Transverse Momentum Spectra in pp collisions (\sqrt{s}\) = 7 TeV and \(\sqrt{s}\) = 13 TeV in ALICE

Abstract: In this project particle production as a function of transverse momentum (\(p_{\rm T}\)) in proton-proton collisions at a center-of-mass energy (\(\sqrt{s}\)) of 7 TeV and 13 TeV has been studied. The transverse momentum is interesting to study since it reflects momentum created in the collision (before the collision, all momentum is in the beam - going in a longitudinal direction) and therefore gives information on the collision dynamics. Firstly, (anti)pions (\( \pi^\pm \)), (anti)kaons (K\( ^\pm\) and K\(_ {\rm S} ^{\rm 0}\)), (anti)protons (p(\(\rm \bar p\))) and (anti)lambdas (\(\rm \Lambda ^{\rm 0}\) and \( \rm \bar \Lambda ^{\rm 0}\)) with their spectra \(dN/dp_{\rm T}\) as a function of transverse momentum (\(p_{\rm T}\)) were studied. Different functions were fitted to these spectra to see how well they could describe the data. A good fitting function is needed to extrapolate to low \(p_{\rm T}\) where the particles can not be measured since they do not have enough momentum to reach the detectors. To get a measure of how well the fits performed two methods were used. The first was to look at the error relative to the fitting function. The second was to look at minimizing the \(\chi^2\)/NDF-value where \(\chi^2\) can be defined as a statistical measure of how good the fit was and NDF being the Number of Degrees of Freedom. Secondly, (anti)pions (\( \pi^\pm \)), (anti)kaons (K\( ^\pm\)) and (anti)protons (p(\(\rm \bar p\))) where studied in 10 multiplicity classes. Multiplicity is here defined as the number of particles coming out from a collision. From these data, each particle's Minimum Bias (MB) spectrum was created. It was observed that the ratio of the lowest multiplicity class over MB behaved like a \(e^{-x}\)-function while the other classes' ratio became a constant for higher \(p_{\rm T}\)-values. Thus the lowest multiplicity class was eliminated from a combined fit involving all other classes. Different functions were tested: all with one common parameter and two adjustable parameters for each class. Finally, so-called Lévy fits were made to each multiplicity class and a Lévy fit to the MB spectrum for each particle. Here, the exponent, \(-n\), to the main \(p_{\rm T}\)-dependent part of the Lévy function was studied. This function was motivated by the fact that the Lévy function behaves like a power law function, in this case being \(p_{\rm T} ^{n-1}\), for high \(p_{\rm T}\). Thus \(n\) was the value that determined how fast the spectra went from a region dominated by particles from soft interactions to a phase dominated by particles from jets.