hadron production in deep inelastic lepton-nucleus scattering, proton-nucleus and heavy-ion collisions, as well as Drell-Yan processes in hadron-nucleus collisions are presented. The existing theoretical frameworks for describing the in-medium interaction of energetic partons and the space-time evolution of their fragmentation into hadrons are discussed and confronted to experimental data. We conclude with a list of…
Within the framework of the constituent quark model, it is shown that the single hadron fragmentation function of a parton can be expressed as a convolution of shower diquark or triquark distribution function and quark recombination probability, if the interference between amplitudes of quark recombination with different momenta is neglected. The recombination probability is determined by the hadron's wavefunction in the constituent quark model. The shower diquark or triquark distribution functions of a fragmenting jet are defined in terms of overlapping matrices of constituent quarks and part…
We use a Monte Carlo approach to study hadron azimuthal angular correlations in high energy proton-proton and central nucleus-nucleus collisions at the BNL Relativistic Heavy Ion Collider (RHIC) energies at mid-rapidity. We build a hadron event generator that incorporates the production of $2\to 2$ and $2\to 3$ parton processes and their evolution into hadron states. For nucleus-nucleus collisions we include the effect of parton energy loss in the Quark-Gluon Plasma using a modified fragmentation function approach. In the presence of the medium, for the case when three partons are produced in …
We investigate how the gravitational form factors of the nucleon undergo changes in nuclear matter, emphasizing the Abel transformation from the three-dimensional (3D) Breit frame to the two-dimensional (2D) light-front frame. Since the gravitational form factors reveal the mechanical structure of the nucleon, we examine also the medium modifications of the energy-momentum, pressure, and shear-force distributions. We scrutinize the stabilities of the nucleon in nuclear matter. For this purpose, we employ the in-medium modified SU(2) Skyrme model to study these mechanical quantities of the nucl…
Medium modification of jet fragmentation function due to multiple scattering and induced gluon radiation leads directly to jet quenching or suppression of leading particle distribution from jet fragmentation. One can extract an effective total parton energy loss which can be related to the total transverse momentum broadening. For an expanding medium, both are shown to be sensitive to the initial parton density and formation time. Therefore, one can extract the initial parton density and formation time from simultaneous measurements of parton energy loss and transverse momentum broadening. Imp…
Mapping jet substructure in heavy-ion collisions with track functions
CERN（欧洲核子研究中心）；Brookhaven National Laboratory（布鲁海文国家实验室）；Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯宇宙科学与技术大学研究所）
