A Comparative Study of kaon to pion ratio in Proton-Proton Collisions at different energies ---Experimental Results vs. Model Simulation

A detailed study of energy dependence of positive kaon to pion, negative kaon to pion and total kaon to pion multiplicity ratio have been carried out in pp collisions at 6.3, 17.3, 62.4, 200 and 900 GeV and also at root s =2.76 TeV and 7 TeV in the framework of UrQMD and DPMJET III model. Energy dependence of positive kaon to pion and negative kaon to pion show different behavior in case of UrQMD and DPMJET III model. The presence of the horn like structure in the variation of positive kaon to pion and negative kaon to pion ratio with energy for the experimental data is supported by the DPMJET III model. Experimentally it has been observed that as energy increases, the total kaon to pion multiplicity ratio increases systematically for pp collisions at lower energies and becomes independent of energy in LHC energy regime. Our analysis on total kaon to pion multiplicity ratio with UrQMD data is well supported by the experimental results obtained by different collaborations in different times. In case of DPMJET III data, the saturation of kaon to pion ratio at LHC region has not been observed.

Experimentally it has been observed that as energy increases, the total kaon to pion multiplicity ratio + + − + + − = increases systematically for pp collisions at lower energies and becomes independent of energy in LHC energy regime. Our analysis on total kaon to pion multiplicity ratio + + − + + − = with UrQMD data is well supported by the experimental results obtained by different collaborations in different times. In case of DPMJET III data, the saturation of ratio at LHC region has not been observed.

Introduction
The study of nucleus-nucleus interactions at high energies has been a subject of major interest to the theoretical and experimental physicists. The nucleus-nucleus interaction can provide valuable information on the spatiotemporal development of multiparticle production process, which is one of the prime interests in view of recent developments of quantum chromodynamics. Along with the study of nucleus-nucleus collisions, a thorough understanding of proton-proton (pp) collisions is also necessary both as input to detailed theoretical models of strong interactions, and as a baseline for understanding the nucleusnucleus collisions at relativistic and ultra-relativistic energies. Soft particle production from ultra-relativistic pp collisions is also sensitive to the flavor distribution within the proton, quark hadronization and baryon number transport. The measurement of charged particle transverse momentum spectra in pp collisions serves as a crucial reference for particle spectra in nucleus-nucleus collisions. A proton-proton reference spectrum is needed for nucleus-nucleus collisions to investigate possible initial-state effects in the collision. The multiplicity distribution of particles produced in proton-proton (pp) collisions and the multiplicity dependence of other global event characteristics represent fundamental observables reflecting the properties of the underlying particle production mechanisms. In high energy collisions along with the pions, kaons are also important as the strange particle production is a powerful probe into the hadronic interaction and the hadronization process in pp and heavy ion collisions at relativistic energies. The study of K π ratio in high energy collisions is an important observable to be studied not only to address questions of the phase transition but also to obtain a better understanding of the pre-equilibrium dynamics, the hadronization processes and dynamics of hadrons in the medium. It is well known that the strangeness enhancement in relativistic nucleus-nucleus collisions has been proposed as a signature of the Quark-Gluon Plasma (QGP) formation in the relativistic heavy ion collisions. The study of K π ratio in pp collisions can provide a baseline to investigate the strangeness enhancement.
In this paper, we are presenting an analysis of energy dependence of + + , − − and total kaon to pion multiplicity ratio K + +K − π + +π − = K π at  s 6.3, 17.3, 62.4, 200 and 900 GeV and also at √ =2.76TeV and 7 TeV in the framework of UrQMD and DPMJET III model in proton-proton (pp) collisions. We have also compared our results with available experimental results obtained so far. Before going into the details of the analysis it will be convenient for the readers to have brief introductions about the two models.

UrQMD and DPMJET III model----A Brief Introduction
UrQMD model is a microscopic transport theory, based on the covariant propagation of all the hadrons on the classical trajectories in combination with stochastic binary scattering, color string formation and resonance decay. It represents a Monte Carlo solution of a large set of coupled partial integro-differential equations for the time evolution of various phase The Monte Carlo event generator DPMJET can be used to study particle production in highenergy nuclear collisions including photo-production and deep inelastic scattering off the nuclei. It is a code system based on the Dual Parton Model and unifies all features of the DTUNUC-2, DPMJET-II and PHOJET1.12 event generators. DPMJET-III allows the simulation of hadron-hadron, hadron-nucleus, nucleus-nucleus, photon-hadron, photon-photon and photon-nucleus interactions from a few GeV up to the highest cosmic ray energies. DPMJET is an implementation of the two-component Dual Parton Model for the description of interactions involving nuclei. This model is based on the Gribov-Glauber [4][5][6] approach.
Gribov theory of high-energy interactions of hadrons and nuclei is based on general properties of amplitudes in relativistic quantum theory and provides a unified approach to a broad class of processes. According to this theory, the Glauber approximation [6] to nuclear dynamics is valid in the region of not too high energies and should be modified at energies of RHIC and LHC. Gribov theory then allows to determine the corrections to the Glauber approximation [6] for inclusive particle spectra by relating them to cross sections of largemass diffraction. The technique has been applied to calculation of shadowing effects for structure functions of nuclei and a good agreement with experimental data on these processes has been obtained. The same approach predicts a strong reduction of particle densities at super-high energies as compared to predictions of the Glauber approximation [6]. Since its first implementations [7][8] DPMJET model uses the Monte Carlo realization of the Gribov-Glauber multiple scattering formalism according to the algorithms of [9] and allows the calculation of total, elastic, quasi-elastic and production cross sections for any high-energy nuclear collision. DPMJET III is a string model and the generalization of the string model to hadron-nucleus and nucleus-nucleus collisions was done by the Glauber-

Energy Dependence Study of
The values of + + ratio have been calculated from the generated output of both UrQMD and DPMJET III model. Table 1   GeV and go on increasing again signifying the presence of the horn like structure. Here it should be mentioned that there are two possible mechanisms of kaon production, the associated production mechanism and the pair production mechanism. According to the associated production mechanism only  K mesons are produced by the following two interactions:

Energy Dependence Study of
Where N is the nucleon and X is either  hyperons or  hyperons. On the other hand pair production mechanism produces  K and  K according to the interaction given by At the lower energy, the associated production mechanism dominates. As the energy increases, the pair production, which produces the same number of  K and  K becomes more significant. At higher energy the anti kaon excitation function is steeper than that of the kaon because of a higher threshold.
So at higher energy the anti kaon production cross section increases faster than that of kaon and the − − ratio increases.

Energy Dependence Studies of Total kaon to pion multiplicity ratio
We have also calculated the total kaon to pion multiplicity ratio ratio from the analysis of PHENIX collaboration [17] at √ =62.4GeV and from the analysis of STAR collaboration at √ =200GeV [18]. At √ =900 GeV and √ =2.76TeV, the K π ratio have been calculated from the study of ALICE collaboration [24]. ALICE Collaboration [20] studied the pion, kaon and proton production in pp collisions at √ =7 TeV also. In that paper they calculated the values of K π ratio in pp collisions. They have mentioned the values of K π ratio in pp collisions at different energy studied earlier and presented a study of energy dependence. In ref [24] the values of K π ratio at √ =200GeV and √ =900 GeV have been mentioned in the text with proper references.
The experimental values of K π ratio at different energies have been calculated from the plot given in [19] with the help of a high accuracy digitized graphical software as mentioned earlier.
Experimentally calculated values of ratio in pp collisions at ratio are found to be lower than the corresponding experimental values. We have also studied the variation of ratio with energy graphically for the experimental, UrQMD simulated events and DPMJET III simulated events. Figure 3 depicts the variation of kaon to pion ratio with energy in case of pp collisions from 6.3 GeV to 7 TeV for experimental, UrQMD simulated and DPMJET III simulated events. From figure 3 it can be noticed that no horn like structure is observed for the experimental data when the energy dependence of total kaon to pion multiplicity ratio is studied.
It may be mentioned here that Hai-Yan Long et al [25] utilized the parton and hadron cascade model PACIAE based on PYTHIA to investigate the kaon to pion ratio in pp collisions at RHIC and LHC energy. They found that the PACIAE model calculated values of at √ =17.2, 200 and 900 GeV agree with the NA49 [16,[22][23], STAR [18] and ALICE data [24,26].
With the inclusion of the results for √ =2.36, 7 and 14 TeV, it was found that the K π ratio increase slightly from √ =0.2 to 0.9TeV and then saturates. Our study with UrQMD model predicts the same result. It should be mentioned here that ALICE collaboration also in their published papers [24,26] studied the energy dependence of K π ratio in pp collisions.

Conclusions and Outlook
To summarize we recall that we have presented a systematic study of Before we come to the end of our paper, let us discuss some important points. It has already been mentioned in the introduction that pp collisions provide a baseline for studying nucleus-nucleus collisions. In this regard the study is interesting and the main focus of the paper is on proton-proton collisions only. We are not interested to study the nucleus-nucleus collisions in the present paper. We have applied two popular models to study the energy dependence of Our study allows to discriminate between the two models which are based on two      Table 3 represents the values of total kaon to pion multiplicity ratio