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

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

Antonio Ortiz Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Ciudad de México, Del. Coyoacán 04510, México
Lizardo Valencia Palomo Departamento de Investigacíon en Física, Universidad de Sonora,
Blvd Luis Encinas y Rosales S/N, Col. Centro, Hermosillo, Sonora, México
Abstract

In this work we study the underlying-event (UE) activity as a function of the highest jet or charged-particle transverse momentum ( or ) in terms of number and summed- densities of charged particles in the azimuthal region transverse to the leading jet or particle direction. Contrary to inelastic LHC data, the UE observables normalised to the charged-particle density obey an approximate Koba-Nielsen-Olesen (KNO) scaling. Based on PYTHIA 8.2 simulations of collisions at LHC energies, we show that the small breaking of the KNO scaling is due to the increasing importance of multiple partonic interactions (MPI) at higher . This in turn makes that with increasing energy, the spectra in the UE get harder than in inelastic collisions.

Color reconnection (CR) models the interactions among outgoing partons just before the hadronization, therefore it modifies the -spectral shape. Motivated by this, we studied the UE activity considering charged particles within different intervals in collisions at  TeV. Although MPI saturate for  GeV/, the UE still increases with increasing . We demonstrate that the saturation of both number and summed- densities, which are commonly claimed, are only observed for low- charged particles ( GeV/). Moreover, for the -integrated case ( GeV/) the summed- density is not sensitive to the variation of CR, however at low- it is reduced with increasing CR, whereas an opposite behavior is found at intermediate- ( GeV/). Finally, we show that CR produces flow-like behavior only in the UE region and the effects are reduced with increasing due to the hardening of UE. The outcomes encourage the measurement of inclusive and identified charged-particle spectra (over a wide range of ) associated to UE aimed at better understanding the similarities between and heavy-ion data discovered at the LHC.

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1 Introduction

In the context of event generators, one single inelastic (non-diffractive) proton-proton () 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 PhysRevD.36.2019 () and the multiplicity-dependent event shape studies Abelev:2012sk (). The importance of the UE relies on the fact that it can shed light in the search for new physics phenomena at hadron colliders Martin:2016igp () or even in the quest for precise Standard Model measurements Harnik:2008ax ().

The UE observables have been measured in collisions in dijet and Drell-Yan processes at CDF at and 1.96 TeV Acosta:2004wqa (); Aaltonen:2010rm (). 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 Aad:2010fh () 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 Aaboud:2017fwp (). 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 data Ortiz:2015cma (); Abelev:2013haa (); Khachatryan:2016txc (); ALICE:2017jyt (). We should therefore go beyond the traditional UE analysis for better understanding the similarities between and heavy-ion data.

In order to understand the physics behind high-multiplicity collisions, we have performed several studies using PYTHIA 8 Sjostrand:2014zea () event generator. We have found that CR together with MPI can produce radial flow patterns via boosted color strings Ortiz:2013yxa (). The analysis as a function of event multiplicity allows to study events with different amount of MPI, however we have shown that high-multiplicity collisions are effected by the so-called fragmentation bias Abelev:2013sqa (); Ortiz:2016kpz (). 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 Weber:2018ddv ().

Given that heavy-ion data feature remarkable differences between the particle production associated to bulk (everything outside the jet peaks) and jets Veldhoen:2012ge (); Richert:2016bwd (), we have decided to perform an analogous analysis in collisions simulated with PYTHIA 8. The advantage is that cutting on the highest charged-particle transverse momentum () or highest 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 intervals are considered. We also aim to understand how the underlying-event activity is affected when either or are varied. The analysis is not restricted to the traditional average quantities, instead we study the spectra of unidentified and identified charged particles within UE environments modified with a selection on . The measurements of the spectra sensitive to UE as a function of 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- densities, section 4 presents the results on how CR affects the UE observables and the distribution of identified charged particles, and finally section 5 contains the summary and outlook.

2 Simulations and analysis

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 () relative to the leading object (e.g. jet or charged particle) axis. Unless specified, those particles with (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 () and the mean scalar sum of transverse momentum per pseudorapidity unit and per azimuthal separation unit (). hereafter and are referred to as number density and summed- density, respectively. PYTHIA 8.212 Sjostrand:2014zea () tune Monash 2013 Skands:2014pea (), hereafter referred to as PYTHIA 8, was used to simulate inelastic collisions at the LHC energies. Since simulations are intended to be compared to CMS Chatrchyan:2011id (), ATLAS Aaboud:2017fwp () and ALICE ALICE:2011ac () results available on HEPData Maguire:2017ypu (), different selections at particle and event levels were implemented:

1. The comparison of simulations with CMS data ( collisions at and 7 TeV) requires a leading jet with transverse momentum larger than 1 GeV/ within the pseudorapidity interval: . Jets are defined using the SISCone algorithm Salam:2007xv () as implemented in FastJet 3.3 Cacciari:2011ma () with the clustering radius given as . Furthermore, jets are built using charged particles with  GeV/ and . The UE observables are computed using charged particles within and  GeV/. Notice the 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. The comparison with ALICE data ( collisions at and 7 TeV) requires charged particles with GeV/ and with the transverse momentum of the leading charged particle above 0.5 GeV/.

3. The comparison with ATLAS data ( collisions at  TeV) requires charged particles with GeV/ and with the transverse momentum of the leading charged particle above 1 GeV/.

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.

3 Energy dependence of the underlying event

In a previous publication Ortiz:2017jaz (), we have shown that within 10% the UE observables as a function of collapse on -independent curves once they are scaled to the corresponding average charged-particle density (). This quantity is obtained for inelastic 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 ), now we use the CMS data since they are reported for a wide interval. This allows the study of events with exceptional high- jets. In order to obtain the charged-particle density, the transverse momentum distributions of charged particles in collisions at and 7 TeV Khachatryan:2010xs (); Khachatryan:2010us () were integrated for and  GeV/. The total uncertainties (quadratic sum of statistical and systematic uncertainties) associated to the spectrum were propagated to the integral and assigned as systematic uncertainty to . For collisions at and 7 TeV, the computed values were and , respectively. Therefore, the relative variation () of the average charged-particle density in collisions at  TeV with respect to collisions at TeV was found to be .

Figure 1 shows the number (left panel) and the summed- (right panel) densities as a function of after scaling by a 1/ 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 was used instead Ortiz:2017jaz (). 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  GeV/. Regarding the behavior of data, a steep rise of the underlying activity with increasing is observed. This fast rise is followed by a change of the slope above  GeV/. The change of the slope is understood as due to very small impact parameter collisions which yields to a saturation of the MPI activity. Different publications state that above 10 GeV/ the UE observables saturate, reaching nearly constant values ALICE:2011ac (); Aaboud:2017fwp (); Khachatryan:2015jza (). However, we want to stress the fact that both data and PYTHIA 8 still show a rise of the UE activity with increasing . 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) Koba:1972ng () 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 collisions). This ratio has been studied by ALICE using data at and 7 TeV ALICE:2011ac (). To obtain the numerator, ALICE fitted a first degree polynomial to the number density as a function of for  GeV/. 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 bins were neglected. The left-hand side of Fig. 2 shows a comparison of the KNO variable as a function of measured by ALICE and ATLAS. ALICE data points were taken from ALICE:2011ac () while the ATLAS point was derived following the strategy already described. PYTHIA 8 inelastic events were simulated in order to test the scaling of UE over the wide interval covered at the LHC. Going from collisions at to 13 TeV, PYTHIA 8 simulations show a increase of the KNO variable. Within uncertainties, the data exhibit the same trend. The small dependence is also observed if we consider the average number of MPI in events with  GeV/ (central collisions) normalised to this same observable but in inelastic collisions (i.e. without any selection on ). The ratio as a function of 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 collisions, we studied the spectra of unidentified charged particles. The CMS collaboration has reported such spectra for collisions at and 7 TeV. The UE corresponds to events with  GeV/ within . To study the evolution of the -differential particle production with increasing energy, the 7 TeV 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 was obtained using the spectra of inelastic collisions at the same energies Abelev:2013ala (). Within uncertainties, both ratios are consistent up to  GeV/. For higher the ratio increases faster for the UE activity than for inelastic collisions. The results suggest that, with increasing , intermediate- particle production increases faster in the UE than in inelastic collisions. This effect could explain the faster rise of the number density in the UE relative to the corresponding inelastic events ALICE:2011ac (). Transverse momentum distributions sensitive to UE for other and are needed in order to confirm the validity of this conclusion.

4 CR studies using UE observables

We have shown that, with increasing , the spectra sensitive to UE get harder than that in inelastic events as a consequence of the dependence of MPI. Since in events with large number of MPI color reconnection modifies the particle production Ortiz:2013yxa (), 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 () to join low and high partons. Therefore, (ColourReconnection:range in PYTHIA 8) allows to control the amount of interactions which partons feel just before the hadronization. For our study, we computed and in three different ranges depending on the transverse momentum of the charged particles present in the UE: integrated ( GeV/), low ( GeV/) and intermediate ( GeV/) transverse momentum. Each -dependent UE quantity was in turn computed for three different values of : 0, 1.8 and 10, corresponding to the minimum, nominal (tuned to LHC data Skands:2014pea ()) 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 interval. Since we claim an approximate scaling of the particle production associated to UE, we report results only for collisions at  TeV. The conclusions should hold for other energies.

Modification of the particle production at low and intermediate pT

Figure 3 shows the number density as a function of for collisions at  TeV. For the -integrated case, CMS data are compared with PYTHIA 8 simulations considering three different values of . Within uncertainties, data are well described by simulations with . As expected, the number density decreases with increasing due to the reduction of the number of color strings that connect the outgoing partons. Though, the dependence of the number density is the same for the different values. For the low- case, we observe the same ordering reported for the -integrated case. However, the number density is reduced by % relative to the -integrated case. The number density associated to intermediate- particles exhibits an opposite trend with increasing , i.e. going from low- to high- values the number density increases suggesting a hardening of UE with increasing .

The corresponding plots for the summed- density are shown in Fig. 4. Contrary to the number density, this observable presents a steeper rise with increasing and no color-reconnection effects are visible for the -integrated case. However, this does not happen when the summed- density is calculated considering low- or intermediated- charged particles. Namely, for low- particles the summed- density shows a saturation for 10 GeV/. Moreover, the summed- density decreases with increasing values of (the CR effect amounts to 5%). For the intermediate- case, the summed- density rises with increasing more or less at the same rate that the -integrated case.

In order to avoid any possible jet effect (at small values of ) that could bias the previous results, an extra cut on was tested. In this sense only particles with were selected, but no significant differences were observed.

In short, the behavior of the number density as a function of is determined by low-momenta particles while for summed- density is determined by intermediate- particles. It was verified that, qualitatively, the same behavior is obtained for both UE observables at  GeV. It is worth mentioning that UE measurements considering different intervals are not available. Our work suggests the necessity of such measurements in order to test the picture of PYTHIA 8, i.e. the hardening of the UE structure with increasing (or ) by means of MPI and CR.

Flow-like effects within a hard UE environment

It has been shown that CR produces flow-like effects that increase with increasing  Ortiz:2013yxa (). This is because the number of strings connecting scattered partons naturally increases with increasing . CR allows the color fields of the event to be redirected, relative to the case of color-separated MPI, in such a way that the total string length is reduced. This produces a transverse boost to reconnected string pieces, that e.g. provides to heavier hadrons higher  Sjostrand:2018xcd (). It has been shown that in events with enhanced UE activity, relative to inelastic collisions, the flow-like effects increase. This has been achieved by selecting highly-spherical events where no jet structure is present Ortiz:2017jho (). Motivated by the similarity of the event-shape selection results with those for heavy-ion collisions where the proton-to-pion ratio (sensitive to radial flow Adam:2015kca ()) is studied for the regions sensitive to bulk production and jet fragmentation, separately. We decided to perform an analogous Monte Carlo analysis but considering the underlying event accompanying a very high- jet. The goal of the study is to understand how the selection affects observables sensitive to radial flow in the UE region.

Figure 5 shows the proton-to-pion ratio as a function of the hadron transverse momentum in the underlying-event region for two bins and for three different values of : 0, 1.8 and 10. The left-hand side of Figure 5 shows the results for  GeV/. Going from independent fragmentation () to the largest value of , the proton yield is suppressed with respect to the pion one for  GeV/, whereas for intermediate transverse momentum the proton yield is enhanced relative to the pions. This is the mass effect attributed to color reconnection that was previously reported for the inclusive event Ortiz:2013yxa (), i.e. without any separation of the soft and hard components. It is worth noting that the size of the bump shown in Fig. 5 is smaller than that seen in the inclusive case Ortiz:2013yxa (). The reduction is understood in terms of the hardness of the underlying event that increases with increasing . The right-hand side of Fig. 5 shows the results when we move from  GeV/ to higher jet transverse momentum ( GeV/). Going from low- to high- values the structure at  GeV/ is reduced. Moreover, the results show a smaller dependence on indicating that the ratio is more sensitive to the fragmentation of hard partons.

Finally, in order to show the distinct behavior of the UE with respect to jet fragmentation, Figure 6 presents the proton-to-pion ratio as a function of obtained for the towards region (). In particular, only pions and protons within are considered. Notice that, opposite to Figures 3 and 4, the ratios in the bottom panels of Figures 5 and 6 are performed relative to . The reason is because in the latter case the goal is to quantify the flow-like effect, if any, that is observed when color reconnection is present.

Overall in Figure 6, the ratio is significantly smaller than the corresponding for the underlying-event region. For example, while for the transverse region the ratio shows a maximum amounting to at  GeV/; for the jet peak ( GeV/) it reaches 0.1 and the value is subsequently reduced with increasing . It is worth mentioning that although a color-reconnection effect is observed in the jet region as a consequence of the UE contamination, its effect is smaller than what is seen in the transverse side. The effects observed for the UE and jet regions are qualitatively similar to those measured in heavy-ion collisions resulting from the jet-bulk separation using leading-hadron correlations. The statement there Veldhoen:2012ge () is that the flow-like peak observed in proton-to-pion ratio for the most central Pb-Pb collisions at the LHC energies is a medium effect.

The effects reported in this paper should be searched in data; the outcome would contribute to the understanding of the unexpected heavy ion-like signals discovered in small systems by LHC experiments Khachatryan:2016txc (); ALICE:2017jyt (); Acharya:2018orn ().

5 Conclusion

Motivated by the results of our previous work Ortiz:2017jaz (), 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 collisions (KNO variable). Both two quantities were calculated considering charged-particles with  GeV/. The ratio was found to increase with increasing , the trend was well described by PYTHIA 8. In particular going from collisions at to 7 TeV, the ratio increased by 8-10%. In PYTHIA 8 the rate of such an increase with increasing was close to that for multiple partonic interactions. Moreover, using the limited available data we found indications that particle production at intermediate- ( GeV/) increased faster in UE than in inelastic events. Whereas at lower , 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 intervals. We found that color reconnection modifies the spectra of unidentified charged particles, producing a variation in the number and summed- 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 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 spectra of unidentified and identified charged particles in the transverse side. The variation of such spectra as a function of center-of-mass energy, (or ), and system size would add key information on the origin of the heavy ion-like effects observed in collisions.

6 Acknowledgments

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.

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