We compare medium induced energy loss and $p_{\perp}$-broadening in perturbative QCD with that of the trailing string picture of SYM theory. We consider finite and infinite extent matter as well as relativistic heavy quarks which correspond to those being produced in the medium or external to it. When expressed in terms of the appropriate saturation momentum, we find identical parametric forms for energy loss in perturbative QCD and SYM theory. We find simple correspondences between $p_{\perp}$-broadening in QCD and in SYM theory although $p_{\perp}$-broadening is radiation dominated in SYM theory and multiple scattering dominated in perturbative QCD.
We study the radiative correction to $p_\perp$-broadening of a fast quark in a quark-gluon plasma beyond the soft gluon approximation. We find that the radiative contribution to quark $\langle p_\perp^2\rangle$ for RHIC and LHC conditions is negative.
We study contribution of radiative processes to $p_{\perp}$-broadening of fast partons in an expanding quark-gluon plasma. It is shown that the radiative correction to $\langle p_{\perp}^2\rangle$ for the QGP produced in $AA$-collisions at RHIC and LHC may be negative, and comparable in absolute value with the non-radiative contribution. We have found that the QGP expansion enhances the radiative suppression of $p_\perp$-broadening as compared to the static medium.
The contribution of radiative processes to $p_\perp$-broadening of fast partons in a quark-gluon plasma is investigated. Calculations are performed beyond the soft gluon approximation. It is shown that the radiative correction to $\langle p_{\perp}^2\rangle$ for conditions of heavy ion collisions at RHIC and LHC is negative and can be comparable in absolute value with the nonradiative contribution. This prediction differs radically from the essentially positive contribution of radiative processes to $p_{\perp}$-broadening, which was predicted earlier in the literature.
It has been known for many years that soft radiation can give potentially large double-logarithm corrections to $p_\perp$ broadening of a high-energy particle traveling through QCD matter, but that this soft radiation correction can be absorbed into an effective value $\hat q_{\rm eff}$ for the medium $p_\perp$-broadening parameter $\hat q$. Here "soft" means high energy compared to medium scales but soft compared to the original high-energy particle traveling through the medium. A similar situation arises in the case of soft corrections to hard splitting of a high-energy particle, such as har…
We calculate the probability distribution P(k_\perp) for the momentum perpendicular to its original direction of motion that an energetic quark or gluon picks up as it propagates through weakly coupled quark-gluon plasma in thermal equilibrium.
We study radiative $p_{\perp}$-broadening of high energy quarks passing through hot and cold QCD matter. With $L$ the length of the matter and $l_{0}$ the size of constituents of the matter we find $\avg{p_{\perp}^{2}}$ has both double logarithmic terms, $\ln^{2}(L/l_{0})$, and single logarithmic terms, $\ln(L/l_{0})$, coming from gluon radiation induced by the matter. We use a (slight) extension of a formalism developed by B. Zakharov for studying energy loss, a formalism which, for much of our calculation, reduces to a simple dipole scattering analysis. We estimate the radiative contribution…
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 calculate P(k_\perp), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k_\perp, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \hat q is the second moment of P(k_\perp), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P(k_\perp) in its entire…
We study the contributions from radiation to $p_{\perp}$-broadening of a high energy parton traversing a QCD medium with a finite length $L$. The interaction between the parton and the medium is described by decorrelated static multiple scattering. Amplitudes of medium-induced gluon emission and parton self-energy diagrams are evaluated in the soft gluon limit in the BDMPS formalism. We find both the double-logarithmic correction from incoherent scattering, which is parametrically the same as that in single scattering, and the logarithmic correction from the LPM effect. Therefore, we expect a …
In ultrarelativistic heavy-ion collisions, in the 2 GeV$<p_\perp<$ 6 GeV transverse momentum region, the soft and semi-hard multiple scattering of the incoming nucleons in the nuclear medium results in the broadening of the expected hadronic (e.g. pion) $p_\perp$ spectra relative to proton-proton ($pp$) collisions. Thus, higher transverse-momentum regions are populated than in $pp$ collisions. In a perturbative QCD based calculation we include the intrinsic transverse momentum ($k_\perp$) of the partons in the nucleon (determined from $pp$ collisions), augmented by the extra broadening obtaine…
We give the modification of formulas for $p_{\perp}$-broadening and energy loss which are necessary to calculate parton interactions in a medium with flow. Arguments are presented leading to the conclusion that for large $p_{\perp}$-spectra observed in heavy ion collisions at RHIC, the influence of transverse flow on the determination of the "quenching power" of the produced medium is small. This leaves open the question of the interpretation of data in a consistent perturbative framework.
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 …
We compute O(g) NLO corrections to the transverse scattering kernel and transverse momentum broadening coefficient $\hat{q}$ of weakly-coupled $\mathcal{N}=4$ SYM. Based on this, we also compute NLO correction to the collinear splitting rates. For $\hat{q}$ we find that the NLO/LO ratio is similar to the QCD one, with large NLO corrections. This is contrasted by our findings for the collinear splitting rate, which show a much better convergence in SYM than in QCD, providing further support to earlier expectations that NLO corrections have signs and relative magnitudes controlled by the specifi…
The typical transverse momentum $Q_s(t)$ (or "saturation" momentum) acquired by a hard particle propagating through a $\mathcal{N}=4$ SYM plasma increases over time like $t^γ$, with an anomalous exponent $γ>1/2$ characteristic of super-diffusion. This anomalous exponent is a function of the 't Hooft coupling $λ=g^2N_c$. Recently, a method has been proposed to systematically compute the perturbative series of $γ(λ)$ at weak coupling. This method relies on the traveling wave interpretation of the time evolution of $Q_s(t)$ and on the dominance of soft-collinear radiative corrections at large tim…
We consider heavy-quark energy loss and pT-broadening in a strongly-coupled N=4 Super Yang Mills (SYM) plasma, and the problem of finite-extend matter is addressed. When expressed in terms of the appropriate saturation momentum, one finds identical parametric forms for the energy loss in pQCD and SYM theory, while pT-broadening is radiation dominated in SYM theory and multiple scattering dominated in pQCD.
We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently for large system sizes $L$ to a universal distribution that only depends on a single scaling variable $k^2_\perp/Q^2_s$ where the typical transverse momentum scale increases with time as $\ln Q_s^2 \simeq (1+2 β) \ln L - \frac{3}{2}(1+β)\,\ln\ln L$ up to non-universal terms, with an anomalous dimension $β\sim \sqrt{α_s} $. This property is analogous to geomet…
We study the radiative processes that affect the propagation of a high energy gluon in a dense medium, such as a quark-gluon plasma. In particular, we investigate the role of the large double logarithms corrections, $\simα_s \ln^2 L/τ_0$, that were recently identified in the study of $p_\perp$-broadening by Liou, Mueller and Wu. We show that these large corrections can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-loca…
Using a rather complete description of the in-medium $ρ$ spectral function - being constrained by various independent experimental information - we calculate pertinent dilepton production rates from hot and dense hadronic matter. The strong broadening of the $ρ$ resonance entails a reminiscence to perturbative $q\bar q$ annihilation rates in the vicinity of the phase boundary. The application to dilepton observables in Pb(158AGeV)+Au collisions - incorporating recent information on the hadro-chemical composition at CERN-SpS energies - essentially supports the broadening scenario. Possible impl…
