Baryon production from cluster hadronisation
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Abstract
We present an extension to the colour reconnection model in the Monte Carlo event generator Herwig to account for the production of baryons and compare it to a series of observables for soft physics. The new model is able to improve the description of chargedparticle multiplicities and hadron flavour observables in pp collisions.
1 Introduction
With increasing precision from the LHC it becomes apparent that many nonperturbative aspects of elementary particle production are far from understood. Especially the description of the transition from the deconfined state to final state particles that are observed in the detectors has many unknown variables and raises a lot of questions. With the help of Monte Carlo event generators [1, 2, 3, 4, 5] different models can be evaluated. Among the problems that are being observed are the correct description of highmultiplicity events and the flavour composition of final states. One striking observation, made recently by the ALICE collaboration, was that in highmultiplicity pp events properties similar to that of AA and pA collisions are observed [6].
Possible explanations of these effects are rooted in the possibility that partonic matter shows some collective behaviour as in a hydrodynamical description; see e.g. [7]. The other route to introduce strong and possibly quite longrange correlations among different hard partons in a single interaction goes via colour reconnections. Here, states of high partonic density may lead to some kind of absorption or neutralisation of colour charge. These ideas have been advocated in some way e.g. in the Dipsy rope model [8] where many overlapping strings are combined into a colour field of a higher representation. Thermodynamical string fragmentation in Pythia also addresses this issue where shifts of the transverse momentum of heavier particles to higher values are the main result [9]. The possibility to form string junctions within the Lund string fragmentation model has been introduced in [10].
In Herwig an accurate description of Minimum Bias (MB) and Underlying Event (UE) observables has been achieved with the recent development of a new model for soft and diffractive interactions [11], building on the earlier developments in [12, 13, 14, 15]. Here, the importance of colour reconnections has already been observed. However, in this work only charged particles have been addressed as such and we have already pointed out shortcomings in the description of highmultiplicity tails. This observation lead to the consideration that the mere production of baryons by itself would lead to a reduction of charged multiplicity in favour of a rise of the multiplicity of heavier particles. We do not address effects that arise at high multiplicity in particular but rather aim at an improved global description of particle production in MB events.
In this study we therefore introduce a possible extension to the model for colour reconnection to account for the production of baryons. At the same time we reconsider the production of strange particles and find that with a slight modification of our parameters we can improve the production rates of strange mesons as well as baryons quite significantly. We compare these effects to recent observations made by CMS and ALICE. Especially chargedparticle multiplicities and ratios of identified hadrons are of main interest.
2 Colour reconnection
In order to describe the full structure of a particle scattering process additional soft effects that are not accessible by perturbation theory have to be considered. Such effects include hadronisation, Multiple Parton Interactions (MPIs) and fragmentation processes. In general these nonperturbative effects are based on phenomenological considerations. The basis for the hadronisation model in Herwig is the cluster model [16], which forms colourless singlets from colour connected partons. The fragmentation of these clusters into hadrons depends on the invariant cluster mass and the flavour of the quarks inside the cluster. The colour connections between the partons in an event are determined by the \(N_C\rightarrow \infty \) approximation which leads to a planar representation of colour lines [17]. Every quark is connected to an antiquark and gluons, carrying both colour and anticolour, connected to two other partons. The goal of colour reconnection is to study whether different connection topologies, other than the predefined colour connection, are possible between the partons.
In hadronic collisions the colour reconnection mostly aims at a resurrection of the colour correlation between different hard partonic interactions. In the Monte Carlo modelling of MPIs, different hard partonic scatters are layered on top of each other without a clear understanding of how to introduce a preconfined state when comoving partons from different scattering centres should also lead to ‘closeness’ in colour space, i.e. to short colour lines between those partons. The importance of the effect has first been observed in [18]. The colour reconnection leads to a decrease of the charged multiplicity for a given partonic configuration and hence an increase of the average transverse momentum per charged particle. The effect gets stronger with denser states, e.g. as we increase the CM energy of the hadronic collider.
The effects of colour reconnection have also been studied in the context of \(\mathrm{W}^+\mathrm{W}^\) production at LEP2 [19, 20]. Due to the large spacetime overlap of the decaying bosons the two hadronic systems may be in contact with each other which leads to colour interchange and can cause one quark of the \(\mathrm{W}^+\) boson to hadronize together with an antiquark of the \(\mathrm{W}^\) boson.
2.1 The colour reconnection model in Herwig
The statistical colour reconnection on the other hand uses a simulated annealing algorithm to find the configuration of clusters that results in the absolute lowest value of the colour length \(\lambda \). While intensively computing, it was also found in [22] that the statistical colour reconnection prefers a quick cooling, which does not result in a global minimum of colour length \(\lambda \) in order to describe the data best. In a recent paper the colour reconnection model was changed in a way, that it is forbidden to make a reconnection which would lead to a gluon produced in any stage of the partonshower evolution becoming a coloursinglet after hadronisation [23].
2.2 Extension to the colour reconnection model
2.3 Algorithm
 1.
Shuffle the list of clusters in order to prevent the bias that comes from the order in which we consider the clusters for reconnection.
 2.
Pick a cluster \((\mathrm{A})\) from that list and boost into the rest frame of that cluster. The two constituents of the cluster \((q_{\mathrm{A}}, \bar{q}_{\mathrm{A}})\) are now flying back to back and we define the direction of the antiquark as the positive zdirection of the quark axis.
 3.
Perform a loop over all remaining clusters and calculate the rapidity of the cluster constituents with respect to the quark axis in the rest frame of the original cluster for each other cluster in that list \((\mathrm{B})\).
 4.Depending on the rapidities the constituents of the cluster \((q_{\mathrm{B}}, \bar{q}_{\mathrm{B}})\) fall into one of three categories:If the cluster neither falls into the mesonic nor in the baryonic category listed above, the cluster is not considered for reconnection.

Mesonic: \(y(q_{\mathrm{B}})> 0 > y(\bar{q}_{\mathrm{B}})\).

Baryonic: \(y(\bar{q}_{\mathrm{B}})> 0 > y(q_{\mathrm{B}})\).

Neither.

 5.
The category and the absolute value \(y(q_{\mathrm{B}}) +y(\bar{q}_{\mathrm{B}})\) for the clusters with the two largest sums is saved (these are clusters B and C in the following).
 6.
Consider the clusters for reconnection depending on their category. If the two clusters with the largest sum (B and C) are in the category baryonic consider them for baryonic reconnection (to cluster A) with probability \(p_{\mathrm{B}}\). If the category of the cluster with the largest sum is mesonic then consider it for normal reconnection with probability \(p_{\mathrm{R}}\). If a baryonic reconnection occurs, remove these clusters (A, B, C) from the list and do not consider them for further reconnection. A picture of the rapiditybased reconnection for a mesonic configuration is shown in Fig. 2 and a simplified sketch for baryonic reconnection is shown in Fig. 3.
 7.
Repeat these steps with the next cluster in the list.
3 Tuning

The pseudorapidity distributions for \(N_{\mathrm{ch}}\ge 1\), \(N_{\mathrm{ch}}\ge 2\), \(N_{\mathrm{ch}}\ge 6\), \(N_{\mathrm{ch}}\ge 20\).

The transverse momentum of charged particles for \(N_{\mathrm{ch}}\ge 1\).

The chargedparticle multiplicity for \(N_{\mathrm{ch}}\ge 2\).

The mean charged transverse momentum vs. the multiplicity of charged particles for \(p_{\perp }>500\,\mathrm{MeV}\) and \(p_{\perp }>100\,\mathrm{MeV}\).

The pion and the proton yield in the central rapidity region \(y<0.5\).
Results of the parameter values from the tuning procedure that resulted in the smallest \(\chi ^2 / N_{\mathrm {dof}}\) value for \(\sqrt{s}=7\, \mathrm {TeV}\) centreofmass energy compared with the default tune from Herwig 7.1
\(p_{\perp ,0}^{\mathrm{min}}/\mathrm{GeV}\)  \(\mu ^2/\,{\mathrm{GeV}^2}\)  \(p_{\mathrm{R}}\)  \(p_{\mathrm{B}}\)  

Default  3.502  1.402  0.5  0 
Tune  3.269  1.963  0.543  0.2086 
Results of the parameter values from the tuning procedure that resulted in the smallest \(\chi ^2 / N_{\mathrm {dof}}\) value for \(\sqrt{s}=7\, \mathrm {TeV}\) centreofmass energy compared with the default tune from Herwig 7.1
\(p_{\perp ,0}^{min}/\mathrm{GeV}\)  \(\mu ^2/\,{\mathrm{GeV}^2}\)  \(p_{\mathrm{R}}\)  \(p_{\mathrm{B}}\)  PwtSquark  SplitPwtSquark  

Default  3.502  1.402  0.5  0  0.665  0 
Tune  3.053  1.282  0.772  0.477  0.291  0.824 
4 Results
Changes in the colour reconnection model are always deeply tied with the peculiarities of the hadronisation model. In principle one would have to retune all parameters that govern hadronisation in Herwig. This is usually done in a very dedicated and long study with LEP data. We propose a simplified procedure since little to no changes are expected with the extension to the colour reconnection model in the \(\mathrm{e}^++\mathrm{e}^\) environment. At LEP the colour structure of an event is not changed significantly through colour reconnection since it is already well defined by the parton shower. This was confirmed by comparing the new model to a wide range of experimental data from LEP. We therefore keep the hadronisation parameters that were tuned to LEP data (see Refs. [1, 3]) at their default values. We also note that this does not replace a dedicated study concerned with the tuning and validation of hadronisation parameters. Especially at pp collisions a different model for colour reconnection leads to changes in the interplay between the clusters and the hadronisation in an unforeseeable way. A possible way out of this dilemma would be to make a distinguished LHC tune and compare the results with LEP. Nonetheless we restrain ourselves to the explained simplified method in order to make qualitative statements about the new model for colour reconnection. The new model with the tuned parameters improves the description of all observables considered in the tuning procedure. The effect of the baryonic colour reconnection was already demonstrated in Fig. 4. In Fig. 6 we show the same distribution of the chargedparticle multiplicity for the central region \(y < 1\) with the tuned parameter values. Again we see the expected fall off for high multiplicities. The new model is able to describe the whole region fairly well compared to the old model. Only the low multiplicity region \(n<10\) is overestimated by a factor of \(\approx 10\%\) and for \(n<5\) underestimated. In Fig. 6 we also show a similar observable for a wider rapidity region \(y<2.4\) and up to \(n=200\) as measured by CMS [28]. Again the central multiplicity region shows a significant improvement. For multiplicities \(n>80\) we note a slight overestimation of the data but are still within error bars.
This can be understood quite simply: the more activity in an event, the more likely it becomes that a cluster configuration that leads to baryonic reconnection is found. The highmultiplicity events therefore exhibit a disproportionately large fraction of baryonic reconnections. Due to the highly restricted phase space for the production of baryons from baryonic clusters less particles are produced than with mesonic clusters of the same invariant mass, which lowers the charged multiplicity.
In addition to the tuned observables, many hadron flavour observables which were not considered in the tuning procedure show a significant improvement as well.
In order to compare the different effects from the new colour reconnection model and the possibility to produce strange quarks during gluon splitting we made runs with the default model (Herwig 7.1 default), the pure baryonic colour reconnection model (baryonic reconnection), one run where we allow the gluons to split into strange quarks (\(g\rightarrow s\bar{s}\) splittings) and use the old colour reconnection model and a run where we use both extensions and the parameters that we obtained from the tuning (new model).
In a recent analysis by ALICE a significant enhancement of strange to non strange hadron production with increasing particle multiplicity in pp collisions was observed [6]. Since we are developing a model that incorporates strangeness production and the enhanced production of baryons it is instructive to compare our model to the data published by the ALICE collaboration.
In Fig. 14 we show we show the \((\Lambda +\bar{\Lambda })/(\pi ^++\pi ^)\) and the \(\mathrm {K}_{\mathrm{s}}^0/(\pi ^{+}+\pi ^{})\) ratio for the old model and the new model for colour reconnection. While the \(\mathrm {K}_{\mathrm{s}}^0/(\pi ^{+}+\pi ^{})\) ratio is reasonably well described, the \(\Lambda /\pi \) ratio is underestimated by both, the old and the new model. The new model, on the other side, is able to capture the general trend of the observable and describe the rise of the fraction of \(\Lambda \) baryons with respect to increasing particle multiplicity correctly. Also the increase in the fraction of multistrange baryons \((\Xi ^{}+\bar{\Xi }^+)\) and \((\Omega ^{}+\bar{\Omega }^+)\) can qualitatively be described by the new model as is also shown in Fig. 14. Note that the Herwig 7.1 default model did not produce clusters heavy enough in order to account for the production of any \(\Omega \)baryons.
4.1 Spectra of cluster masses
5 Conclusion and outlook
We have implemented a new model for colour reconnection which is entirely based on a geometrical picture instead of an algorithm that tries to directly minimize the invariant cluster mass. In addition, we allow reconnections between multiple mesonic clusters to form baryonic clusters which was not possible in the old model. With this mechanism we get an important lever on the baryon to meson ratio which is a necessary starting point in order to describe flavour observables. The amount of reconnection also depends on the multiplicity of the events which can be seen by comparing the model to the chargedparticle multiplicities which get significantly better. In addition we allow for nonperturbative gluon splitting into strange quark–antiquark pairs. Only with this additional source of strangeness it is possible to get a good description of the \(p_{\perp }\) spectra of the kaons. The description of the heavy baryons \(\Lambda \) and \(\Xi ^{}\) improves once we combine the new model for colour reconnection and the additional source of strangeness. The model was tuned to 7 TeV MB data and various hadron flavour observables. With the new model the full range of MB data can be described with a similar good quality as the old model and in addition we improve the description of hadron flavour observables significantly.
A comparison with ALICE data concerning the enhancement of (multi)strange baryons led us to the conclusion that our simple model is able to reproduce the general trend of some of the observables, but fails to describe the data in its entirety. Nonetheless we see indications that the increase in the strange baryon fraction can also be explained by an approach with colour reconnection in combination with the cluster model. In order to arrive at a satisfying description of highmultiplicity events we suggest a model were these events are originating from less and heavier clusters instead of many lighter ones. This is necessary to raise the probability for producing heavy and strangeness containing hadrons. This could also in principle be solved in the framework of a colour reconnection model were many overlapping clusters (or a region of high cluster density) fuse together to form a heavy cluster which opens up the phase space for the production of strangeness and baryons in the cluster decay stage.
This issue could possibly be addressed by a spacetime picture of cluster evolution which will be left for future work.
A shortcoming of the model lies in the algorithm which is biased by the order of clusters which are considered for reconnection and the fact that baryonic clusters cannot be rereconnected. This will ultimately yield clusters which do not consist of the nearest neighbours in phase space but a small overlap between the clusters will still be present. Due to the sheer amount of possibilities on how to assign baryonic clusters we are forced to introduce some sort of arbitrariness when it comes to the cluster assignment. When comparing the new model with the old model, we see that the new colour reconnection model does not have the same effect on the invariant mass distribution in terms of reduction of cluster masses but fuses mesonic clusters together in order to form baryonic clusters and therefore adds an additional possibility to produce heavy baryons. According to the data a significant reduction in cluster mass is not favoured. The data prefers more fluctuations in cluster size and explicitly shows the possibility to produce baryonic clusters. Otherwise the production of heavy strange baryons is not possible and highly suppressed.
Understanding soft physics remains difficult but new approaches and models are necessary in order to improve the quality of Monte Carlo event generators. Overall, we have shown that small changes in the model for colour reconnection and the gluonsplitting mechanism can have significant effects on some observables.
Notes
Acknowledgements
We are grateful to the other members of the Herwig collaboration for critical discussions and support. We would also like to thank Christian Bierlich and Christian Holm Christensen for providing us with the ALICE data and the analysis. This work has received funding from the European Union’s Horizon 2020 research and innovation programme as part of the Marie SkłodowskaCurie Innovative Training Network MCnetITN3 (Grant Agreement No. 722104). This work has been supported in part by the BMBF under grant number 05H15VKCCA. SP acknowledges the kind hospitality of the Erwin Schrödinger Institute and the Particle Physics group at the University of Vienna while part of this work has been completed.
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