Tau pairs production from new generation ultra-relativistic particle accelerators

From recent years until now, physicsts have done a lot of explorations and experiment for understanding basic structure of matter. For this reason, many scientists have done a lot of experiments and studies to understand building stone of patricles. In recent years, the most important studies done surely in Large Hadron Collider and Relativistic Heavy-Ion Collider which are known new generation particle accelerators. Aim of this study, to make collide nuclear matter in high temperature and speed and having important details of matter by observing creation of new basic particles. To make this, it is required to collide completely ionize heavy ions. Completely ionize heavy ions are collided per nucleon in Large Hadron Collider and per nucleon in Relativistic Heavy-Ion Collider by center of mass frame. Experimentally, lead ions were collided in Large Hadron Collider and also gold ions were collided in Relativistic Heavy Ion Collider. So, in this thesis, we have done calculations aim of the compare with the experiment. Colliding heavy ions which are accelerated in high energy colliders, generate large electromagnetic fields around them. When this acceleration reach ultra-relativistic speed, heavy ions are exposed to Loretz effect and for this reason, strength of electromagnetic field become larger in sharp points of ions. During the peripheral collision, by reason of interacting electromagnetic fields around ions in other words interaction of virtual photons, it is possible to creation of new particle pairs for instance electron-positron, muon-anti muon, tau-anti tau pairs. It is important to analyze creation and annihilation lepton pairs for understanding hadrons because leptons give more information about their region of spacetime. Possibility of creating particles is couch in cross section. Large value of cross section mean high possibility of creating particles. In this study, lepton cross section from large electromagnatic fields as a result of collision totally ionized heavy gold and lead ions, will be calculated with the help of quantum electrodynamics, Feynman diagrams and form factors. Because of consisting ten multidimension integrals, analytical solution of this cross section is very difficult. For this reason, FORTRAN codes and also method of Monte Carlo will be used to find cross section. The change cross section datas of tau pairs compared to form factors, will be shown in graphes. Begining 19.yy, after understanding heavy ions have momentum and charge distribution, researches shifted particles in ions. There is important difference between colliding point particles and nucleus, because each nucleon in nucleus has own relativistic speed and momentum. So, form factor give information of nucleons structure and charge distribution of nucleus. Fourier transformation of this charge distribution of nucleus gives atomic form factor. There ara a lot of form factors, but in this study we will mention three of them. First one is Gaussian form factor, which is found by Fourier transforming of Gussian charge distribution. Second one is Uniform form factor, which is found by Fourier transforming of uniform charge distribution. And the last one is Wood-Saxon (fermi) form factor, which is found by Fourier transforming of fermi charge distribution. In this thesis, all calculations were done in momentum space, so having Fourier transformed each charge distributions from position space to momentum space, were found form factors. Tau pairs cross section change depend on this form factors. So, this changing presented in graphes and tables for no form factor, uniform distribution, gaussian distribution and wood-saxon distribution. Exchanging differential cross section by generated tau pairs's energy, longitudinal and transverse momentum is graphed in section 7. Longitudinal momentum is defined, momentum component of direction collision of lepton pairs by produced from heavy ion collisions. Transverse momentum is also defined, orthogonal momentum component of lepton pairs by produced from heavy ion collisions. Also rapidity graphes for tau-anti tau, muon-anti muon and electron-positron pairs are drawn a comparison. These graphes showed that, mass of generated particles and form factors are very important to define changing. Add to this, these graphes are also showed that, energy of colliding heavy ionized nucleus is important. This work will touch on from gauge theories to quantum electrodynamic, so more information about mechanism of matter's basic structure come to light. Respectively, first we will touch on Dirac spinors and Feynman interpretation on these spinors. Then gauge theory will be announced shortly, and this theory will be applied on the Dirac Lagrangian. After this, interaction Lagrangian and also interaction Hamiltonian of pair product process will be found. To calculate this interaction Hamiltonian, we will use perturbasyon approach method. As a result of calculations, result of first term of integral will be zero, so second term of integral will be use other calculations. It is difficult to solve this integral so ten dimensional integral will be calculated for tau-anti-tau pairs with the help of fortran codes. Results are written into schemas, and also these results compared with other particle pairs, such as muon-anti muon and electron-positron pairs. The purpose of doing it, to see influence of cross section depending on the change of mass. Will proceed as before, these datas are graphed depending products' energy, longitudinal momentum and transverse momentum to differential cross section of lepton pairs. Each graphes were drawn separately for LHC and RHIC energies and they were compared each other. All the results obtained, one at a time announced in section results and discussions. This thesis shows that, if the production of particles are the order of the size of the core, we have to take into account form factors for the calculation of cross section. Especially, gaussian form factor have the most impact on cross section and form factors effect tau pairs cross section most. Near future if such an experiment is done, importance of the data obtained as a result of the graphs are plotted in section 7 will be seen.