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 density distribution. Comparisons with the experimental results on two hadron correlations as obtained by the HERMES collaboration at DESY are presented.
Quark and gluon parton dihadron fragmentation functions and their evolution are studied in the process of e+e- annihilation. We provide definitions of such dihadron fragmentation functions in terms of parton matrix elements and derive the momentum sum rules and their connection to single hadron fragmentation functions. We parameterize results from the Lund Monte Carlo model JETSET as the initial conditions for the parton dihadron fragmentation functions at the scale Q_0^2=2 GeV^2. The evolution equations for the quark and gluon fragmentation functions are solved numerically and the results at …
Dihadron fragmentation functions and their evolution are studied in the process of $e^+e^-$ annihilation. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) is shown to factorize into a short distance parton cross section and a long distance dihadron fragmentation function. We provide the definition of such a dihadron fragmentation function in terms of parton matrix elements and derive its DGLAP evolution equation at leading log. The evolution equation for the non-singlet quark fragmentation …
We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) in e+ e- annihilation is shown to factorize into a short distance parton cross section and the long distance dihadron fragmentation function. We also derive the DGLAP evolution equation of this function at leading log. The evolution equation for the non-singlet quark fragmentation function is solved numerically with a simple ansatz for the init…
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…
We study the dihadron fragmentation functions (DiFF) of longitudinally polarized quarks into pion pairs. The quark-jet framework is used to model the sequential hadronization of a polarized quark into hadrons, where the polarization transfer to the remnant quark in each hadron emission step is calculated using the spin density matrix formalism. Using Monte Carlo (MC) simulations of the hadronization process, we find a nonvanishing helicity dependent DiFF, $G_1^\perp$ , which is also related to the longitudinal jet handedness. A method is developed for extracting the angular moments of this DiF…
Two particle correlations within a single jet produced in deeply inelastic scattering (DIS) off a large nucleus as well as in heavy-ion collisions are explored. This is performed within the framework of the medium modified dihadron fragmentation functions. The modification occurs due to gluon bremsstrahlung induced by multiple scattering. 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 cor…
We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) in e+ e- annihilation is shown to factorize into a short distance parton cross section and the long distance dihadron fragmentation function. We also derive the DGLAP evolution equation of this function at leading log. The evolution equation for the non-singlet and singlet quark fragmentation function and the gluon fragmentation function are so…
Within the most recent extension of the quark-jet hadronization framework, we explore the transverse-polarization-dependent dihadron fragmentation functions (DiFFs) $H_1^\sphericalangle$ and $H_1^\perp$ of a quark into $π^+π^-$ pairs. Monte Carlo (MC) simulations are employed to model polarized quark hadronization and calculate the corresponding number densities. These, in turn, are used to extract the Fourier cosine moments of the DiFFs $H_1^\sphericalangle$ and $H_1^\perp$. A notable finding is that there are previously unnoticed apparent discrepancies between the definitions of the so-calle…
We calculate the one-loop corrections to dihadron production in Deep Inelastic Scattering (DIS) at small x using the Color Glass Condensate formalism. We show that all UV and soft singularities cancel while the collinear divergences are absorbed into quark and anti quark-hadron fragmentation functions. Rapidity divergences lead to JIMWLK evolution of dipoles and quadrupoles describing multiple-scatterings of the quark anti-quark dipole on the target proton/nucleus. The resulting cross section is finite and can be used for phenomenological studies of dihadron angular correlations at small x in …
Probing Gluon Linear Polarization with Dihadron Fragmentation in $χ_b$ Decays
Beijing University of Chemical Technology（北京化工大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；China Center of Advanced Science and Technology（中国科学技术中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Transverse-spin dependent energy-energy correlators in proton-proton collisions within the dihadron fragmentation framework
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·布海米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（纽约州立大学石溪分校核科学前沿中心）；Temple University（天普大学）；Lebanon Valley College（黎巴嫩谷学院）
Dihadron fragmentation framework for near-side energy-energy correlators
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Stony Brook University（石溪大学）；Temple University（天普大学）；Lebanon Valley College（黎巴嫩谷学院）
We present preliminary results for an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity, while di-hadron fragmentation functions are taken from the semi-inclusive production of two pion pairs in back-to-back jets in $e^+ e^-$ annihilation. The latter data from Belle have been reanalyzed using the replica method and a mor…
We study the suppressions of high transverse momentum single hadron and dihadron productions in high-energy heavy-ion collisions based on the framework of a next-to-leading-order perturbative QCD parton model combined with the higher-twist energy loss formalism.Our model can provide a consistant description for the nuclear modification factors of single hadron and dihadron productions in central and non-central nucleus-nucleus collisions at RHIC and the LHC energies. We quantitatively extract the value of jet quenching parameter $\hat q$ via a global $χ^2$ analysis, and obtain ${\hat{q}}/{T^3}…
We report on the first extraction of interference fragmentation functions from the semi-inclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite π+π- pairs is related to the transverse polarization of fragmenting quarks through a significant polarized dihadron fragmentation function. Extraction of the latter requires the knowledge of its unpolarized counterpart, the probability density for a quark to fragment in a π+π- pair. Since data for the unpolarized cross section are missing, we extrac…
Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders
School of Physics, Peking University（北京大学物理学院）；School of Physics, Zhengzhou University（郑州大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；China Center of Advanced Science and Technology（中国高等科学技术中心）
Back-to-back dihadron spectra in high-energy heavy-ion collisions are studied within the next-to-leading order (NLO) perturbative QCD parton model with jet quenching incorporated via modified jet fragmentation functions due to radiative parton energy loss in dense medium. The experimentally observed appearance of back-to-back dihadrons at high $p_T$ is found to originate mainly from jet pairs produced close and tangential to the surface of the dense matter. However, a substantial fraction of observed high $p_T$ dihadrons also comes from jets produced at the center of the medium after losing fi…
Probing the Color-Octet Mechanism via Dihadron Fragmentation in $χ_b$ Decays
Beijing University of Chemical Technology（北京化工大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；China Center of Advanced Science and Technology（中国高等科学技术中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ($p_{\rm T}$) 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 $p_{\rm T}$ hadron productions, we extract $\hat{q}$ quantitatively via a global fit to d…
STAR measurements of dihadron azimuthal correlations ($Δϕ$) are reported in mid-central (20-60\%) Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV as a function of the trigger particle's azimuthal angle relative to the event plane, $ϕ_{s}=|ϕ_{t}-ψ_{\rm EP}|$. The elliptic ($v_2$), triangular ($v_3$), and quadratic ($v_4$) flow harmonic backgrounds are subtracted using the Zero Yield At Minimum (ZYAM) method. The results are compared to minimum-bias d+Au collisions. It is found that a finite near-side ($|Δϕ|<π/2$) long-range pseudorapidity correlation (ridge) is present in the in-plane direct…
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 present a new proposal to study the helicity-dependent dihadron fragmentation functions (DiFF), which describe the correlations of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recent experimental searches for this DiFF via azimuthal asymmetries in back-to-back hadron pair production in $e^+e^-$ annihilation by the ${\tt BELLE}$ Collaboration did not yield a signal. Here we propose a new way to access this DiFF in $e^+e^-$ annihilation, motivated by the recently recalculated cross section of this reaction, which explains why th…
Dihadron azimuthal correlations in Au+Au collisions at $\sqrt{S_{NN}}$=200 GeV have been explored by using a multi-phase transport (AMPT) model. In order to obtain the contributions from jet-medium interactions, the combined harmonic flow background is subtracted from the raw dihadron correlation functions. The signals are compared in three associated transverse momentum ($p_{T}^{assoc}$) bins: 0.2-0.8 GeV/c, 0.8-1.4 GeV/c and 1.4-2.0 GeV/c from central to semi-peripheral geometries. The medium modifications are observed from changes in the signal shape and the relative jet contribution has be…
Using a recently-developed perturbative-QCD approach for jet evolution in a dense quark-gluon plasma, we study the nuclear modification factor for the jet fragmentation function. The qualitative behaviour that we find is in agreement with the respective experimental observations in Pb+Pb collisions at the LHC: a pronounced nuclear enhancement at both ends of the spectrum. Our Monte Carlo simulations are supplemented with analytic estimates which clarify the physical interpretation of the results. The main source of theoretical uncertainty is the sensitivity of our calculations to a low-momentu…
The discovery of collectivity in proton-proton collisions, is one of the most puzzling outcomes from the two first runs at LHC, as it points to the possibility of creation of a Quark-Gluon Plasma, earlier believed to only be created in heavy ion collisions. One key observation from heavy ion collisions is still not observed in proton-proton, namely jet-quenching. In this letter it is shown how a model capable of describing soft collective features of proton-proton collisions, also predicts modifications to jet fragmentation properties. With this starting point, several new observables suited f…
The Sivers effect describes the correlation of the unpolarized parton's transverse momentum with the transverse spin of the nucleon. It manifests as a sine modulation of the cross section for single hadron semi-inclusive deep inelastic scattering (SIDIS) on a transversely polarized nucleon with the azimuthal angle between the produced hadron's transverse momentum and the nucleon spin ($φ_h$ and $φ_S$, respectively). It has been recently suggested that the Sivers effect can also be measured in two hadron SIDIS process as sine modulations involving the azimuthal angles $φ_T$ and $φ_R$ of both th…
We compute the inclusive unpolarized dihadron production cross section in the far from back-to-back region of $e^+ e^-$ annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation ro…
We discuss nuclear modification of fragmentation functions in the context of the so-called ``rescaling models''. These models implement partial deconfinement inside nuclei by modifying the fragmentation functions perturbatively. We apply these models to the analysis of nuclear hadron production in deep inelastic scattering processes at the HERMES and EMC experiments.
In ultrarelativistic heavy ion collisions, charm quark fragmentation is modified due to the melting of strings inside the high density partonic matter. D mesons produced in hadronization can further produce J/psi particles. Using a multiphase transport model, we investigate the effect on the rapidity distribution of the produced J/psi particles with two different charm quark fragmentation functions. It is shown that the J/psi rapidity distribution is sensitive to the nuclear modification of charm quark fragmentation and thus is a good indicator of the onset of string melting and the production…
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…
The physics of the quenching of hard jets in dense matter is briefly reviewed. This is presented within the framework of the partonic medium modification of the fragmentation functions. Modifications in both deeply inelastic scattering (DIS) off large nuclei and high-energy heavy-ion collisions are presented.
Multiple scattering, induced radiative energy loss and modified fragmentation functions of a heavy quark in nuclear matter are studied within the framework of generalized factorization in perturbative QCD. Modified heavy quark fragmentation functions and energy loss are derived in detail with illustration of the mass dependencies of the Landau-Pomeranchuk-Migdal interference effects and heavy quark energy loss. Due to the quark mass dependence of the gluon formation time, the nuclear size dependencies of nuclear modification of the heavy quark fragmentation function and heavy quark energy loss…
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…
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…
We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-p_T particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the NRQCD formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include nonabelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at NNLO, and verify that they are absorbe…
Probing Quark Electromagnetic Properties via Entangled Quark Pairs in Fragmentation Hadrons at Lepton Colliders
Peking University（北京大学）；Zhengzhou University（郑州大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；China Center of Advanced Science and Technology（中国高等科学技术中心）
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 study inclusive jet suppression and modifications in the quark-gluon plasma (QGP) with a transport-based model. The model includes vacuum-like parton shower evolution at high-virtuality, a linearized transport for jet-medium interactions, and a simple ansatz for the jet-induced hydrodynamic response of the medium. Model parameters are calibrated to nuclear modification factors for inclusive hadron $R_{AA}^{h}$ and single inclusive jets $R_{AA}^{j}$ with cone size $R=0.4$ in 0-10% central Au-Au and Pb-Pb collisions measured at the RHIC and LHC. The calibrated model consistently describes the…
Recent progresses in the study of jet modification in hot medium and their consequences in high-energy heavy-ion collisions are reviewed. In particular, I will discuss energy loss for propagating heavy quarks and the resulting modified fragmentation function. Medium modification of the parton fragmentation function due to quark recombination are formulated within finite temperature field theory and their implication on the search for deconfined quark-gluon plasma is also discussed
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.
Modified quark fragmentation functions in deeply inelastic $eA$ collisions and their QCD evolution equations are derived for the first time in the framework of multiple parton scattering. Induced radiation gives rise to additional terms in the evolution equations and thus softens the modified quark fragmentation functions. The results in the next-leading-twist depend on both diagonal and off-diagonal twist-four parton distributions and the combination of which clearly manifests the LPM interference pattern. The predicted modification depends quadratically on the nuclear size ($A^{2/3}$). Gener…
Multiple parton scattering and induced parton energy loss is studied in deeply inelastic scattering (DIS) off nuclei. The effect of multiple scattering of a highly off-shell quark and the induced parton energy loss is expressed in terms of the modification to the quark fragmentation functions. We derive such modified quark fragmentation functions and their QCD evolution equations in DIS using generalized factorization of higher twist parton distributions. We consider double-hard, hard-soft parton scattering as well as their interferences in the same framework. The final result, which depends o…
We study the fragmentation function of jets propagating through a dense quark-gluon plasma within perturbative QCD. Our results for its nuclear modification factor are in qualitative agreement with the experimental data in Pb+Pb collisions at the LHC. In particular, we reproduce the enhancements seen in the data at both relatively soft and relatively large transverse momenta, with clear physical interpretations. The perturbative predictions however are quite sensitive to the value of the infrared cutoff mimicking the confinement scale, due to the fact that the fragmentation function is not an …
We study the transverse momentum spectrum of hadrons in jets. By measuring the transverse momentum with respect to a judiciously chosen axis, we find that this observable is insensitive to (the recoil of) soft radiation. Furthermore, for small transverse momenta we show that the effects of the jet boundary factorize, leading to a new transverse-momentum-dependent (TMD) fragmentation function. In contrast to the usual TMD fragmentation functions, it does not involve rapidity divergences and is universal in the sense that it is independent of the type of process and number of jets. These results…
Medium modification of γ-tagged jets in high-energy heavy-ion collisions is investigated within a Linearized Boltzmann Transport model for jet propagation that includes both elastic parton scattering and induced gluon emission. Inclusion of recoiled medium partons in the reconstruction of partonic jets is found to significantly reduce the net jet energy loss. Experimental data on γ-jet asymmetry and survival rate in Pb + Pb collisions at \sqrt{s}=2.76 TeV can be reproduced. Medium modifications of reconstructed jet fragmentation function, transverse profile and energy flow outside the jet-cone…
We study modification of the photon-tagged and inclusive jets in $pp$ collisions at $\sqrt{s}=7$ TeV due to mini-quark-gluon plasma which can be produced in high multiplicity events. We show that for underlying events with $dN_{ch}/dη\sim 20-60$ the medium effects lead to a considerable modification of the photon-tagged and inclusive jet fragmentation functions. For inclusive jets the magnitude of the effect is surprisingly large. The effect is quite strong even for typical underlying events. We find that at $\sqrt{s}=7$ TeV the spectrum of charged hadrons is suppressed by $\sim 35-40$ % at $p…
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…
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…
The fragmentation functions of the pion with distinction between $D_{u}^{π^{+}}$, $D_{d}^{π^{+}}$, and $D_{s}^{π^{+}}$ are studied in the Field-Feynman recursive model, by taking into account the flavor structure in the excitation of quark-antiquark pairs by the initial quarks. The obtained analytical results are compatible with available empirical results. The framework is also extended to predict the fragmentation functions of the kaon with distinction between $D_{\bar{s}}^{K^{+}}(z)$, $D_{u}^{K^{+}}(z)$, $D_{s}^{K^{+}}(z)$, and $D_{d}^{K^{+}}(z)$. This work gives a significant modification …
