# STANDARD MODEL THEORY

**Academic Year 2022/2023**- Teacher:

**SALVATORE PLUMARI**

## Expected Learning Outcomes

The course aims to introduce the Standard Model both in its theoretical and phenomenological aspects. Students should become familiar with the path-integral formulation of relativistic quantum field theory with emphasis on generating functionals of Green's functions, connected Green's functions and irreducible Green's functions. In particular, the quantization of Abelian and non-Abelian gauge theories will be discussed as a starting point for Quantum Chromodynamics (QCD) and Electroweak theory (EW). During the course the student will become familiar with the concept of spontaneous symmetry breaking and with the Higgs mechanism. Some exercises are planned for the calculation of generator functionals and the related Green’s functions and the calculation of cross sections of some elementary processes.

**Knowledge and understanding**. The aim is for students to develop a critical understanding of the topics covered during the course and to develop an adequate knowledge of the methods applied in theoretical physics. The student will understand the main approaches for dealing with problems of gauge theories.

**Applying knowledge and understanding.** Ability to apply the knowledge acquired for the description of physical phenomena using rigorously the scientific method. Ability to apply the acquired knowledge to solve simple process problems in the framework of Electroweak or Strong Interaction.

**Making judgments**. The aim of the course is that the student develops critical reasoning skills. Ability to identify the most appropriate methods to critically analyse and interpret the results obtained.

**Communication skills**. Ability to discuss about advanced physical concepts, both in Italian and in English.

**Learning skills**. Ability to acquire adequate tools for the continuous updating of knowledge in the field of modern particle physics.

## Course Structure

The course consists of 5 CFU (35 hours) of frontal lectures and 1 CFU (15 hours) for the exercises in the class. There will be however also some exercise during the class held as practical tests to verify the understanding of some main part of the course like to calculate the generating functional and the related correlation functions or cross sections of some processes. Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

## Required Prerequisites

The skills acquired in Relativistic Quantum Mechanics and Quantum Field Theory 1 and 2 are considered indispensable.## Attendance of Lessons

Attendance to the course is usually mandatory (consult the Academic Regulations of the Course of Studies). The study through the textbooks of gauge theories can be dispersive and the study through the teacher's notes is not enough. Participation in lessons allows you to focus on essential elements of the course.## Detailed Course Content

Path Integral for scalar quantum Fields. Generating Functional and Green’s Function. Generating functional for interacting fields. Connected Green’s function. One particle Irreducible Green’s function, Effective Action and Effective Potential. Path integrals for Fermion fields and generating functional for Fermion fields.

Local symmetries, gauge principle in QED. Yang Mills theories and gauge principle for nonabelian groups. Quantization of abelian and non-Abelian gauge fields, gauge fixing and Faddeev-Popov ghost. Vertices and propagators in different gauges.

Spontaneous symmetry breaking of global symmetry, Goldstone’s theorem.

QCD lagrangian and its symmetries. Chiral symmetry breaking and hadron masses. NJL model. Asymptotic freedom and UV regime. QCD infrared regime: confinement and hadronization. Polyakov loop. Finite temperature and density.

Higgs mechanism in abelian and nonabelian theories. Massive gauge bosons and longitudinal polarization.

Weak decays and parity violation. V-A interactions. Non-renormalizable 4-fermion interactions.

Charged and neutral Current-Current lagrangian. Weak isospin. Weak hypercharge and construction of the SU(2)_{L}U(1)_{Y} model. Electroweak theory. Quark masses, Cabibbo angle. Absence of Flavor Changing Neutral Currents and GIM mechanism. Kobayashi-Maskawa mixing matrix.

Decay of W and Z^{0} bosons, cross sections e^{+}e^{-} -> µ^{+}µ^{-}

Neutrino Dirac masses and mixing matrix. Neutrino oscillation.

## Textbook Information

1) S. Weinberg, The quantum theory of fields Vol.I and Vol.II

2) L.H. Ryder, Quantum field theory

3) I.J.R. Aitchison e A.J.G. Hey, Gauge Theories in Particle Physics: A Practical Introduction, Volume 2

4) S. Pokorski, Gauge field theories

5) Peskin-Schroeder, An introduction to quantum field theory

## Course Planning

Subjects | Text References | |

1 | Path Integral for scalar quantum Fields. Generating Functional and Green’s Function. Generating functional for interacting fields. Connected Green’s function. One particle Irreducible Green’s function, Effective Action and Effective Potential. | 1,2,5 |

2 | Path integrals for Fermion fields and generating functional for Fermion fields. | 1,2,5 |

3 | Local symmetries, gauge principle in QED. Yang Mills theories and gauge principle for nonabelian groups. Quantization of abelian and non-Abelian gauge fields, gauge fixing and Faddeev-Popov ghost. Vertices and propagators in different gauges. | 1,2,4 |

4 | Spontaneous symmetry breaking of global symmetry, Goldstone’s theorem. | 1,2,4 |

5 | QCD lagrangian and its symmetries. Chiral symmetry breaking and hadron masses. NJL model. Asymptotic freedom and UV regime. QCD infrared regime: confinement and hadronization. Polyakov loop. Finite temperature and density. | 1,2,3,4 |

6 | Higgs mechanism in abelian and nonabelian theories. Massive gauge bosons and longitudinal polarization. | 1,2,3,4 |

7 | Weak decays and parity violation. V-A interactions. Non-renormalizable 4-fermion interactions. Charged and neutral Current-Current lagrangian. Weak isospin. Weak hypercharge and construction of the SU(2)LU(1)Y model. Electroweak theory. Quark masses, Cabibbo angle. Absence of Flavor Changing Neutral Currents and GIM mechanism. Kobayashi-Maskawa mixing matrix. | 1,2,3 |

8 | Decay of W and Z0 bosons, cross sections e+e- -> µ+µ- | 3 |

9 | Neutrino Dirac masses and mixing matrix. Neutrino oscillation. | 3 |