Elastic, Inelastic, and Path Length Fluctuations in Jet Tomography

TL;DR

Non-photonic electron data at RHIC challenge the view that heavy-quark quenching is radiative-dominated under realistic bulk densities. The authors extend jet quenching theory to include both elastic and inelastic energy losses and to incorporate jet path length fluctuations, along with fluctuations in energy loss, to create a more complete perturbative QCD description. They demonstrate that these three effects together can reconcile the observed electron suppression $R_{AA}(p_T)$ with the multiplicity constraint $dN_g/dy$ and with pion suppression data out to $p_T\sim 20$ GeV, highlighting the crucial roles of geometric and elastic fluctuations. This work improves the reliability of jet tomography in the sQGP and highlights remaining theoretical and experimental uncertainties, including baselines for $p+p$ electrons and the need for direct heavy-flavor measurements and more complete treatments of coherence and finite-size effects.

Abstract

We propose a possible perturbative QCD solution to the heavy quark tomography problem posed by recent non-photonic single electron data from central Au+Au collisions at $\sqrt{s} = 200$ AGeV. Jet quenching theory is extended to include (1) elastic as well as (2) inelastic parton energy losses and (3) jet path length fluctuations. The three effects combine to reduce the discrepancy between theory and the data without violating the global entropy bounds from multiplicity and elliptic flow data. We also check for consistency with the pion suppression data out to 20 GeV. Fluctuations of the geometric jet path lengths and the difference between the widths of fluctuations of elastic and inelastic energy loss play essential roles in the proposed solution.

Figures (11)

• Figure 1: The suppression factor, $R_{AA}(p_T)$, of non-photonic electrons from decay of quenched heavy quark (c+b) jets is compared to PHENIX Adare:2006nq and STAR elecQM05_STAR data in central Au+Au reactions at 200 AGeV. Shaded bars indicate systematic errors, while thin error lines indicate statistical ones. All calculations assume initial $dN_g/dy=1000$. The upper yellow band from Djordjevic:2005db takes into account radiative energy loss only, using a fixed $L=6$ fm; the lower yellow band is our new prediction, including both elastic and inelastic energy losses as well as jet path length fluctuations. The bands provide a rough estimate of uncertainties from the leading log approximation for elastic energy loss. The dashed curves illustrate the lower extreme of the uncertainty from production, by showing the electron suppression after both inelastic and elastic energy loss with bottom quark jets neglected.
• Figure 2: Average $\Delta E/E$ for $u,c,b$ quarks as a function of $E$. A Bjorken expanding QGP with path length $L=5$ fm and initial density fixed by $dN_g/dy=1000$ is assumed. The curves are computed with the coupling $\alpha_s = 0.3$ held fixed. For Debye mass $\mu_D\propto(dN_g/dy)^{(1/3)}$, the gluon mass is $\mu_D/\surd 2$, the light quark mass is $\mu_D/2$, the charm mass is $1.2$ GeV, and the bottom mass is $4.75$ GeV. Radiative DGLV first order energy loss is compared to elastic parton energy loss (in TG or BT approximations). The yellow bands provide an indication of theoretical uncertainties in the leading log approximation to the elastic energy loss.
• Figure 3: Transverse coordinate $(x,0)$ distribution of surviving $p_T=15$ GeV, $Q=g,u,c,b$ jets moving in direction $\phi=0$ as indicated by the arrows. Units are arbitrary for illustration. The transverse (binary collision) distribution of initial jet production points, $\rho_{\rm Jet}(x,0)$, is shown at midrapidity for Au+Au collisions at $b=2.1$ fm. The ratio $\rho_Q/\rho_{\rm Jet}$ (see Eq.(\ref{['rhoQ']})) gives the local quenching factor including elastic and inelastic energy loss though the bulk QGP matter distributed as $\rho_{\rm QGP}(x,0)$.
• Figure 4: Distribution of path lengths (given by Eq. (\ref{['Leff']})) traversed by hard scatterers in 0-5% most central collisions; the lengths, $L({\vec{x}}_\perp,\phi)$, are weighted by the probability of production and averaged over azimuth. An equivalent formulation of Eq. (\ref{['power']}) is $R_Q^I=\int dL 1/N_{bin} dN_{bin}/dL \int d\epsilon (1-\epsilon)^n P_Q^I(\epsilon;L)$. Since the distribution $1/N_{bin} dN_{bin}/dL$ is a purely geometric quantity, it is the same for all jet varieties. Also displayed are the single, representative pathlengths, $L_Q$, used as input in approach II. Note the hierarchy of scales with glue requiring the shortest, then charm, light quarks, and bottom the longest effective pathlength.
• Figure 5: Partonic nuclear modification, $R_{Q}^{II}(p_T)$ via Eq.(\ref{['power2']}), for $g,u,c,b$ as a function of $p_T$ for fixed L=5 fm path length and $dN_g/dy=1000$. Dashed curves include only radiative energy loss, while solid curves include elastic energy loss as well.