A theory of jet shapes and cross sections: from hadrons to nuclei

TL;DR

The paper proposes jet shapes and jet cross sections as differential probes of QCD in the quark-gluon plasma, linking medium induced energy loss to observable jet structure under realistic experimental acceptance. It provides a vacuum baseline via LO, resummation, and power corrections for p-p collisions and then applies the GLV formalism to quantify medium induced radiation and the resulting energy-loss distributions. A central result is the energy sum rule and the observable $R_{AA}^{jet}(R^{max},\omega^{min})$, which captures how much of the lost energy is recovered within a jet cone and how jet observables respond to the medium. The study shows that even large jet attenuation can correspond to only modest broadening of the mean jet radius, with broadening more evident in the tails of the intra-jet energy flow, offering a path toward QGP tomography with high-statistics LHC data.

Abstract

For jets, with great power comes great opportunity. The unprecedented center of mass energies available at the LHC open new windows on the QGP: we demonstrate that jet shape and jet cross section measurements become feasible as a new, differential and accurate test of the underlying QCD theory. We present a first step in understanding these shapes and cross sections in heavy ion reactions. Our approach allows for detailed simulations of the experimental acceptance/cuts that help isolate jets in such high-multiplicity environment. It is demonstrated for the first time that the pattern of stimulated gluon emission can be correlated with a variable quenching of the jet rates and provide an approximately model-independent approach to determining the characteristics of the medium-induced bremsstrahlung spectrum. Surprisingly, in realistic simulations of parton propagation through the QGP we find a minimal increase in the mean jet radius even for large jet attenuation. Jet broadening is manifest in the tails of the energy distribution away from the jet axis and its quantification requires high statistics measurements that will be possible at the LHC.

Figures (15)

• Figure 1: (Color online) Comparison of numerical results from our theoretical calculation to experimental data on differential jet shapes at $\sqrt{s}=1960$ GeV by CDF II Acosta:2005ix. Insert shows the $E_T$ dependence of $R_{sep}$.
• Figure 2: (Color online) Numerical results for the differential jet shapes in p+p collisions at $\sqrt{s}=5.5$ TeV at the LHC. Solid lines represent jet shapes with $R=0.7,\, \omega^{\min}=0$ GeV, dashed lines stand for jet shapes with $R=0.4,\; \omega^{\min}=0$ GeV, and dashed-dotted lines are for jet shapes with $R=0.7,\; \omega^{\min}=10$ GeV. The inserts show integrated jet shapes $\Psi_{\rm int}(r;R)$.
• Figure 3: (Color online) 3D plot of the differential jet shapes at three different jet energies $E_T=20$ GeV (top panel), $E_T=100$ GeV (middle panel), and $E_T=500$ GeV (bottom panel) with $R=0.7,\, \omega^{\min}=0$ GeV in p+p collisions with $\sqrt{s}=5500$ GeV at the LHC. From low jet energy to high jet energy, jet shape becomes much steeper.
• Figure 4: (Color online) Schematic illustration of the cone radius $R$ and the particle/tower $p_T$ / $E_T$ selection. The measured energy is the one that comes from particles with $p_T > \omega_{min}$ and within $R$.
• Figure 5: (Color online) 3D plot for the ratio of the energy that a partons loses inside a jet cone of opening angle $R^{\max}$ with $\omega > \omega^{\min}$ to the total parton energy. We have chosen a jet of energy $E_{jet} = 20$ GeV in $b=3$ fm Pb+Pb collisions at LHC and varied the jet radius $R^{\max}$ and the acceptance cut $\omega^{\min}$. The upper surface is for a gluon jet and the lower surface is for a quark jet.