Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma

We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium q→gq transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.     

Jet quenching versus jet enhancement: a quantitative study of the BDMPS-Z gluon radiation spectrum

We study the gluon radiation spectrum off a hard in-medium produced quark in the multiple soft-rescattering formalism of Baier–Dokshitzer–Mueller–Peigné–Schiff and of Zakharov (BDMPS-Z). Its dependence on the quark and gluon energy, on the gluon transverse momentum, on the in-medium pathlength and on the rescattering properties of the nuclear medium is analyzed quantitatively. The two components of gluon radiation, the hard vacuum radiation associated to the quark production vertex, and the medium-induced rescattering contribution interfere destructively. For small spatial extensions of the medium, this destructive interference overcompensates the hard vacuum radiation, and the total medium-induced radiative energy loss decreases as ΔE∝− L³. Medium-induced gluon production dominates only above a finite critical length L>L_crit which varies between 3 and more than 6 fm depending on the rescattering properties of the medium. Deviations from the BDMPS-L²-behaviour persist above L_crit. The medium-dependence of the angular gluon distribution is dominated by transverse brownian k-broadening. This results in a depletion of the low transverse momentum part of both the hard and the medium-induced contribution. As a consequence, the medium-induced energy loss outside a finite angular cone size Θ can be more than a factor two larger than the total medium-induced radiative energy loss. We discuss implications of these results for the jet quenching signal in relativistic heavy-ion collisions at RHIC and LHC.     

Gluon emission of heavy quarks: Dead cone effect

The lowest-order induced soft gluon radiation processes of heavy quarks have been analysed to quantify the dead cone effect. This effect is most likely expected to suppress significantly the energy loss of charm quarks passing an amorphous color-neutral deconfined medium, as has been concluded from recent experiments at RHIC.     

<Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript>-tagged quark jets at the large hadron collider

The Large Hadron Collider will allow studies of hard probes in nucleus-nucleus collisions which were not accessible at the Relativistic Heavy Ion Collider—even the study of small cross-section Z ⁰-tagged jets becomes possible. Going beyond the measurement of back-to-back correlations of two strongly interacting particles to measure plasma properties, we replace one side by an electromagnetic probe which propagates through the plasma undisturbed and therefore provides a measurement of the energy of the initial hard scattering. We show that at sufficiently high transverse momentum the Z ⁰-tagged jets originate predominately from the fragmentation of quarks and anti-quarks while gluon jets are suppressed. We propose to use lepton-pair tagged jets to study medium-induced partonic energy loss and to measure in-medium parton fragmentation functions to determine the opacity of the quark gluon plasma.     

Charm quark energy loss at RHIC

Heavy quark energy loss in a hot QCD plasma is computed taking into account the competing effects due to suppression of zeroth order gluon radiation below the plasma frequency and the enhancement of gluon radiation due to first order medium induced bremsstrahlung. The results suggest a surprising degree of cancellation between the two medium effects for charm quarks and provide a possible explanation for the null effect observed by PHENIX in the prompt electron spectrum in Au+Au at √s = 130 AGeV. In this paper only the main results for heavy quark energy loss will be presented. For more detailed version see [1] and references therein.     

Probing the medium-induced energy loss of bottom quarks by dimuon production in heavy ion collisions at LHC

The potential of coming experiments on the Large Hadron Collider (LHC) to observe the rescattering and energy loss of heavy quarks in the dense matter created in heavy ion collisions is discussed. We analyze the sensitivity of high-mass pairs from semileptonic decays and secondary 's from single B decays to the medium-induced bottom quark energy loss. Received: 18 December 2000 / Revised version: 17 May 2001 / Published online: 6 July 2001     

Nonlinear dynamics of soft boson collective excitations in hot QCD plasma III: Bremsstrahlung and energy losses

Within the framework of semiclassical approximation a general formalism for deriving an effective current generating bremsstrahlung of arbitrary number of soft gluons (longitudinal or transverse ones) in scattering of higher-energy parton off thermal parton in hot quark-gluon plasma with subsequent extension to two and more scatterers is obtained. For the case of static color centers, an expression for energy loss induced by usual bremsstrahlung of lowest-order with allowance for an effective temperature-induced gluon mass and finite mass of the projectile (heavy quark) is derived. The detailed analysis of contribution to radiation energy loss associated with existence of effective three-gluon vertex induced by hot QCD medium is performed. It is shown that in general, the bremsstrahlung associated with this vertex has no sharp direction (as in the case of usual bremsstrahlung) and therefore here, we can expect an absence of suppression effect due to multiple scattering. For the case of two-color static scattering centers it was shown that the problem of calculation of bremsstrahlung induced by four-gluon hard thermal loop (HTL) vertex correction can be reduced to the problem of the calculation of bremsstrahlung induced by three-gluon HTL correction. It was shown that for limiting value of soft gluon occupation number N_k 1/α_s all higher processes of bremsstrahlung of arbitrary number of soft gluons become of the same order in coupling, and the problem of resummation of all relevant contributions to radiation energy loss of fast parton, arises. An explicit expression for matrix element of two soft gluon bremsstrahlung in small angles approximation is obtained.     

Q-PYTHIA: a medium-modified implementation of final state radiation

We present a Monte Carlo implementation of medium-induced gluon radiation in the final-state branching process. Medium effects are introduced through an additive term in the splitting functions. We have implemented such modification within PYTHIA. We show the medium effects on the hump-backed plateau, and the transverse-momentum and angular distributions with respect to the parent parton. As expected, with increasing medium densities there is an increase (decrease) of partons with small (large) momentum fraction, and angular broadening is observed. The effects on the transverse-momentum distributions are more involved, with an enhancement of low- and intermediate-p _T partons and a decrease at large p _T, which is related to energy conservation, and to the lack of momentum exchange with the medium in our approach.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

Suppression of high-pT non-photonic electrons in Au+Au collisions at $\sqrt{s_{NN}}$ =200 GeV

The strong suppression of high p_T hadrons observed at RHIC has led to the interpretation that energetic partons lose their energy via induced gluon radiation in the hot and dense matter before fragmenting into hadrons. The study of heavy quark production can extend our understanding of this scenario. Due to the dead cone effect, the suppression of heavy quark mesons at high p_T is expected to be smaller than that observed for charged hadrons at the same energy. The measurement of non-photonic single electrons up to high p_T provides information on charm and beauty production. The semi-leptonic decays of D and B mesons are the dominant contribution to the non-photonic electron spectra. The preliminary spectra from p+p, d+Au and Au+Au collisions at  =200 GeV have been extracted for mid-rapidity non-photonic electrons in the range 1.5<p_T (GeV/c)<10. The corresponding nuclear modification factors (R_AA) are presented and show a large suppression in central Au+Au collisions, indicating an unexpectedly large energy loss for heavy quarks in the hot and dense matter created at RHIC. This observed suppression is compared to recent theoretical models. PACS  13.85.Qk; 13.20.Fc; 13.20.He; 25.75.Dw     

Heavy quark results from STAR

I report the most recent measurements on open heavy flavor production at RHIC on behalf of the STAR collaboration. The total charm production cross section in midrapidity at RHIC energy is found to approximately scale by number of binary collisions in d + Au, Cu + Cu and Au + Au collisions. The nuclear modification factor of non-photonic electrons is strongly suppressed in central Au + Au collisions, suggesting substantial heavy quark energy loss at RHIC. The bottom decay contribution to non-photonic electrons was studied via the e–h and e–D ⁰ azimuthal angular correlations. The bottom contribution is found to be important at p _T >5 GeV/c, and is consistent with the FONLL calculation within uncertainties. Charm production through gluon jet splitting was measured by studying the D ^*± contents in the fully reconstructed jets in p+p collisions. This rate is consistent with pQCD evaluation of gluon splitting into a pair of charm quarks and subsequent hadronization.     

Explanation of dijet asymmetry in Pb-Pb collisions at the Large Hadron Collider

We investigate the medium modification of a partonic jet shower traversing in a hot quark-gluon plasma. We derive and solve a differential equation that governs the evolution of the radiated gluon distribution as the jet propagates through the medium. Energy contained inside the jet cone is lost by dissipation through elastic collisions with the medium and by scattering of shower partons to larger angles. We find that the jet energy loss at early times is dominated by medium effects on the vacuum radiation, and by medium-induced radiation effects at late times. We compare our numerical results for the nuclear modification of the dijet asymmetry with that recently reported by the ATLAS Collaboration.     

Medium-induced emissions of hard gluons

We present a derivation of the medium-induced gluon radiation spectrum beyond the current limitation of soft gluon emission. Making use of the path integral approach to describe the propagation of high-energy particles inside a medium, we study the limiting case of a hard gluon emission. Analytical and numerical results are presented and discussed within the multiple soft scattering approximation. An ansatz interpolating between soft and hard gluon emissions is provided. The Landau–Pomeranchuk–Migdal effect is observed in the expected kinematic region.     

T-matrix approach to heavy quark diffusion in the QGP

We assess transport properties of heavy quarks in the quark–gluon plasma (QGP) using static heavy-quark (HQ) potentials from lattice-QCD calculations in a Brueckner many-body T-matrix approach to evaluate elastic heavy-quark–light-quark scattering amplitudes. In the attractive meson and diquark channels, resonance states are formed for temperatures up to ∼1.5T _c, increasing pertinent drag and diffusion coefficients for heavy-quark rescattering in the QGP beyond the expectations from perturbative-QCD calculations. We use these transport coefficients, complemented with perturbative elastic HQ gluon scattering, in a relativistic Langevin simulation to obtain HQ p _t distributions and elliptic flow (v ₂) under conditions relevant for the hot and dense medium created in ultrarelativistic heavy-ion collisions. The heavy quarks are hadronized to open-charm and -bottom mesons within a combined quark-coalescence fragmentation scheme. The resulting single-electron spectra from their semileptonic decays are confronted with recent data on “non-photonic electrons” in 200 A GeV Au–Au collisions at the Relativistic Heavy-Ion Collider (RHIC).     

Comparison of radiative energy loss models in a hot QCD medium

The suppression of high pT$p_T$ hadron production in heavy ion collisions is thought to be due to energy loss by gluon radiation off hard partons in a QCD medium. Existing models of QCD radiative energy loss in a color-charged medium give estimates of the coupling strength of the parton to the medium which differ by a factor of 5. We will present a side-by-side comparison of two different formalisms to calculate the energy loss of light quarks and gluons: the multiple soft scattering approximation (ASW-MS) and the opacity expansion formalism (ASW-SH and WHDG-rad). A common time-temperature profile is used to characterize the medium. The results are compared to the single hadron suppression R_AA$R_{AA}$ at RHIC energies.     

Investigation of the splitting of quark and gluon jets

The splitting processes in identified quark and gluon jets are investigated using longitudinal and transverse observables. The jets are selected from symmetric three-jet events measured in Z decays with the Delphi detector in 1991-1994. Gluon jets are identified using heavy quark anti-tagging. Scaling violations in identified gluon jets are observed for the first time. The scale energy dependence of the gluon fragmentation function is found to be about two times larger than for the corresponding quark jets, consistent with the QCD expectation . The primary splitting of gluons and quarks into subjets agrees with fragmentation models and, for specific regions of the jet resolution , with NLLA calculations. The maximum of the ratio of the primary subjet splittings in quark and gluon jets is . Due to non-perturbative effects, the data are below the expectation at small . The transition from the perturbative to the non-perturbative domain appears at smaller for quark jets than for gluon jets. Combined with the observed behaviour of the higher rank splittings, this explains the relatively small multiplicity ratio between gluon and quark jets. Received: 18 February 1998 / Published online: 24 April 1998     

Meson hyperfine splittings and asymptotic freedom

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F¹-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.     

A new tool for the study of fundamental interactions: Parity-odd correlations in quark fragmentation

Parity-odd correlations among the fragmentation products of quarks should reveal the longitudinal polarization of these quarks. Possible applications of this idea include a new way to determine the Weinberg angle from data on neutrino reactions, a sensitive test of the quark-antiquark creation picture in e⁺e^? annihilation, a way to determine the weak coupling of hypothetical heavy particles to light quarks and a test for the parton-parton scattering model with elementary gluon exchange for high p⊥ events in nucleon-nucleon collisions.     

Antiangular ordering of gluon radiation in QCD media

We investigate angular and energy distributions of medium-induced gluon emission off a quark-antiquark antenna in the framework of perturbative QCD as an attempt toward understanding, from first principles, jet evolution inside the quark-gluon plasma. In-medium color coherence between emitters, neglected in all previous calculations, leads to a novel mechanism of soft-gluon radiation. The structure of the corresponding spectrum, in contrast with known medium-induced radiation, i.e., off a single emitter, retains some properties of the vacuum case; in particular, it exhibits a soft divergence. However, as opposed to the vacuum, the collinear singularity is regulated by the pair opening angle, leading to a strict angular separation between vacuum and medium-induced radiation, denoted as antiangular ordering. We comment on the possible consequences of this new contribution for jet observables in heavy-ion collisions.     

Self-consistent method for calculation of reflection coefficients of the interface with the dielectric tensor’s rotation

We give an interface between two same media whose orientation of optical axis, however, is rotated, and describe a method in detail to show how to calculate reflectance coefficient in this interface. We also give the theoretical simulation of the reflectance coefficient and discuss the effect of the rotation angle and the direction of electron vector on the reflectance coefficient. For the un-polarized lights the theoretical calculated results show that the reflectance coefficients (r _x1 and r _y1) are very small when the rotated angle is small, and they arrive at the maximum value as the rotation angle is equal to a decided value. For the polarized light, when the rotation angle is small, the reflectance coefficients (r _x1 and r _y1) are also small. Only when the rotation angle increases to a certain extent, they can reach the maximum values and be strongly affected by the direction of electronic vector. However, this effect on the reflectance coefficient in the direction of the maximum refraction is different from that in the direction of minimum refraction.