Sensitivity of Jet Observables to Molière Scattering Off Quasiparticles in Quark-Gluon Plasma

Abstract

Quark-gluon plasma (QGP) is a strongly coupled liquid when viewed at length scales of order the inverse of its temperature and longer. However, when it is probed at short enough length scales, asymptotic freedom mandates the presence of quark- and gluon-like quasiparticles. Partons in jets can trigger perturbative, high momentum-exchange $2\rightarrow2$ Molière scatterings off quasiparticles in the medium, making jets useful probes of the microscopic structure of QGP. Prior to this work, soft strongly coupled momentum-exchanges between jet partons and the QGP droplet produced in a heavy-ion collision, as well as the wakes that jets excite in the droplet, had been accounted for in the Hybrid Model of jet quenching. Here, we present a full calculation of Molière scattering off a QGP quasiparticle which results in the deflection of the jet parton and the excitation of a parton from the thermal medium that recoils after being kicked, and describe how it is implemented in the Hybrid Model. The scattered jet and recoil partons continue to propagate through the QGP, lose energy and momentum, excite wakes, and may further re-scatter. Using the Hybrid Model, we study how Molière scatterings impact jet shapes and fragmentation functions, the Soft Drop angle $R_g$, jet girth $g$, and observables that focus on the number and angular distribution of subjets within jets. We demonstrate that photon-tagged jets provide a particularly sensitive probe: selecting events by the photon energy mitigates the selection bias inherent in inclusive jet measurements and enhances sensitivity to rare large-angle scatterings. We find that Molière scatterings broaden both the $R_g$ and $g$ distributions when jets significantly softer than the photon are included. Our results point the way towards distinctive model-independent experimental signatures of hard scattering of jet partons off quasiparticles in QGP.

Figures (13)

• Figure 1: Schematic of a $2\rightarrow 2$ Molière scattering process, where an incoming particle of type $C$ with momentum $p_{\rm in}$ in the $+\hat{z}$ direction scatters off a thermal particle of type $D$ with momentum $k_T$. The outgoing particle of type $A$ has momentum $p$ and scatters in the $(z,x)$ plane at an angle $\theta$ relative to the direction of propagation of the incoming hard parton. The other outgoing parton of type $B$ has momentum $k_\chi$ and scatters at an angle which can be determined using energy-momentum conservation. For example, momentum conservation means that $k_\chi$ has the same $\hat{y}$ component as $k_T$, as indicated in the diagram. $A$, $B$, $C$, and $D$ can each be a gluon, quark, or antiquark.
• Figure 2: Probability distributions $F^{G \rightarrow \rm all}(p, \theta; p_{\rm in})$ for finding a scattered parton with energy and angle $(p,\theta)$ from the Molière scattering of an incoming gluon with $p_{\rm in} = 20T$ (top panels), $50T$ (middle panels), and $200T$ (bottom panels) that has traveled for a time $\Delta t=6/T$ through a "brick" of QGP with a constant temperature $T$. We have chosen the two parameters that specify the elastic scattering probabilities (see text for their definition and description) to be $g_s=2.25$ and $a=4$ in the left panels, and $g_s=2.25$ and $a=10$ in the right panels.
• Figure 3: Probability for an incoming quark with energy $E=20$ GeV (left panels) or $E=80$ GeV (right panels) to obtain a transverse momentum $k_T$ after traversing a brick of QGP with length $L=2$ fm and temperature $T=0.3$ GeV. Different colors correspond to different choices of the parameter $K$ that governs the magnitude of the soft Gaussian transverse momentum broadening. The bands include Molière scattering with squared momentum transfer greater than $a m_D^2$, where we have chosen the threshold parameter as $a=4$ (upper panels) or $a=10$ (lower panels). The points with a given color show the results with that value of $K$ in the absence of Molière scattering. All probability distributions are normalized. (In the case of the grey bands, where $K=0$, the most probable outcome is $k_T=0$, no Molière scattering; this is not depicted.)
• Figure 4: Left: Hybrid Model calculations of $R_{\rm AA}$ of inclusive anti-$k_t$ jets with $R=0.4$ as a function of jet $p_T$. Right: Hybrid Model calculations of $R_{\rm AA}$ of single inclusive charged hadrons with transverse momentum $p_T$. In both panels, $R_{\rm AA}$ is the suppression in PbPb collisions with 0-5% centrality and $\sqrt{s_{\rm NN}}=5.02$ TeV relative to pp collisions. The four colored bands show results from Hybrid Model calculations with and without Molière scattering with $g_s=2.25$ and $a=10$, and with and without the soft hadrons originating from jet wakes. Soft Gaussian transverse momentum broadening with $K=15$ is included in all calculations. Calculations with Molière scattering (red and green bands) have the parameter that controls the magnitude of strongly coupled energy loss set to $\kappa_{\rm sc}=0.37$ so as to match prior calculations for jet and hadron suppression without Molière scattering (blue and black bands) calculated with $\kappa_{\rm sc}=0.404$, the value obtained by fitting Hybrid model calculations including jet wakes but without Molière scattering to data in Ref. Casalderrey-Solana:2018wrw.
• Figure 5: Hybrid Model results for the ratios between the jet shapes (left panel) and jet fragmentation functions (right panel) in PbPb collisions with $\sqrt{s_{\rm NN}}=5.02$ TeV and 0-5% centrality and pp collisions for inclusive samples of anti-$k_t$ jets with $p_T^{\rm jet}>100$ GeV and $R=0.4$.