Master · elective · 2026/27
Beyond the Standard Model Neutrino Physics
One-semester graduate course · 24–32 hours · from the electroweak structure to mass-generation mechanisms and their observable consequences.
Prerequisites & method
How the course is taught
A working knowledge of the Standard Model, relativistic quantum mechanics and the basics of quantum field theory. The course keeps the oscillation formalism to the minimum needed for notation and phenomenology, and emphasizes the minimal theoretical tools that connect BSM mass-generation mechanisms to measurable neutrino observables.
Long algebraic derivations in the spinor and seesaw chapters are treated as lecture material plus guided self-study.
Reference texts
- Giunti & Kim, Fundamentals of Neutrino Physics and Astrophysics (Oxford, 2007) — comprehensive standard reference for the phenomenology.
- Mohapatra & Pal, Massive Neutrinos in Physics and Astrophysics, 3rd ed. (World Scientific, 2004) — the model-building backbone of the course.
- Huang, Quarks, Leptons and Gauge Fields (World Scientific, 1992) — gauge-theory background for the SM review.
- Foundational papers: Minkowski (1977); Gell-Mann–Ramond–Slansky and Yanagida (1979); Weinberg, Baryon- and Lepton-Nonconserving Processes (1979).
Programme
Fourteen modules, one per chapter of the notes: a core of nine (M1–M9, 26 hours) — a compact field-theoretic foundation, the construction of neutrino mass beyond the Standard Model, and the experimental and cosmological phenomenology — followed by an optional block on flavour model building (M10–M13, 5 hours) and a closing synthesis (M14, 1 hour).
Part I · Foundations · M1–M4 · 11 h
M1 · Motivation and neutrino puzzles · 2 h. Why neutrino masses imply physics beyond the Standard Model; experimental landmarks; the global conventions used throughout the notes.
M2 · Minimal SM review and EWSB · 3 h. The gauge structure $SU(2)_L \times U(1)_Y$ and the weak interactions; the Higgs mechanism; gauge-boson and fermion masses from Yukawa couplings, and the absence of a renormalizable neutrino mass term.
M3 · Spinors, chirality and neutrino mass terms · 3 h. Weyl, Dirac and Majorana fields; charge conjugation and chiral projectors; the general neutrino mass term, three generations and the PMNS matrix.
M4 · Dirac vs Majorana masses and effective operators · 3 h. Lepton number as an accidental symmetry; the Weinberg operator and its UV completions; neutrinoless double beta decay.
Part II · The seesaw mechanism · M5 · 4 h
M5 · Seesaw frameworks · 4 h. Type-I, Type-II and Type-III seesaws and their mass-scale estimates; inverse, linear and double seesaw; flavour structure. The core BSM construction of the course.
Featured construction: the Type-I seesaw formula
$$ m_\nu \simeq -\, m_D\, M_R^{-1}\, m_D^{T} $$derived three ways — by block diagonalization, from the equations of motion, and via the effective Lagrangian.
Part III · Phenomenology and cosmology · M6–M9 · 11 h
M6 · Experimental status · 3 h. Oscillation parameters, neutrinoless double beta decay, the beta-decay endpoint and cosmological bounds: the data-driven constraints on any model.
M7 · Minimal oscillation review · 2 h. Vacuum oscillations and matter effects in compact form — the framework needed for notation and phenomenology, not a full oscillation course.
M8 · EFT and BSM neutrino interactions · 3 h. SMEFT operators, non-standard interactions, sterile states: a model-independent view of new neutrino physics.
M9 · Leptogenesis and cosmology links · 3 h. The CP asymmetry, the Davidson–Ibarra bound, sphaleron conversion and the baryon-to-photon ratio $\eta_B$ — connecting mass generation to the matter–antimatter asymmetry of the Universe.
Part IV · Flavour model building (optional) · M10–M13 · 5 h
M10 · Non-Abelian flavour symmetries · 1.5 h. Discrete groups such as $A_4$ for model building in the lepton sector.
M11 · Modular symmetries · 1 h. Modular forms and weights; a conceptual overview plus one worked flavour model.
M12 · Radiative neutrino masses · 1.5 h. The Zee, Zee–Babu and scotogenic mechanisms.
M13 · Left–right symmetric models · 1 h. Gauge structure, the combined seesaw, and the implications for $0\nu\beta\beta$.
Part V · Synthesis · M14 · 1 h
M14 · Synthesis and open problems · 1 h. The final map of the course, project ideas and unresolved questions.
Appendix A. Conventions and a group-theory quick reference — reference material, not lectured.
Module Mn is chapter n of the notes. Pacing: 24 h covers M1–M8 plus a compressed synthesis; 27 h adds M9; 29.5 h adds M10–M11; the full 32 h covers every module, with the longest derivations of M3 and M5 as guided self-study.
Interactive course map
What must we add to the Standard Model to give neutrinos mass?
From the Weinberg operator to the seesaw
A central thread of the course.
A single dimension-five operator — the unique gauge-invariant way to give neutrinos mass with Standard Model fields alone —
$$ \mathcal{L}_5 = \frac{c_{\alpha\beta}}{\Lambda}\, \left(L_\alpha^{\mathsf{T}} \tilde{H}\right) \left(\tilde{H}^{\mathsf{T}} L_\beta\right) + \text{h.c.} $$encodes the smallness of neutrino masses as a window onto a high ultraviolet scale $\Lambda$. Its three tree-level UV completions are exactly the three seesaw mechanisms. The same operator controls neutrinoless double beta decay, tying the Majorana nature of neutrinos to a single, falsifiable experimental signature.
Interactive figure
Where did the heavy particle go?
Press Play, or drag the energy scale, and follow the three seesaw diagrams as the probe scale runs down from 1016 GeV. Above the heavy mass M the mediator is resolved; at M it shrinks to a point; below M all three leave behind the same dimension-five operator; and when the Higgs takes its vacuum value the operator becomes a Majorana mass. Move M to see which scale gives the observed neutrino masses.
Oscillation parameters from the Bari global analysis, with δm² = m₂² − m₁² and Δm² = m₃² − (m₁² + m₂²)/2: δm² and sin²θ₁₂ from Phys. Rev. D 114, 016026 (first JUNO results included), |Δm²| from Phys. Rev. D 111, 093006 (see Results). Direct and Majorana mass limits from KATRIN and KamLAND-Zen.
Interactive figure
Neutrino mass observables
The three absolute-mass observables — the beta-decay mass mβ, the effective Majorana mass mββ and the cosmological sum Σ — as functions of the lightest mass, the ordering and the two Majorana phases, set against the current bounds. Move the phases to see how mββ can cancel in normal ordering but not in inverted ordering.
Class material and communications
The GGI lecture notes cover a substantial part of the BSM material in a self-contained form and can be used as the main written reference alongside the textbooks above.
Contact me by email for any clarification or to arrange a meeting: antonio.marrone@ba.infn.it · antonio.marrone@uniba.it.