Neutrino Mass and Grand Unification – Übersicht

Course synopsis

The Standard Model (SM) is a greatly successful high precision theory of all the known interactions but gravity: strong, electromagnetic and weak. We know today that it is incomplete since it predicts a vanishing neutrino mass, but the completion may well lie at astronomically large scales, not reachable in the near future.

At its core, however, lies a great puzzle, the miracle of charge quantization. This miracle finds its natural explanation in the context of grand unification that says that the particle forces unify in a single simple gauge group. This leads from the outset to the profound predictions of proton decay and magnetic monopoles, the subject of this course. Moreover, if offers an arena to study the neutrino mass.

We shall cover the basics of grand unification, both from the group theory and phenomenological points of view. Special emphasis will be put on the minimal SU(5) and SO(10) theories that serve as the prototypes and laboratories to study proton decay and magnetic monopoles. We shall then focus on the question of neutrino mass in these theories - this will require modifying the original SU(5) model. On the other hand, the SO(10) theory leads structurally to neutrino mass and the seesaw mechanism behind its smallness, to be covered in detail.

The prerequisite for the course is knowledge of the Standard Model. Some command of elementary group theory, SU(2) and SU(3), is needed too - the rest will be developed as we go along, with a special attention paid to spinorial representations of the SO(2N) groups.

Outline of the course

I. The SO(3) = SU(2) Schwinger-Glashow attempt at electroweak unification. The resulting charge quantization, with a phenomenological failure.

II. Dirac magnetic monopole and charge quantization. Charge quantization and ’t Hooft-Polyakov monopole.

III. The Standard Model: QCD and the SU(2) x U(1) cure of the Schwinger-Glashow failure. Charge quantization lost - how to regain it? Grand unification principle and proton decay. Unification of gauge couplings and the weak mixing angle. Supersymmetry and unification.

IV. The minimal SU(5) theory of Georgi and Glashow. Symmetry breaking. Predictions for fermion masses and proton decay branching ratios. The failure of neutrino mass and a failure of unification.

V. Saving SU(5) theory. The issue of neutrino mass in SU(5).

VI. Pati-Salam quark-lepton unification and left-right symmetry. Neutrino mass.

VII. SO(2N) groups. Spinorial representations.

VIII. SO(10) theory: unification of interactions and a family of fermions.

IX. SO(10): a theory of neutrino mass.

X. The common features of all GUT models: effective theory of baryon and lepton number violation.

XI. Going beyond SO(10): SO(2N, N>5) and family unification. Mirror fermions.

References

• Lie Algebras in Particle Physics - Howard Georgi
• Lecture notes, posted. Original papers, posted.
• Grand unified theories - Graham Ross
• Unification and supersymmetry. The frontiers of quark-lepton physics - Rabindra N. Mohapatra
• Quantum Field Theory and Topology - Albert Schwarz
• Classical Theory of Gauge Fields - Valery Rubakov
• Advanced Topics in Quantum Field Theory - Mikhail Shifman
• Quantum Field Theory - Mark Srednicki
• An Introduction to Quantum Field Theory - Michael E. Peskin, Daniel. V. Schroeder
• Quantum field theory in a nutshell - Anthony Zee
• The Quantum Theory of Fields - Steven Weinberg
• Path Integrals and Quantum Anomalies - Kazuo Fujikawa, Hiroshi Suzuki.