Observables for possible QGP signatures in central pp collisions

Proton-proton (pp) data show collective effects, such as long-range azimuthal correlations and strangeness enhancement, which are similar to phenomenology observed in heavy ion collisions. Using simulations with and without explicit existing models of collective effects, we explore new ways to probe pp collisions at high multiplicity, in order to suggest measurements that could help identify the similarities and differences between large- and small-scale collective effects. In particular, we focus on the properties of jets produced in ultra-central pp collisions in association with a Z boson. We consider observables such as jet energy loss and jet shapes, which could point to the possible existence of an underlying quark-gluon plasma, or other new dynamical effects related to the presence of large hadronic densities.


Introduction
There has been a recent surge of interest in collective effects in small systems with high final state multiplicity due to measurements of strangeness enhancement from ALICE [1] and large-angle particle correlations (the 'ridge') by ATLAS [2] and CMS [3,4]. These effects are not reproduced by the standard Monte Carlo (MC) event generators for pp collisions, based on standard Quantum Chromodynamics (QCD) evolution and well-tested models of hadronization [5][6][7][8][9][10]. The features of these phenomena resemble those exhibited by the Quark Gluon Plasma (QGP) formed in heavy ion (HI) collisions. If parameterized in terms of dN/dη, the evolution of the observed effects with dN/dη in pp smoothly matches to the size of the effects observed in HI collisions, where they are interpreted in terms of QGP dynamics. It is therefore tempting to speculate that a sort of "mini-QGP" might be formed in (or might be responsible for) the highest dN/dη events in pp. Alternative interpretations have nevertheless been put forward, relying on a more complex description of the fragmentation phase of the event generation [11,12]. These descriptions of the collective phenomena make no reference to a QGP, and derive their results from a more extended network of interactions among the partons emerging from the usual (T = 0) evolution of the partonic final state. More in general, these experimental facts raise the question of whether the description of 1 large-multiplicity final states in pp collisions boils down to finding the right knobs to tune in some fragmentation model, or whether it requires the understanding of a new dynamical phase of high-energy hadronic interactions.
In this paper we propose a set of observables that, while being sensitive to the reported collective effects, would likely lead to different results depending on whether the QGP is active or not. In particular, we consider jet observables, which in the presence of a QGP are expected to undergo quenching effects. We analyze Z+jet events, and study the properties of the jets and of the surrounding environment, as a function of the track multiplicity. We focus on both the strangeness enhancement and on the potential quenching of the jet recoiling against the Z boson. We show that the MC models predicting strange enhancement in highmultiplicity minimum bias events continue exhibiting large differences in the modeling of strange hadron production, with respect to the standard MCs. We also show, perhaps not surprisingly, that those models do not lead to an observable quenching of the jet energy, and an observable such as p T,J /p T,Z shows no significant dependence on dN/dη, matching the prediction of MCs that do not model collective effects.
This paper is organized as follows. Section 2 describes the simulation setup before the results are presented in Sec. 3. Inclusive strangeness enhancement is demonstrated in Sec. 3.1 in addition to probing strangeness inside jets. Momentum balancing is investigated in Sec. 3.2 and additional observables related to jet substructure are studied in Sec. 3.3. We present our conclusions in Sec. 4.

Simulation
The only publicly available simulation for pp → Z+jets 1 with a model for collective effects is Pythia 8 with the rope hadronization plugin [84]. We use Pythia 8.226 [9] with the default tune for pp collisions at 2 √ s = 7 TeV. The Z-boson is required to decay into muons and |m µµ − m Z | < 15 GeV. Stable particles (cτ ≤ 10 mm) excluding muons and neutrinos are clustered into jets with FastJet 3.1.3 [85] using the anti-k t algorithm [86] with a jet radius of R = 0.4. Unstable strange hadrons are assigned to jets via ghost association [87]. Jet catchment areas are calculated using the median area from the Voronoi method applied to k t jets clustered from particles out to |η| = 2. Signal jets are required to have p T > 20 GeV. For some technical plots below we shall also use 'soft jets', with 10 GeV < p T < 20 GeV (too low to be reconstructed in practice). All events are required to have exactly one signal jet and |∆φ(jet, Z)| > 1 rad to reduce the likely presence of a second jet that is below threshold. In HI and pP b collisions, the 'centrality' of an event is often quantified by the number of particles measured in the event. Therefore, we study event and jet properties as a function of the measured multiplicity. There are many ways to quantify the multiplicity: 1. Total track multiplicity (TTM). General purpose detectors like ATLAS and CMS have tracking coverage up to |η| < 2.5 and p T 200 MeV. Tracks are excluded if they are within an annulus of ∆R < 0.6 around the signal jet axis.
2. Z-side track multiplicity (ZTM). Despite an annulus cut around the jet axis, the TTM may be biased by the presence of a jet due to large angle radiation from the parton(s) recoiling from the Z. One way around this is to count the number of tracks that are in the Z boson hemisphere defined by cos(∆φ(Z, track)) > 0.
3. Forward Multiplicity (FM). Even if the tracks from the jet side are removed, the hard Q 2 process can still influence the central multiplicity. Therefore, the number of very forward particles can be used as measure of event activity. This is a tradeoff between sensitivity to the underlying event activity that might influence the hard Q 2 process and a potential bias from the hard Q 2 process itself influencing the multiplicity. We use a cutoff of 4 < |η| < 5, which is consistent with the ALICE forward scintillators [88] and ATLAS/CMS forward calorimeters [89,90]. Figure 1 shows the number of predicted events with a multiplicity defined by TTM, ZTM, and FM. One key advantage of Z (or γ)+jets in pp collisions versus pP b is that the integrated luminosities collected by ATLAS and CMS of the former are much larger than all four experiments' datasets for the latter. With only the √ s = 7 TeV dataset, of about 5 fb −1 , there are many hundreds of Z → µ + µ − events with a single jet that are in the > 99% percentile of the multiplicity distribution. The n th quantile is defined such that there are a fraction n of events that have this multiplicity or smaller. It is a useful notion for normalizing the multiplicity to make direct comparisons between definitions. Events in the 99% percentile are such that only 1% of events have a higher multiplicity.
The actual multiplicity distributions for the three definitions are shown in Fig. 2. By construction, ZTM is less than or equal to the TTM and is typically a factor of two smaller. The Rope hadronization model predicts a different multiplicity distribution; to control for any effects to these differences, the multiplicity distribution for the standard hadronization is re-weighted to match the Rope distribution. The median TTM/ZTM/FM multiplicities are 44/22/36, respectively.

Stangeness Enhancement
We present here some strangeness enhancement variables, considering the multiplicities of strange hadrons produced inside and outside the leading jet. These are shown plotted against the track multiplicities defined by the TTM, ZTM and FM criteria, in Figs 3, 4 and 5, respectively. The left (right) panels represent the case of default (Rope) Pythia hadronization. For all definitions of underlying track multiplicity we notice similar behaviors: no evidence of strangeness enhancement in the case of pure Pythia, compared to the expected clear enhancement in the case of Rope fragmentation. We note the overall increase of strange production in the case of Rope fragmentation with respect to Pythia, independently of the track multiplicity. We also point out that the ratio of strange hadron fractions inside and outside the jet remains rather constant, for all track multiplicity definitions, for all quantile values, and is also approximately the same for the Rope vs Pythia fragmentations (Fig. 6). Part of the enhancement inside jets is simply due to the fact that the UE happens to lie inside the jet.
Ratio of yields to (    Figure 6: Same as Fig. 3, but comparing the multiplicity inside jets with the average momentum fraction carried by those hadrons.

Jet Balancing
We study in this section a typical observable associated with the presence of a quark-gluon plasma, namely the jet energy loss, leading to an imbalance in the transverse momentum between a jet and its recoil. The cleanest final state in which such phenomenon can be exposed is the recoil of a jet against an electroweak gauge boson, which does not interact with the possible plasma. In particular, we focus on the case of a Z boson decaying to leptons, whose momentum can be well measured, and whose identification is largely free of backgrounds. The study of the Z-jet balance at large transverse momentum, as a function of track multiplicity, requires however some caution, since radiation from the hard process will influence the momentum balance, and at the same time it will sculpt the underlying track multiplicity. A different track multiplicity could also reflect a different composition of the initial and final states (qq → gZ vs qg → qZ). All these effects might in principle induce an imbalance that emulates a quenching trend at the highest track multiplicities. The extent of such correlations between track multiplicity, hard radiation and initial state composition is shown in Fig. 7. The left plot shows the average multiplicity of soft (p T,J > 10 GeV) jets versus the multiplicity quantile, showing that high multiplicity events (lower quantiles) are correlated to a larger radiation activity. As expected, the correlation is strongest for TTM, then ZTM, and weakest for FM. This will influence the ratio of the Z boson p T to the jet p T and can also be observed to broaden the ratio distribution, as is Fig. 8. The right plot of Fig. 7 shows on the other hand a minor, if any, dependence of the gluon final-state fraction versus track multiplicity. Similarly, there is little correlation between the jet or Z p T itself on the event multiplicity, as shown in Fig. 9. With these observations in mind, we show in Fig. 10 the average fractional transverse momentum imbalance between leading jet and Z boson, ∆ ZJ = p T,J /p T,Z , as a function of track multiplicity quantile, for TTM, ZTM and FM. Each plot contains results for the two thresholds of p T,Z > 20 and > 50 GeV, considering the cases of Pythia and Rope fragmentation. Except where indicated by the caption "no ρ×A", an average subtraction of the underlying event activity inside the jet cone is performed. The radiation/multiplicity correlations from Fig. 7 are clearly exposed by the two plots in Fig. 10 corresponding to the TTM and ZTM cases. In the former case, we notice a quenching-like slope, caused by finalstate radiation that reduces the jet momentum. In the latter case, an increased multiplicity on the Z hemisphere signals initial-state radiation in the Z direction, which calls for a larger balancing jet momentum. This tilts the ∆ ZJ distribution lower at higher ZTM (smaller quantile), faking a "anti-quenching" behavior. In both cases the simulations with or without Rope fragmentation show identical behavior. However, in a possible comparison against data, one would be forced to assume a precise modeling of the radiative effects in order to decide whether the data show some intrinsic quenching or not. It therefore appears that the choices of TTM or ZTM are not ideal to study a possible quenching at high multiplicity using this observable. Nevertheless, we notice that the distributions with respect to the FM quantile are totally flat, and appear not to be influenced by a possible hard radiation bias. This suggests that FM would be a more robust variable to explore the possible presence of quenching-induced imbalance. Figure 11 shows the full distribution of the ratio in three bins of multipicity. Nearly independent of the percentile, the standard deviation of the ratio distribution is about 20%. With about 500 jets in the 1% percentile category (Fig. 1), the statistical precision in the determination of ∆ ZJ will be 1%. The experimental resolution should be comparably small. The high multiplicity single pp collisions have comparable multiplicity to low/moderate pileup bunch crossings, similar to the levels with early Run 2. Therefore, one can estimate the uncertainty in the reconstructed jet energy due to pileup as an estimate of the uncertainty for high multiplicity single pp collisions [91,92]. As a figure of merit, a 1 GeV energy loss would correspond, for a 20 GeV jet, to a 5% effect on ∆ ZJ . The middle panel shows the ratio of the distribution for high to low multiplicity for both hadronization models (standard hadronization with a dotted line). In the lower panel, the ratio between the Rope and standard hadronization models is displayed for all three multiplicity regions. 13

Jet Substructure
In addition to reducing the total energy inside a jet, interactions with the QGP in HI collisions distort the radiation pattern. Scattering with the medium results in jets with a broader distribution of energy and therefore jet substructure tools may be used to search for a QGP in central pp collisions. The soft drop jet grooming procedure [93] (the generalization of modified mass drop [94] when β = 0) has gained a lot of recent attention theoretically and experimentally because of its insensitivity to non-global logarithms and robustness to wide angle and soft radiation. Therefore, soft drop jet observables are useful for probing if the structure of a jet has changed in events with high multiplicity. In addition to the jet mass, another important soft drop jet observables is the fraction of the groomed jet's momentum carried by the subleading subjet, z g . This observable has the interesting property that it is independent of α s at leading order and is directly related to the QCD splitting functions [95]. Therefore, any change in the z g distribution in high multiplicity events would be an indication of a modification of the partonic fragmentation function. Preliminary results from CMS are suggestive of medium-induced modifications of the z g distribution [96], which are also predicted by various models of jet quenching [97][98][99][100], although there is tension with preliminary STAR results [101]. Figure 12 shows the distribution of the soft drop mass and z g as a function of TTM, ZTM, or FM with the standard and Rope hadronization models using z cut = 0.1 and β = 0. The mass does show a dependence on the multiplicity, which may be due in part to a residual contribution within the catchment area of the subjets not removed from grooming. There is also a significant difference in the shape of the mass distribution between the two hadronization models, though there is little dependence of the difference on multiplicity. The multiplicity dependence is much reduced in the case of the z g spectra, and in particular the FM dependence is particularly flat, confirming the smaller radiation bias of the FM distributions. As for the mass distributions, the z g spectra are different in the case of Pythia and Rope fragmentation, but the difference is not affected by the multiplicity. However, there is a small difference in the impact of the Rope hadronization on the effect of high multiplicity for the z g distribution. Fitting the lower ratio panel of the FM z g distribution to a polynomial 3 , as shown in Fig. 13, results in a constant term that significantly differs within the MC statistics, which are about 30% higher than the 7 TeV data statistics (the linear and quadratic terms also differ, but not as significantly). The size of the effect is about 10%.
Another well-studied jet substructure observable is the fraction of a jet's momentum carried by identified particles. Figure 14 shows this variant of the fragmentation function in various regions of TTM with and without the Rope hadronization model. For both models, a higher multiplicity corresponds to a softer spectrum. This is due in part to the increased multiplicity of UE that happens to fall in the jet catchment area. Interestingly, there is a multiplicity-dependent difference in this effect between the Rope and standard hadronization models for pions, though it is less clear for kaons (due in part to limited MC statistics).   Figure 13: The quadratic fits to the low-and high-multiplicity Rope/NoRope z g spectra shown for FM in Fig. 12.  Figure 14: The distribution of the momentum fraction (z) carried by pions (left) and kaons (right) for low (< 50), medium (50 < TTM < 100), and high (> 100) TTM for both the default and Rope hadronization models. The middle panel shows the ratio of the distributions for high to low multiplicity for both hadronization models. In the lower panel, the ratio between the Rope and standard hadronization models is displayed for all three multiplicity regions.

16
Proton-proton interactions can be much more complex than vacuum parton-parton interactions. When collided with significant overlap, collective effects observed also in more extended systems are suggestive of a common origin. Using MC simulations of a model with collective effects, we have studied observables related to jets that may be sensitive to the source of the observed phenomena. Interpreting the strangeness enhancement in high multiplicity pp as a sign of a QGP, it will be interesting to next try to quantify the expected size of such a QGP by scaling up to HI and then predicting the magnitude of potential jet quenching. This would require setting up an event simulation framework incorporating the possible development of a QGP in pp collisions, a task that goes beyond the scope of our simple study, and which will hopefully be picked up by more expert colleagues. Independently of the possible quenching effects induced by a mini-QGP, our study shows some interesting features of the Rope fragmentation, and differences with respect to the standard Pythia fragmentation at the level of several percent, when considering jet-related quantities, such as the groomed mass and the z g spectra. The experimental study of these quantities can therefore provide additional handles in the tuning of these alternative fragmentation models, or in the development of new ones. Measurements with Z/γ+jets should be possible with high precision using ATLAS and CMS and the observables and trends presented here provide a baseline for a full experimental investigation.