Master · elective · 2025/26
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
Three core parts — 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 and a closing synthesis.
Part I · Foundations
Ch. 1 · Context and open questions. Why neutrino masses imply physics beyond the Standard Model; historical milestones; why oscillations measure only mass-squared differences; the map of open questions and their associated observables.
Ch. 2 · SM review and EWSB. The gauge principle; the electroweak structure $SU(2)_L \times U(1)_Y$; the Higgs mechanism; fermion masses via Yukawa couplings; the weak currents relevant for neutrino physics.
Ch. 3 · Spinors, chirality and mass terms. Chiral decomposition of the Dirac Lagrangian; helicity versus chirality; charge conjugation and the Majorana field; the general neutrino mass term, its diagonalization, and the PMNS matrix with a rigorous parameter count.
Ch. 4 · Dirac vs Majorana and global symmetries. Structural comparison of Dirac and Majorana neutrinos; lepton number and global symmetries; the Weinberg operator and $B-L$ violation; UV completions; neutrinoless double beta decay as the key probe.
Part II · The seesaw mechanism
Ch. 5 · Seesaw frameworks. The central puzzle of light neutrino masses; Type-I (heavy right-handed neutrinos), Type-II (scalar triplet) and Type-III (fermionic triplet) seesaws, each derived in full; low-scale variants — inverse, linear and double seesaw; the Dirac and pseudo-Dirac limits; experimental tests at colliders, in $0\nu\beta\beta$ and via lepton flavour violation.
Featured construction: the Type-I seesaw formula
$$ m_\nu \simeq -\, m_D^{T}\, M_R^{-1}\, m_D $$derived three ways — by block diagonalization, from the equations of motion, and via the effective Lagrangian — and connected to leptogenesis.
Part III · Phenomenology and cosmology
Ch. 6 · Experimental status. The neutrino parameter space and mass ordering; solar neutrinos and the MSW effect; direct kinematic mass measurements (KATRIN); neutrinoless double beta decay; cosmological bounds on the sum of masses.
Ch. 7 · Minimal oscillation review. The mixing matrix; oscillations in vacuum; oscillations in matter and the MSW resonance — the compact framework needed for the phenomenological context.
Ch. 8 · EFT and selected BSM extensions. The Standard Model Effective Field Theory (SMEFT); non-standard interactions (NSI); sterile-neutrino extensions — a model-independent view of new neutrino physics.
Ch. 9 · Leptogenesis and cosmology links. Neutrinos in cosmology; the baryon asymmetry problem; thermal leptogenesis — connecting the scale of neutrino mass generation to the matter–antimatter asymmetry of the Universe.
Part IV · Flavour model building (optional)
Ch. 10 · Non-abelian flavour symmetries. The flavour puzzle; discrete groups for the lepton sector; the residual-symmetry approach to mixing.
Ch. 11 · Modular symmetries. Beyond traditional flavour symmetries; modular forms as Yukawa couplings; a worked modular-invariant model.
Ch. 12 · Radiative neutrino masses. Why generate mass at loop level; the scotogenic model of Ma, linking neutrino mass to dark matter.
Ch. 13 · Left–right symmetric models. Parity as a broken symmetry; field content and quantum numbers; the combined Type-I + Type-II seesaw; gauge phenomenology and the link to $0\nu\beta\beta$.
Part V · Synthesis and technical toolkit
Ch. 14 · Summary and open problems. From the Standard Model to massive neutrinos; current status of the key measurements; open theoretical questions; experimental paths forward.
Appendix A. A group-theory quick reference for the flavour-model chapters.
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.
Values quoted in the course notes from a three-flavour global analysis; each is reproduced in the lectures from the underlying theory.
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.