A Breath of Fresh Air for Molière: Detecting Molière Scattering using Jet Substructure Observables in Oxygen Collisions

Abstract

Ultra-relativistic oxygen-oxygen (OO) collisions are a promising arena in which to probe rare, large-angle, high momentum-transfer $2\rightarrow2$ Molière scatterings between energetic jet partons and quasiparticles in quark-gluon plasma (QGP). As a jet propagates through the droplet of QGP formed in the same collision, its constituents lose energy to and excite wakes in the medium, and may scatter off quark- and gluon-like quasiparticles in QGP. Using the hybrid strong/weak coupling model, we show that including Molière scatterings between jet partons and medium quasiparticles is essential to reproduce recent CMS measurements of charged-particle suppression in OO collisions with this model. We then present the first theoretical study of how jet-medium interactions modify the internal structure of jets in OO collisions. We find that Molière scatterings broaden the Soft Drop splitting angle $R_g$, enhancing the population of $R=0.4$ and $R=0.8$ jets with $R_g\gtrsim0.2$ in OO collisions relative to pp collisions. Energy-energy correlators (EECs) provide a complementary probe, exhibiting enhanced large-angle correlations within jets due to jet-induced wakes and Molière scattering. In both cases, we propose an experimental measurement where the relevant OO/pp ratio can, if enhanced above unity in future data as in our calculations, be a distinctive, model-independent, detection of hard scattering off QGP quasiparticles. We furthermore use our calculations of EECs to show how the angular scale corresponding to the deflection of jet or medium partons by Molière scattering is imprinted in the EEC for jets with radius $R_{\rm jet}\sim0.8$ in OO collisions. These results demonstrate that jet substructure measurements in OO collisions are promising avenues to probe the quasiparticles that emerge at short distances within an otherwise strongly coupled medium.

Figures (7)

• Figure 1: Hybrid Model calculations of $R_{\rm AA}$ of charged hadrons with $|\eta| < 1$ in OO collisions versus $p_T$ without energy loss or Molière scattering (gray), with energy loss and wakes (blue), and with energy loss, wakes, and Molière scatterings (red). Points denote CMS measurements CMS:2025bta, with statistical, systematic, and normalization errors added in quadrature.
• Figure 2: Hybrid Model calculations of the OO/pp ratio of the $R_g$/$R_{\rm jet}$ distributions in $R_{\rm jet} = 0.4$ (left) and $R_{\rm jet} = 0.8$ (right) jets with $40<p_T^{\rm jet}<60$ GeV, calculated using charged particles with $p_T^{\rm ch~track} > 150$ MeV, Soft Drop grooming parameters $z_{\rm cut} = 0.1$ and $\beta = 0$, and OO and pp distributions normalized by the number of jets selected.
• Figure 3: Hybrid Model calculations of OO/pp ratios of EECs for $R_{\rm jet} = 0.4$ (top panels) and $R_{\rm jet} = 0.8$ (bottom panels) jets with $40 < p_T < 80$ GeV versus $R_L$. EECs are calculated using charged hadrons with $p_T>0.5\, {\rm GeV}$ (left panels), and $p_T>2\, {\rm GeV}$ (right panels). To the right of the dashed vertical lines at $R_L = R_{\rm jet}$, EECs probe correlations between points separated by an $R_L$ that is greater than the jet radius and less than its diameter.
• Figure 4: Hybrid Model calculations of OO/pp ratios of EECs with (red) and without (blue) Molière scattering for $R_{\rm jet} = 0.8$ jets with $p_T \in [40, 80]$ GeV, $[80, 120]$ GeV, and $[120, 160]$ GeV, calculated using charged hadrons with $p_T>2$ GeV. The dashed vertical line corresponds to $R_L = R_{\rm jet}$. Each dotted vertical line marks a local maximum of the EEC with $R_L < R_{\rm jet}$, whose location in $R_L$ encodes the typical angle of deflection due to Molière scatterings in the corresponding jet sample.
• Figure 5: Suppression $R_{\rm AA}$ of charged hadrons (left panel) and jets reconstructed with anti-$k_t$$R_{\rm jet}=0.4$ (right panel) in 0--5% central PbPb collisions with collision energy $\sqrt{s_{\rm NN}} = 5.02$ TeV. The black curves show Hybrid Model results using event-averaged hydrodynamic backgrounds Shen:2014vra, with $\kappa_{\rm sc}^{\rm No\,Moli\grave{e}re}=0.404$, as fitted to data in Ref. Casalderrey-Solana:2018wrw, before Molière scatterings were included in the model and with no soft Gaussian transverse momentum broadening, i.e. with $K=0$. The blue and red curves show Hybrid Model calculations using event-by-event hydrodynamic backgrounds Mantysaari:2025tcg and including soft Gaussian transverse momentum broadening with $K=15$, without (blue) and with (red) Molière scatterings. To obtain the blue curves, with no Molière scattering, we have chosen $\kappa_{\rm sc}^{\rm No\,Moli\grave{e}re}=0.37$. To obtain the red curves, in our calculations that include Molière scttering we have chosen $\kappa_{\rm sc}^{\rm With\,Moli\grave{e}re}=0.335$. As we describe in this Supplemental Material, we have made these choices so as to bring the blue and red curves into reasonable agreement with the black curves in both panels. Note also that the old results in the black curves used EPS09 nPDFs Eskola:2009uj while the new results in the blue and red curves use EPPS21 nPDFs Eskola:2021nhw.