Sorting Out Quenched Jets

We introduce a new “quantile” analysis strategy to study the modification of jets as they traverse through a droplet of quark-gluon plasma. To date, most jet modification studies have been based on comparing the jet properties measured in heavy-ion collisions to a proton-proton baseline at the same reconstructed jet transverse momentum ($p_T$). It is well known, however, that the quenching of jets from their interaction with the medium leads to a migration of jets from higher to lower $p_T$, making it challenging to directly infer the degree and mechanism of jet energy loss. Our proposed quantile matching procedure is inspired by (but not reliant on) the approximate monotonicity of energy loss in the jet $p_T$. In this strategy, jets in heavy-ion collisions ordered by $p_T$ are viewed as modified versions of the same number of highest-energy jets in proton-proton collisions, and the fractional energy loss as a function of jet $p_T$ is a natural observable ($Q_{AA}$). Furthermore, despite nonmonotonic fluctuations in the energy loss, we use an event generator to validate the strong correlation between the $p_T$ of the parton that initiates a heavy-ion jet and the $p_T$ of the vacuum jet which corresponds to it via the quantile procedure ($p_T^{\text{quant}}$). We demonstrate that this strategy both provides a complementary way to study jet modification and mitigates the effect of $p_T$ migration in heavy-ion collisions.

Figure 1

Illustration comparing the ratio and quantile procedures. (a) The inclusive jet $p_T$ spectra measured by CMS [30], for a jet radius of $R=0.4$. The standard jet ratio $R_{AA}$ (blue) compares heavy-ion and proton-proton jet cross sections vertically at the same reconstructed jet $p_T$. (b) The jet $p_T$ cumulative cross sections extracted from Jewel [31, 32]. The quantile procedure $Q_{AA}$ (red) compares heavy-ion and proton-proton jet $p_T$ thresholds horizontally at the same cumulative cross section. From this, one can map each $p_T^{AA}$ (base of red arrows) into the $p_T$ of proton-proton jets in the same quantile, $p_T^{\text{quant}}$ (tip of red arrows). For completeness, we also show the pseudoquantile ${\tilde{Q}}_{AA}$ (orange, with corresponding ${\tilde{p}}_T^{\text{quant}}$) defined on the cross section and pseudoratio ${\tilde{R}}_{AA}$ (purple) defined on the cumulative cross section. Though we will not explore the use of ${\tilde{Q}}_{AA}$ or ${\tilde{R}}_{AA}$ in the present study, we note that in Jewel, the values of $p_T^{\text{quant}}$ and ${\tilde{p}}_T^{\text{quant}}$ differ by only a few percents.

Figure 2

Distributions of (a) $R_{AA}$ as a function of $p_T^{\text{jet}}$ and (b) $Q_{AA}$ as a function of $p_T^{\text{quant}}$, for the $Z+\text{jet}$ (dashed) and di-jet (solid) samples in Jewel. Although $R_{AA}$ and $Q_{AA}$ are derived from the same underlying jet $p_T$ spectra, they provide different and complementary information. For example, the $p_T$ dependence of $R_{AA}$ is very different for $Z+\text{jet}$ and di-jet events in Jewel, while the average fractional $p_T$ loss $1-Q_{AA}$ is similar. Note that $R_{AA}$ requires binning of the data, while $Q_{AA}$, which is based on the cumulative cross section, can be plotted unbinned.

Figure 3

Mean of the jet $p_T$ distribution compared to a baseline initial $p_T$ (top), along with the corresponding standard deviation (bottom). Shown are (a) $Z+\text{jet}$ events where the baseline is the physically observable $p_T$ of the recoiling $Z$ boson and (b) di-jet events where the baseline is the unphysical and unobservable $p_T^{\mathrm{MC}}$ of the initial hard scattering obtained from Jewel. The reconstructed jet $p_T$ for proton-proton and heavy-ion jets are shown in dashed black and blue, respectively. The $p_T^{\text{quant}}$ of the heavy-ion sample, shown in red, more closely matches the initial jet $p_T$ than the reconstructed heavy-ion $p_T$ does.

Figure 4

Distribution of $m/p_T$ for proton-proton (dashed black) and heavy-ion (blue) jets in di-jet events with reconstructed $p_T\in [100,200]\mathrm{GeV}$. Heavy-ion jets with $p_T^{\text{quant}}\in [100,200]\mathrm{GeV}$, corresponding to $p_T^{AA}\in [80,173]\mathrm{GeV}$, are in red. The heavy-ion result is normalized to match the proton-proton baseline but the quantile result has the correct normalization by construction. Partially compensating for $p_T$ migration via the quantile procedure shifts $m/p_T$ towards being less modified.