Yüksek rölativistik hızlarda ağır iyon çarpışmaları sonucu müon çifti üretimi
Muon pair production from ultra relativistic heavy ion collisions
Yazar: NİHAL GÖZLÜKLÜOĞLU KARAKUŞ
Danışman: PROF. DR. MEHMET CEM GÜÇLÜ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Ana Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering
Dizin: Diferensiyel tesir kesiti = Differential cross section ; Parçacık hızlandırıcılar = Particle accelerators

Özet:
Parçacık fiziği en temel düzeyde maddenin neden yapıldığını incelemektedir. Atomaltı ölçekte madde çok küçük kitleler ile bu küçük kitleler arasındaki geniş boşlukların birleşiminden oluşur. Temel parçacıkların kütle,spin,elektrik yükü gibi özelliklerine bağlı olarak pek çok çeşitleri bulunmaktadır.Parçacık fiziğinin yanıtlamaya çalıştığı diğer önemli soru ise bu temel parçacıkların birbirleri ile nasıl etkileştiğidir. Bilim insanları bu farklı özelliklerdeki temel parçacıkları ve aralarındaki etkileşimleri inceleyebilmek amacıyla dünyanın pek çok yerinde hızlandırıcılar kurmuşlardır. Günümüzde bu hızlandırıcılardan en çok yararlanılanlarından biri Brookhaven National Laboratory'de bulunan Relativistic Heavy Ion Collider (RHIC), diğeri ise İsviçre'de bulunan Large Hadron Collider (LHC) hızlandırıcılarıdır. Hızlandırıcılarda ivme kazanan temel parçacıklar rölativistik hızlara ulaşmaktadır. RHIC'te tamamen iyonize edilmiş ağır iyonlar kütle merkezi referans çerçevesinde 100 GeV enerji ile LHC'de ise iyonize edilmiş iyonlar kütle merkezi referans çerçevesinde nükleon başına 3400 GeV enerji ile çarpıştırılmaktadır. Bu yeni kuşak hızlandırıcılarda nükleer maddeyi yüksek sıcaklık ve yüksek yoğunluklarda incelemek mümkün olmuştur.
Bu çalışmadaki amaç, ultra rölativistik ağır iyonların çevresel (peripheral) çarpışmaları sonucu  oluşan ağır lepton çiftlerinden müon - antimüonun   tesir kesidini hesaplanmak ve diğer lepton çiftleri olan elektron-pozitron  ve tau-antitau  ile farklarını incelemektir. Ağır iyonlar ultra rölativistik hızlarda çevresel (peripheral) çarpışmalar yaptıklarında Lorentz boyca kısalmasına uğrarlar ve uçlarında çok şiddetli elektromanyetik alanlar oluşur. Bu alanlardan çok sayıda lepton çiftinin elektromanyetik olarak üretimi gerçekleşir. Bu olaylar bütünü Kuantum Elektrodinamiği (QED) kapsamında ele alınmaktadır. Daha önce yapılan çalışmalarda, serbest ve bağlı elektron-pozitron çiftlerinin tesir kesitleri düşük mertebe kuantum elektrodinamik yani ikinci derece Feynman diyagramları kullanılarak hesaplanmıştır. Oluşan elektron-pozitron çiftlerinin Compton dalgaboyu çekirdek boyutlarından çok büyük olduğu için  "çekirdek form faktör" etkisi ihmal edilebilmiştir. Ancak bu çalışmada, ağır leptonların Compton dalga boyları, çekirdeğin boyutundan küçük olduğu için "çekirdek form faktörleri" hesaplamalara dahil edilmiştir. Bir elektronun Compton dalga boyu yaklaşık  = 386 fm mertebesindedir. Fakat müonun dalgaboyu 1.86 fm ve taunun dalgaboyu 0.11fm civarındadır. Ağır iyonların çaplarının yaklaşık 15 fm civarında olduğu göz önüne alınırsa, oluşan ağır leptonların iyon çekirdeği ile etkileşeceği ve çekirdeğin içinde zaman geçireceği öngörülebilir. Bu çalışmada özellikle müon- antimüon çiftlerinin oluşumu ile ilgili daha kapsamlı bir bilgiye sahip olmak amaçlanmıştır.

Abstract:
The traditional goal of particle phyiscs, in response to Newton's challenge , has been to identify what appear to be structurless units of matter and to understand the nature of the forces acting between them. Stated thus, the enterprise has a two -fold aspect, matter on the hand, forces on the other .The expectation is that the smallest units of matter should interact in the simplest way or , that there is a deep connection between the basic units of matter and the basic forces.  To develop this relation Quantum fields are described . fields  which produce  lepton pairs. [1]
High energy nuclear physics studies the behaviour of nuclear matter in energy regimes typical of high energy physics. The primary focus of this field is the study of heavy-ion collisions, as compared to lower atomic mass atoms in other particle accelerators. At sufficent collision energies,  these types of collisions are theorized to produce the quark-gluon plasma. In peripheral nuclear collisions at high energies one expects to obtain information on the electromagnetic production of leptons and mesons which are not accessible in electron-positron colliders due to their much smaller luminosities.
The first heavy ion collisions at modestly relativistic conditions were undertaken at the Lawrance Berkeley National Laboratory , at Berkeley,USA, and at the Joint Institute for Nuclear Research, in Dubna,USSR. At the LBL, a transport line was built to carry heavy ions from the heavy ion accelarator HILAC to the Bevatron. The energy scale at the level of 1-2 GeV per nucleon attained initially yields compressed nuclear matter at few times normal nuclear density. The demonstration of the possibility of studying the properties of compressed and excited nuclear matter motivated research programs at much higher energies in accelerators avaiable at BNL and CERN with relativistic beams targeting fixed target. The first collider experiments started in 1999 at RHIC and LHC begun colliding heavy ions at one order of magnitude higher energy in 2010.
Currently, high-energy phyiscs experiments are being conducted at Brookhaven National Labratory 's Relativistic Heavy Ion Collider (rhıc) and in CERN's new Large Hadron Collider. The four primary experiments at RHIC study collisions of highly relativistic nuclei. Unlike fixed target experiments, collider experiments steer two accelerated beams od ions toward each other at (in the case of RHIC) sizx interaction regions. At RHIC, ions can be accelerated from 100 GeV/nucleon to 250 GeV/nucleon. Since each colliding ion possesses this energy moving in opposite directions, the maximum energy of the collisions can achive a center of mass collision energy of 200 GeV/nucleon for gold and 500GeV/nucleon for protons. The high-energy nuclear physics experiments at CERN use the ALICE (A Large Ion Collider Experiment) detector, which is designed to create Pb-Pb nuclei collisions at a centre of mass energy of 2.76 TeV per nucleon pair.QED fiels is one of the oldest and well understood field theory. In this study we examine for strong electromagnetic fields which produce lepton pairs. The subject in this study is original in a way that QED will be tested for the strong electromagnetic fields. QED works very well for weak electromagnetic fields; however it is not clearly understood for strong electromagnetic fields. Heavy ions can be accelerated up to the 3.5 TeV per nucleon energies, and the electromagnetic fields of the heavy ions reach extremely high values and from this field various particles are produced. Therefore , calculated cross section values will be compared with experimental results and strong QED will be tested . The main goal is to understand the process of lepton pair production and to investigate what happened to matter shortly after the big-bang.[15] Another aim is this study to understan Form Factors effect at high energy collisions. A form factor is introduced in scattering problems to account for the spatial extent of the scatterer. The probability amplitude for a point-like scatterer is modified by a form factor, which takes into account the spatial extent and shape of the target. The scattering probability is expressed as a product of the probability for a point-like target multiplied by the square of the form factor. For example , in electron scattering at low energies, the cross section for a scattering from a point-like target is given by Rutherford scattering formula. If the target has a finite spatial extent, the cross section can be divided into, two factors, the Rutherford cross section and the form factor squared. In Coulomb scattering, the particular property of the spatial extent sampled is the charge distrubution  for the object. Form factors are more general than just in nuclear physics , where measurements give information about charge distirubutions of nuclei. Th form factors measured for electron scattering from nucleus gave some gave some of the first evidence that they were composed of sub-structure.Form factors or structure factors, also arise in the scattering of X-rays from materials and allow the structure of the material to be deduced. At the mathematical form, form factors are really Fourier transforms. [9]
In this study various form factors are examined. They are taken different values for different charge distributions. Three types of them are common in literature and they are examined in this study. When form factors are applied , energy and momentum values are changed for lepton pairs. Muon-antımuon pairs is main subject in this study . Form factors are applied muon-antimuon pair and also tau -antitau , electron-positron pairs. And also form factor effects are compared for each lepton pair.
When nucleus has Gaussian type of charge distrubution, form factor takes the name of Gaussian Form Factor. Gaussian distrubution is an exponantial function because of that gaussian form factor has much more effect on lepton pairs than other types of form factors. 
The electrostatic potential energry , for an electron in a spherically symmetric charge distrubution is a well known expression. Outside the nucleus , this expression reduces to the same potential as a point nucleus. For a homogeneus distrubution within a nuclear radius  , the electrostatic potential can be calculated. There is a discontinuity in the charge distrubution at the nuclear boundary leading to a discontinuity in the second derivative of the potential at   . This charge distrubution defines the Uniform Form Factor.
The two parameter Fermi model gives a realistic description of the nuclear distrubution and at the same time provides considerable flexibility in the analysis. For vanising skin thickness in the formula, Fermi form reduces to the homogeneous distrubution. The shape of the Fermi distrubution is identical to that of the Wood-Saxon potential. The analogy between the nuclear distrubution and potential is related to the short-range character of the strong interaction, which hold the nucleus together. Fermi distrubution makes it possible to obtain good approximation for realistic behavior. [10]
If we consider the atomic nucleus radius and Compton wavelength of the electron, ıt can be seen that electron waveleght is much more  bigger than the atomic radius .So they don't interact with each other. On the other hand tau and muon has smaller wavelength than the atomic radius and it's expected that interaction will occur. Applying form factors to the muon-antımuon and tau-antitau pairs , ıt's possible obtain more realistic results.