Summary of the doctor thesis: Studying of the phase transition in linear sigma model

The aims of thesis: studying of the phase structure of LSM and LSMq with two different forms of symmetry breaking term: the standard case and non – standard case; studying of the effect from neutrality condition on the phase structure of LSM and LSMq; studying of the chiral phase transition in compactified space
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Summary of the doctor thesis: Studying of the phase transition in linear sigma modelMINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE NGUYEN VAN THU STUDYING OF THE PHASE TRANSITION IN LINEAR SIGMA MODEL A SUMMARY OF THE DOCTOR THESIS Speciality: Theoritical and mathematical physics Code : 62.44.01.01 Scientific supervisors PROF. DR. TRAN HUU PHAT DR. NGUYEN TUAN ANH HANOI, 2011THIS THESIS WAS COMPLETED AT INSTITUTE FOR NUCLEAR SCIENCE AND TECHNIQUE – VIETNAM ATOMIC ENERGY INSTITUTE Scientific supervisor: PROF. DR. TRAN HUU PHAT DR. NGUYEN TUAN ANH First referee: Prof. Dr. Nguyen Xuan Han Second referee: Prof. Dr. Nguyen Vien Tho Third referee: Prof. Dr. Dang Van Soa This thesis will be defended in the Scientific Counsil of Vietnam Atomic Energy Institute held on May 28, 2012 THIS THESIS MAY BE FOUND AT THE VIETNAM NATIONAL LIBRARY AND ATOMIC ENERGY LIBRARY INTRODUCTION1. The research topic The phase structure of QCD plays an impotant role in morden physics,attracting intense experimental and theoretical investigations. Some theories and models are used in order to study the phase structureof QCD, for example, chiral pertubative theory, Nambu-Jona-Lasinio (NJL)model, Poliakov-NJL (PNJL) model, linear sigma model (LSM). Up to now the study of linear sigma model is still not complete. It is thereasons why we choose subject “Studying of the phase transition in linearsigma model”.2. History of problem Studying of D. K. Campell, R. F. Dashen, J. T. Manassah is the firstpaper, in which they studied LSM with two different forms of the symmetrybreaking term (standard case and non-standard case) but they are restricted onlywithin tree-level approximation. In higher order approximation, present papers are researched in Hatree-Fock (HF) approximation, expanded N – large or isospin chemical potential(ICP) is neglected. The study of the non-standard case is so far still absent. When constituent quarks are presented, in the framework of NJL andPNJL models the researchs are quite complete. Meanwhile the linear sigmamodel with constituent quarks (LSMq) the present researchs only consider thecase in which ICP is vanished. The studies of chiral phase transition in compactified space – time are infirst stage so far.3. The aims of thesis- Studying of the phase structure of LSM and LSMq with two different forms ofsymmetry breaking term: the standard case and non – standard case. 1- Studying of the effect from neutrality condition on the phase structure ofLSM and LSMq.- Studying of the chiral phase transition in compactified space – time.4. The subject, research problems and scope of thesis- Studying of the phase structure of LSM at finite value of temperature T andisospin chemical potential with and without neutrality condition and twodifferent forms of symmetry breaking term.- Studying of phase structure of LSMq at finite value of temperature, ICP andquark chemical potential (QCP) with and without neutrality condition and twodifferent forms of symmetry breaking term.- Studying of the chiral phase transition in compactified space – time when ICP is zero.5. The method In this thesis we combine the mean – field theory and effective actionCornwall – Jackiw – Tomboulis (CJT) in order to research the phase structureof LSM and LSMq.6. The contribution of thesis This thesis has many contributions in morden physics.7. The structure of thesis The thesis includes 133 pages, 106 figures and 61 references. Besidesintroduction, conclusion, appendices and references, this consists of 3 chapters:Chapter 1. Phase structure of linear sigma model without constituent quarks.Chương 2. Phase structure of linear sigma model with constituent quarks.Chapter 3. Chiral phase transition in compactified space – time. 2CHAPTER 1. PHASE STRUCTURE OF LINEAR SIGMA MODEL WITHOUT CONSTITUENT QUARKS1.1. The linear sigma model- Lagrangian- The standard form- The non – standard form1.2. Phase structure in standard case1.2.1. Chiral phase transition in case isospin chemical potential isvanishing1.2.1.1. Chiral limit In tree – level approximation pions are Goldstone bosons.In two – loop expanded and HF approximation, there Goldstone bosons arenot preserved. In order to preserve Goldstone bosons we introduced improvedHatree – Fock (IHF) approximation. In this approximation we obtain- The gap equatiion- Numerical computation with parameters MeV,MeV, MeV. 3 20 1.0 15 0.8 10 VMeV 3 .fm 0.6u f 5 0.4 0 0.2 ...