Probing color reconnection with underlying-event observables at the LHC energies

In the context of event generators, one single inelastic (non-diffractive) proton-proton ($pp$) collision can be split into two components: the main hard partonic scattering and the underlying event (UE). The latter includes initial- and final-state radiation (ISR/FSR), multiple partonic interactions (MPI) and the fragmentation of beam remnants resulting from the hadronization of the partonic constituents that did not participate in any scatter. On top of that, color reconnection (CR) is a microscopic mechanism that describes the interactions that can occur between color fields during the hadronization transition. It is a key ingredient which is needed to explain the increase of the average transverse momentum as a function of charged-particle multiplicity [1] and the multiplicity-dependent event shape studies [2]. The importance of the UE relies on the fact that it can shed light in the search for new physics phenomena at hadron colliders [3] or even in the quest for precise Standard Model measurements [4].

The UE observables have been measured in $p\bar{p}$ collisions in dijet and Drell-Yan processes at CDF at $\sqrt{s}=1.8$ and 1.96 TeV [5, 6]. At the start of the LHC most of the existing Monte Carlo models were tuned using Tevatron data. In this sense, early measurements provided by the ATLAS experiment [7] showed clear differences between event generators and data. Latest results have shown an improvement on the description of the UE by the new Monte Carlo tunes [8]. However, we should keep in mind that the modelling of UE is more challenging than traditionally assumed because recent results suggest the unexpected presence of heavy ion-like behavior in $pp$ data [9, 10, 11, 12]. We should therefore go beyond the traditional UE analysis for better understanding the similarities between $pp$ and heavy-ion data.

In order to understand the physics behind high-multiplicity $pp$ collisions, we have performed several studies using PYTHIA 8 [13] event generator. We have found that CR together with MPI can produce radial flow patterns via boosted color strings [14]. The analysis as a function of event multiplicity allows to study events with different amount of MPI, however we have shown that high-multiplicity $pp$ collisions are effected by the so-called fragmentation bias [15, 16]. Moreover, for a fixed amount of MPI CR strongly modifies the charged-particle multiplicity, therefore a selection based on multiplicity does not permit the isolation of CR effects in events with the same MPI activity. In this work we propose to exploit the usage of UE in order to increase the sensitivity to events with multiple semi-hard scatterings instead to biased fragmentation of high transverse momentum jets. Similar ideas have been proposed in order to disentangle auto-correlation effects from other physical phenomena by measuring the charged-particle multiplicity in the UE region [17].

Given that heavy-ion data feature remarkable differences between the particle production associated to bulk (everything outside the jet peaks) and jets [18, 19], we have decided to perform an analogous analysis in $pp$ collisions simulated with PYTHIA 8. The advantage is that cutting on the highest charged-particle transverse momentum ($p_{\rm{T}}^{\rm leading}$) or highest jet $p_{\rm{T}}$ (${p_{\rm{T}}^{\rm jet}}$) it is possible to select events with larger (and nearly constant) MPI activity than that associated to inelastic events. This allows to enhance color-reconnection effects on the hadronization.

Specifically, in this paper we study the modification of the traditional UE observables when charged particles within different $p_{\rm{T}}$ intervals are considered. We also aim to understand how the underlying-event activity is affected when either ${p_{\rm{T}}^{\rm jet}}$ or $\sqrt{s}$ are varied. The analysis is not restricted to the traditional average quantities, instead we study the $p_{\rm{T}}$ spectra of unidentified and identified charged particles within UE environments modified with a selection on ${p_{\rm{T}}^{\rm jet}}$. The measurements of the $p_{\rm{T}}$ spectra sensitive to UE as a function of ${p_{\rm{T}}^{\rm jet}}$ are proposed as a tool to probe the QCD Monte Carlo picture using LHC data.

The article is organised as follows: section 2 provides information about the event and particle selection for the simulations, section 3 discusses the energy dependence of the UE in terms of the number and summed-$p_{\rm{T}}$ densities, section 4 presents the results on how CR affects the UE observables and the $p_{\rm{T}}$ distribution of identified charged particles, and finally section 5 contains the summary and outlook.

Quantities sensitive to the UE are constructed as follows. The perpendicular plane to the beam axis is segmented into three regions depending on the azimuthal angular difference ($\Delta\phi$) relative to the leading object (e.g. jet or charged particle) axis. Unless specified, those particles with $\pi/3<\lvert\Delta\phi\rvert<2\pi/3$ (transverse side) are the only ones used for the present analysis since they are the most sensitive to UE. The underlying-event observables are defined as the mean number of charged particles per pseudorapidity unit and per azimuthal separation unit ($\langle N_{\mathrm{ch}}/\Delta\eta\Delta\phi\rangle$) and the mean scalar sum of transverse momentum per pseudorapidity unit and per azimuthal separation unit ($\langle\Sigma p_{\mathrm{T}}/\Delta\eta\Delta\phi\rangle$). hereafter $\langle N_{\mathrm{ch}}/\Delta\eta\Delta\phi\rangle$ and $\langle\Sigma p_{\mathrm{T}}/\Delta\eta\Delta\phi\rangle$ are referred to as number density and summed-$p_{\rm{T}}$ density, respectively. PYTHIA 8.212 [13] tune Monash 2013 [20], hereafter referred to as PYTHIA 8, was used to simulate inelastic $pp$ collisions at the LHC energies. Since simulations are intended to be compared to CMS [21], ATLAS [8] and ALICE [22] results available on HEPData [23], different selections at particle and event levels were implemented:

1. 1.

   The comparison of simulations with CMS data ($pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV) requires a leading jet with transverse momentum larger than 1 GeV/$c$ within the pseudorapidity interval: $\lvert\eta\rvert<2$. Jets are defined using the SISCone algorithm [24] as implemented in FastJet 3.3 [25] with the clustering radius given as $R=\sqrt{(\Delta\phi)^{2}+(\Delta\eta)^{2}}=0.5$. Furthermore, jets are built using charged particles with $p_{\rm{T}}>0.5$ GeV/$c$ and $\lvert\eta\rvert<2.5$. The UE observables are computed using charged particles within $\lvert\eta\rvert<2$ and $p_{\rm{T}}>0.5$ GeV/$c$. Notice the $\eta$ range of particles used to build the jets is larger than that of particles in the UE in order to avoid a kinematic bias.

2. 2.

   The comparison with ALICE data ($pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV) requires charged particles with $p_{\rm{T}}>0.5$ GeV/$c$ and $|\eta|<0.8$ with the transverse momentum of the leading charged particle above 0.5 GeV/$c$.

3. 3.

   The comparison with ATLAS data ($pp$ collisions at $\sqrt{s}=13$ TeV) requires charged particles with $p_{\rm{T}}>0.5$ GeV/$c$ and $|\eta|<2.5$ with the transverse momentum of the leading charged particle above 1 GeV/$c$.

In all cases the configuration used in PYTHIA 8 was the following: Beams:idA = 2212, Beams:idB = 2212, Beams:eCM = 900 (7000 and 13000), Tune:pp = 14 and SoftQCD:inelastic = on.

In a previous publication [26], we have shown that within 10% the UE observables as a function of $p_{\rm T}^{\rm leading}$ collapse on $\sqrt{s}$-independent curves once they are scaled to the corresponding average charged-particle density (${\rm d}N_{\rm ch}/{\rm d}\eta^{\rm inelastic}$). This quantity is obtained for inelastic $pp$ collisions at a given center-of-mass energy. In this paper we want to trace back the origin of the small imperfection of the scaling behavior, i.e. its validity within 10%. Instead of using ATLAS UE data (measured as a function of $p_{\rm T}^{\rm leading}$), now we use the CMS data since they are reported for a wide ${p_{\rm{T}}^{\rm jet}}$ interval. This allows the study of $pp$ events with exceptional high-$p_{\rm{T}}$ jets. In order to obtain the charged-particle density, the transverse momentum distributions of charged particles in $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV [27, 28] were integrated for $\lvert\eta\rvert<2.4$ and $p_{\rm{T}}>0.5$ GeV/$c$. The total uncertainties (quadratic sum of statistical and systematic uncertainties) associated to the $p_{\rm{T}}$ spectrum were propagated to the integral and assigned as systematic uncertainty to $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle^{\rm inelastic}$. For $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV, the computed values were $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle^{\rm inelastic}=1.20\pm 0.04$ and $2.33\pm 0.11$, respectively. Therefore, the relative variation ($f$) of the average charged-particle density in $pp$ collisions at $\sqrt{s}=7$ TeV with respect to $pp$ collisions at $\sqrt{s}=0.9$ TeV was found to be $f=1.94\pm 0.11$.

Figure 1 shows the number (left panel) and the summed-$p_{\rm{T}}$ (right panel) densities as a function of ${p_{\rm{T}}^{\rm jet}}$ after scaling by a 1/$f$ factor. Little or no energy dependence is observed after the implementation of the scaling factor. This is what we called “universality of UE” in our previous work where $p_{\rm{T}}^{\rm leading}$ was used instead [26]. The results are compared with PYTHIA 8 simulations since it reproduces very well many features of LHC data. We observe that the scaling properties hold up to $p_{\rm T}^{\rm jet}=25$ GeV/$c$. Regarding the behavior of data, a steep rise of the underlying activity with increasing $p_{\rm T}^{\rm jet}$ is observed. This fast rise is followed by a change of the slope above $p_{\rm T}^{\rm jet}\sim 10$ GeV/$c$. The change of the slope is understood as due to very small impact parameter $pp$ collisions which yields to a saturation of the MPI activity. Different publications state that above 10 GeV/$c$ the UE observables saturate, reaching nearly constant values [22, 8, 30]. However, we want to stress the fact that both data and PYTHIA 8 still show a rise of the UE activity with increasing ${p_{\rm{T}}^{\rm jet}}$. In the next sections we discuss how color reconnection contributes to that behavior.

The universality of UE can be interpreted as the approximate Koba-Nielsen-Olesen (KNO) [31] scaling of the particle production associated to the UE. For this reason we studied the energy dependence of the KNO variable: number density in the transverse side normalised to the charged-particle density (inelastic $pp$ collisions). This ratio has been studied by ALICE using $pp$ data at $\sqrt{s}=0.9$ and 7 TeV [22]. To obtain the numerator, ALICE fitted a first degree polynomial to the number density as a function of $p_{\rm T}^{\rm leading}$ for $p_{\rm T}^{\rm leading}>5$ GeV/$c$. Within uncertainties the fit slope was found to be consistent with zero and the constant parameter was identified as the average number density in the transverse side. Potential correlations of the systematic uncertainties in different $p_{\rm{T}}$ bins were neglected. The left-hand side of Fig. 2 shows a comparison of the KNO variable as a function of $\log(\sqrt{s})$ measured by ALICE and ATLAS. ALICE data points were taken from [22] while the ATLAS point was derived following the strategy already described. PYTHIA 8 inelastic $pp$ events were simulated in order to test the scaling of UE over the wide $\sqrt{s}$ interval covered at the LHC. Going from $pp$ collisions at $\sqrt{s}=0.9$ to 13 TeV, PYTHIA 8 simulations show a $\sim 8\%$ increase of the KNO variable. Within uncertainties, the data exhibit the same trend. The small $\sqrt{s}$ dependence is also observed if we consider the average number of MPI in events with $p_{\rm T}^{\rm leading}>5$ GeV/$c$ (central $pp$ collisions) normalised to this same observable but in inelastic $pp$ collisions (i.e. without any selection on $p_{\rm T}^{\rm leading}$). The ratio as a function of $\log({\sqrt{s}})$ is described by a first degree polynomial with a slope parameter of 0.13, which is close to what is obtained using the number density (slope 0.17), suggesting a common origin.

In order to investigate the features of particle production associated to UE, in particular the excess of particles in UE with respect to inelastic $pp$ collisions, we studied the $p_{\rm{T}}$ spectra of unidentified charged particles. The CMS collaboration has reported such spectra for $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV. The UE corresponds to events with ${p_{\rm{T}}^{\rm jet}}>3$ GeV/$c$ within $|\eta|<2$. To study the evolution of the $p_{\rm{T}}$-differential particle production with increasing energy, the 7 TeV $p_{\rm{T}}$ spectrum was normalized to the corresponding one at 0.9 TeV. The results are presented in the right-hand side of Fig. 2. An analogous ratio as a function of $p_{\rm{T}}$ was obtained using the $p_{\rm{T}}$ spectra of inelastic $pp$ collisions at the same energies [29]. Within uncertainties, both ratios are consistent up to $p_{\rm{T}}=4$ GeV/$c$. For higher $p_{\rm{T}}$ the ratio increases faster for the UE activity than for inelastic $pp$ collisions. The results suggest that, with increasing $\sqrt{s}$, intermediate-$p_{\rm{T}}$ particle production increases faster in the UE than in inelastic $pp$ collisions. This effect could explain the faster rise of the number density in the UE relative to the corresponding inelastic events [22]. Transverse momentum distributions sensitive to UE for other $\sqrt{s}$ and ${p_{\rm{T}}^{\rm jet}}$ are needed in order to confirm the validity of this conclusion.

We have shown that, with increasing $\sqrt{s}$, the $p_{\rm{T}}$ spectra sensitive to UE get harder than that in inelastic events as a consequence of the $\sqrt{s}$ dependence of MPI. Since in events with large number of MPI color reconnection modifies the particle production [14], CR effects on UE are expected. In order to quantify such effects we used the default CR model of PYTHIA 8 (MPI-based) . The model includes the reconnection probability ($rr$) to join low and high $p_{\rm{T}}$ partons. Therefore, $rr$ (ColourReconnection:range in PYTHIA 8) allows to control the amount of interactions which partons feel just before the hadronization. For our study, we computed $\langle N_{\mathrm{ch}}/\Delta\eta\Delta\phi\rangle$ and $\langle\Sigma p_{\mathrm{T}}/\Delta\eta\Delta\phi\rangle$ in three different $p_{\rm{T}}$ ranges depending on the transverse momentum of the charged particles present in the UE: integrated ($p_{\mathrm{T}}>0.5$ GeV/$c$), low ($0.5<p_{\mathrm{T}}<2$ GeV/$c$) and intermediate ($2<p_{\mathrm{T}}<10$ GeV/$c$) transverse momentum. Each $p_{\rm{T}}$-dependent UE quantity was in turn computed for three different values of $rr$: 0, 1.8 and 10, corresponding to the minimum, nominal (tuned to LHC data [20]) and maximum possible values in PYTHIA 8. Moreover, the results presented here are obtained using leading jets within the CMS kinematic ranges, allowing the comparison between data and PYTHIA 8 over a broad ${p_{\rm{T}}^{\rm jet}}$ interval. Since we claim an approximate scaling of the particle production associated to UE, we report results only for $pp$ collisions at $\sqrt{s}=7$ TeV. The conclusions should hold for other energies.

Motivated by the results of our previous work [26], where we shown that the particle production sensitive to the underlying event (UE observables) exhibited an approximate KNO scaling. In this paper we investigated in more detail the scaling properties using data from three experiments at the LHC, as well as their description using multiple partonic interactions and color reconnection in the context of PYTHIA 8 (version 8.212 tune Monash 2013) event generator.

We studied the number density in the transverse side divided by the charged-particle density in inelastic $pp$ collisions (KNO variable). Both two quantities were calculated considering charged-particles with $p_{\rm{T}}>0.5$ GeV/$c$. The ratio was found to increase with increasing $\sqrt{s}$, the trend was well described by PYTHIA 8. In particular going from $pp$ collisions at $\sqrt{s}=0.9$ to 7 TeV, the ratio increased by 8-10%. In PYTHIA 8 the rate of such an increase with increasing $\sqrt{s}$ was close to that for multiple partonic interactions. Moreover, using the limited available data we found indications that particle production at intermediate-$p_{\rm{T}}$ ($2<p_{\rm{T}}<10$ GeV/$c$) increased faster in UE than in inelastic events. Whereas at lower $p_{\rm{T}}$, such an increase in both UE and inelastic events was the same within uncertainties. This effect could yield the small breaking (10%) of the KNO scaling in the particle production sensitive to UE.

The results above motivated the study of the traditional underlying-event observables considering particles within different $p_{\rm{T}}$ intervals. We found that color reconnection modifies the $p_{\rm{T}}$ spectra of unidentified charged particles, producing a variation in the number and summed-$p_{\rm{T}}$ densities. In short, color reconnection enhanced the particle production at intermediate transverse momenta in regions far from the jet peaks. The modification was mass dependent, e.g. the proton-to-pion ratio as a function of $p_{\rm{T}}$ in the underlying-event region exhibited a flow-like response with the variation of the color reconnection strength. This behavior was very similar to what was observed in the bulk (everything outside the jet peak) region measured in heavy-ion collisions.

Our paper encourages the measurement of $p_{\rm{T}}$ spectra of unidentified and identified charged particles in the transverse side. The variation of such $p_{\rm{T}}$ spectra as a function of center-of-mass energy, ${p_{\rm{T}}^{\rm jet}}$ (or $p_{\rm{T}}^{\rm leading}$), and system size would add key information on the origin of the heavy ion-like effects observed in $pp$ collisions.

We acknowledge the technical support of Luciano Diaz and Eduardo Murrieta for the maintenance and operation of the computing farm at ICN-UNAM. Support for this work has been received from CONACyT under the Grant No. 280362 and PAPIIT-UNAM under Project No. IN102118.