Jet Fragmentation Function Moments in Heavy Ion Collisions

TL;DR

The paper addresses how the large underlying-event in heavy-ion collisions distorts jet fragmentation functions and proposes using fragmentation-function moments $M_N$ to diagnose medium-induced modifications. It develops two jet-area-based background subtraction strategies, one in $z$-space and one in $N$-space, and demonstrates that moments can be corrected for background fluctuations, enabling jet-by-jet analysis. An improved moment-space subtraction incorporating fluctuations and correlations yields closer agreement with quenched fragmentation patterns and enhances the ability to distinguish quenching scenarios. The work provides practical guidance for experimental analyses and a FastJet add-on to implement the methods.

Abstract

The nature of a jet's fragmentation in heavy-ion collisions has the potential to cast light on the mechanism of jet quenching. However the presence of the huge underlying event complicates the reconstruction of the jet fragmentation function as a function of the momentum fraction z of hadrons in the jet. Here we propose the use of moments of the fragmentation function. These quantities appear to be as sensitive to quenching modifications as the fragmentation function directly in z. We show that they are amenable to background subtraction using the same jet-area based techniques proposed in the past for jet p_t's. Furthermore, complications due to correlations between background-fluctuation contributions to the jet's p_t and to its particle content are easily corrected for.

Figures (5)

• Figure 1: Jet fragmentation functions (versus $z$ and $\xi$) and moments (versus $N$) in proton-proton collisions at the LHC ($\sqrt{s_{NN}} = 2.76$ TeV), obtained without quenching, from Pythia 6, and with quenching, from Pyquen.
• Figure 2: Representation of the $\xi$ values that contribute dominantly to the $M_N$ integral for a given $N$, shown as a function of $N$. Shown for the Pythia 6 results and cuts of Fig. \ref{['fig:hard']}.
• Figure 3: Jet fragmentation functions shown for plain Pythia, with the addition of the heavy-ion background (Pythia+Hydjet) and after subtraction of the heavy-ion background ($z$-subtracted and $N$-subtracted). For the results including the heavy-ion background, the jet $p_t$ used to define $z$ is always that after subtraction of the heavy-ion background. As in Fig. \ref{['fig:hard']}, we show the results as a function of $z$ (left), $\xi$ (middle) and for the moments versus $N$ (right). The upper (lower) row has a jet $p_t$ threshold of $100\,\mathrm{GeV}$ ($200\,\mathrm{GeV}$).
• Figure 4: The quantities $\rho_N$, $\sigma_N$ and the correlation coefficient $r_N$, shown as a function of $N$ for $0-10\%$ central Pb Pb collisions $\sqrt{s_{NN}} = 2.76 \,\mathrm{TeV}$ as obtained from simulations with Hydjet.
• Figure 5: Jet fragmentation function moments, showing the plain Pythia result, the result after embedding in Hydjet and applying plain subtraction moment-space subtraction ("N-subtracted") and after the additional improvement to account for correlations ("+ correl"), Eq. (\ref{['eq:subimp-v3']}). A quenched result ("Pyquen") is also shown, to help give an indication of the order of magnitude of quenching effects as compared to residual misreconstruction effects.