Towards the understanding of jet shapes and cross sections in heavy ion collisions using soft-collinear effective theory

TL;DR

The paper addresses how jets modify in the quark-gluon plasma and how to predict jet shapes and cross sections in heavy ion collisions. It develops a soft-collinear effective theory framework (SCET) extended with Glauber interactions (SCET_G) to compute medium-modified jet observables, resumming to next-to-leading-log accuracy and incorporating medium-induced splitting functions and CNM effects. The key contributions include a first-principles calculation of jet shape modification and jet cross-section suppression in Pb+Pb at LHC energies, with data comparisons at $\sqrt{s_{NN}}=2.76$ TeV and predictions for $\sqrt{s_{NN}}\approx 5.1$ TeV, including photon-tagged jets and jet-radius dependence. This framework enables precision extraction of medium properties from jet observables and offers a controlled approach to disentangle initial-state and final-state effects in heavy ion collisions.

Abstract

We calculate the jet shape and the jet cross section in heavy ion collisions using soft-collinear effective theory (SCET) and its extension with Glauber gluon interactions in the medium (SCET$_{\rm G}$). We use the previously developed framework to systematically resum the jet shape at next-to-leading logarithmic accuracy, and we consistently include the medium modification by incorporating the leading order medium-induced splitting functions. The calculation provides, for the first time, a quantitative understanding of the jet shape modification measurement in lead-lead collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC. The inclusive jet suppression is also calculated within the same framework beyond the traditional concept of parton energy loss, and the dependence on the centrality, the jet radius and the jet kinematics is examined. In the end we present predictions for the anticipated jet shape and cross section measurements in lead-lead collisions at $\sqrt{s_{\rm NN}}\approx5.1$ TeV at the LHC.

Figures (12)

• Figure 1: Illustration of the phase space regions for the calculations of the jet energy function (left panel) and the jet energy lost (right panel) at leading order. In both cases, a collinear parton splits into partons with momenta $k=(xp_0^+,k_\perp^2/xp_0^+,k_\perp)$ and $p-k$. Depending on the kinematics of the splitting, the partons which can contribute to the energy measured inside the subcone of size $r$ may change. Similarly, the partons reconstructed in the jet may also differ.
• Figure 2: Comparison of theoretical calculations for the nuclear modification factor $R_{AA}$ of inclusive jets as a function of the jet transverse momentum to experimental data in central Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC. Bands correspond to the theoretical uncertainty estimated by varying the coupling between the jet and the medium ($g=2.0 \pm 0.2$). The blue band corresponds to the calculations with $\mu_{\textcolor{black}{\rm CNM}}=0$ GeV, the green band corresponds to the calculations with $\mu_{\textcolor{black}{\rm CNM}}=0.18$ GeV and the red band corresponds to the calculations with $\mu_{\textcolor{black}{\rm CNM}}=0.35$ GeV. Left panel: comparison to the ATLAS measurement Aad:2014bxa with $R=0.4$. Right panel: comparison to the CMS preliminary result CMS:prelim with $R=0.3$.
• Figure 3: Comparison of theoretical calculations for the suppression of inclusive jets with $R=0.3$ as a function of the jet transverse momentum to experimental data in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. The curves are the jet $R_{AA}$ calculations for central colliisons, but we have included the data from the ALICE charged jets $R_{CP}$Abelev:2013kqa, ATLAS calorimeter jet $R_{CP}$Aad:2012vca and CMS jet $R_{AA}$CMS:prelim measurements for comparison, assuming that the suppression in peripheral collisions is small. Shown are the same studies as in Fig. 2 of the theory sensitivity on the coupling $g$ between the jet and the QGP medium, as well as the momentum transfer $\mu_{\textcolor{black}{\rm CNM}}$ between the initial-state parton and the nucleus.
• Figure 4: Left panel: comparison of theoretical calculations for the nuclear modification factor $R_{AA}$ of inclusive jets as a function of the jet transverse momentum to experimental data in $\sqrt{s_{\rm NN}}=2.76$ TeV Pb+Pb collisions at the LHC, with different collision centralities. Two centrality classes, 0 - 10% and 30 - 40%, are considered. The bands corresponds to the variation of the coupling $g=2\pm 0.2$ between the jet and the medium in the calculations, and CNM effects with $\mu_{\textcolor{black}{\rm CNM}}=0.35$ GeV are implemented. The data is from ATLAS Aad:2014bxa with $R=0.4$. Right panel: comparison of theoretical calculations for the ratios of jet $R_{AA}$'s within different pseudo-rapidity bins as a function of the jet transverse momentum to the ATLAS experimental data Aad:2014bxa in central Pb+Pb collisions. The blue band corresponds to the ratio $R_{AA}(0.0<|\eta|<0.8)/R_{AA}(0.0<|\eta|<2.0)$, and the red band corresponds to the ratio $R_{AA}(0.8<|\eta|<2.0)/R_{AA}(0.0<|\eta|<2.0)$. The derived data corresponds to $R_{AA}(0.3<|\eta|<0.8)/R_{AA}(0.0<|\eta|<2.1)$ and $R_{AA}(1.2<|\eta|<2.1)/R_{AA}(0.0<|\eta|<2.1)$.
• Figure 5: Left panel: theoretical calculations for the nuclear modification factor $R_{AA}$ of inclusive jets with $R=0.2$, 0.3, 0.4 and 0.5 as a function of the jet transverse momentum in central Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC. The calculations implement CNM effects with $\mu_{\textcolor{black}{\rm CNM}}=0.35$ GeV, and a reduced range of the coupling between the jet and the medium ($g=2\pm 0.1$) is used for estimating theoretical uncertainties. This way the bands do not overlap much and the jet-radius dependence of jet quenching can be better illustrated. Right panel: comparison of theoretical calculations for the central-to-peripheral $R_{CP}$ ratios as a function of the jet transverse momentum for inclusive jets with different jet radii to data in central Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC. The bands and the data correspond to $R_{CP}(R=0.3,~0.4,~0.5)/R_{CP}(R=0.2)$. The data is from ATLAS Aad:2012vca.