Yüksek-rölativistik enerjilerde müon çifti üretimi

The main purpose of high energy physics is to help us to understand and explain the elementary particles that constitutes matter. For this aim the various particle accelerators have been constructed. At the RHIC(Relativistic Heavy-Ion Collider) and LHC(Large Hadron Collider) which are the largest particle accelerators, the particles produced as a result of the heavy-ion collisions performed at the center of mass frame with relativistic velocities are investigated. In heavy ion collisions, the collided particles undergo a Lorentz contraction due to their high relativistic velocities, and very strong electromagnetic fields occur at their ends. The vertical distance between the colliding particles is called the impact-parameter. If the impact-parameter is greater than the sum of the radii of the two nuclei, the peripheral collision is concerned, otherwise the central collision occurs. Central collisions occur as the form of nucleus-nucleus(or head-to-head) collision, and are thought to cause the creation of quark-gluon plasma(QGP), which is known to exist at the first formation of the universe. In the case of peripheral collisions, the interaction of strong electromagnetic fields at the ends of heavy-ions is involved. In both collisions, many particles are produced. Investigation of lepton pairs produced in these collisions has an important place in high energy physics, since it is thought to contribute to the understanding of the QGP phase state of matter. In this thesis, the process of lepton-pairs production with electromagnetic interactions in heavy ion collisions at high relativistic velocities is discussed. Firstly, it was shown how to calculate cross-sections for muon-antimuon and electron-positron pairs. For this, low-order quantum electrodynamics(QED), Gauge theory and Feynmann diagrams were used. The obtained cross-section expression were numerically solved by the Monte-Carlo method using the FORTRAN program since it contains 9-fold integrals that are difficult to solve analytically. Form factors that provide information about the charge densities of atomic nuclei were also taken into account. There are different approaches for charge distributions such as Gaussian, Uniform and Woods-Saxon (Fermi). Form factors are obtained by taking Fourier transforms of these spatial charge distributions. In this study, the cases with form factor of Woods-Saxon and Gausyen and without any form factor were examined, and the effect of these different form factors on the cross-sections of the electron-positron and muon-antimuon pairs were shown. However, the electron is hardly interacting with the atomic nucleus, because its reduced Compton wavelength (386 fm) is too large for the size of the nucleus. Therefore, the form factor effect for the electron is negligible. For the muon with a reduced Compton wavelength of 1.86 fm, the effect of form factors is of great importance. The effect of the form factor on the differential cross-sections was also clearly seen on the obtained graphs. In this study, two methods, which are method of perturbative QED including second xxi order Feynman diagrams and EPA (Equivalent Photon Approach), were emphasized to calculate the cross-section. Calculations using perturbative QED were used to obtain differential cross-section graphs based on the impact-parameter. In the graphs, it was seen that the production amount of muon-antimuon pair was lower since it is 207 times heavier than the electron. Then, the contribution of the cross-section from the electromagnetic interactions to the central collisions of heavy ions was calculated by limiting the impact-parameter in the range of 0􀀀14 fm. This calculation means that all of the measured cross-section for the central collisions do not come from the Drell-Yan process. After that, the total eperipheral cross-section value was obtained for the production of muon-antimuon pairs at RHIC, and compared with the results calculated by EPA method. In the next part, the change of the cross-section according to quantities such as rapidity, transverse momentum, longitudinal momentum, energy and invariant mass which give information about the nature of the lepton-pairs produced in collisions were investigated. It was observed that the maximum lepton-pair production happened for the cases which the scattering angle is in the range of 45 < q < 90 in the plots obtained for rapidity. In the graphs obtained for lepton-pairs, it was observed that the differential cross-section of electron-positron pair was more than muon-antimuon pair. For the energy, momentum and invariant mass, the values of the electron are smaller. On the other hand, it is very difficult to examine the results of the heavy-ion collision experiments at LHC and RHIC without any limitation on parameters such as energy, momentum, invariant mass of the produce lepton-pairs. In the last part of this thesis, by applying the conditions used for the Pb+Pb heavy ions collision performed at LHC with 5:02TeV energy, the total cross-section value and the graphs for rapidity and invariant mass were obtained. Then, the calculated total cross-section value was compared with the experiment result.