[Paper Review] Neutrino Sources and Properties

Francesco Vissani|arXiv (Cornell University)|Dec 29, 2014

Astrophysics and Cosmic Phenomena8 references4 citations

TL;DR

This lecture provides a comprehensive overview of neutrino physics for PhD students, covering weak interactions, neutrino sources, oscillations, and the extension of the Standard Model to include neutrino masses via the Weinberg operator. It explains how neutrino masses arise from dimension-5 operators, leading to Majorana masses and lepton number violation, with key implications for neutrinoless double beta decay and the origin of neutrino mass.

ABSTRACT

In this lecture, prepared for PhD students, basic considerations on neutrino interactions, properties and sites of production are overviewed. The detailed content is as follows: Sect. 1, Weak interactions and neutrinos: Fermi coupling; definition of neutrinos; global numbers. Sect. 2, A list of neutrino sources: Explanatory note and examples (solar pp- and supernova-neutrinos). Sect. 3, Neutrinos oscillations: Basic formalism (Pontecorvo); matter effect (Mikheev, Smirnov, Wolfenstein); status of neutrino masses and mixings. Sect. 4, Modifying the standard model to include neutrinos masses: The fermions of the standard model; one additional operator in the standard model (Weinberg); implications. One summary table and several exercises offer the students occasions to check, consolidate and extend their understanding; the brief reference list includes historical and review papers and some entry points to active research in neutrino physics.

Motivation & Objective

• To provide a foundational understanding of neutrino interactions, properties, and sources for early-career researchers in particle physics.
• To explain the theoretical framework behind neutrino oscillations and the role of matter effects (MSW effect) in neutrino propagation.
• To explore how neutrino masses can be incorporated into the Standard Model through the Weinberg operator, leading to Majorana masses.
• To connect neutrino masses to lepton number violating processes such as neutrinoless double beta decay.
• To prepare researchers for advanced topics in neutrino physics by introducing key formalisms, symmetries, and open questions in the field.

Proposed method

• Uses the Fermi coupling constant $ G_F $ to describe low-energy weak interactions, linking it to the $ W $-boson exchange in the Standard Model via $ G_F / \sqrt{2} = g^2 / (8M_W^2) $.
• Defines neutrino flavors via charged-current weak interactions, using chiral projectors $ P_L $ to identify left-handed neutrinos and right-handed antineutrinos.
• Applies the Pontecorvo formalism to describe neutrino oscillations, including the MSW effect for neutrinos propagating through matter.
• Introduces the Weinberg operator $ \frac{1}{M} (H^T \sigma_2 \ell)(H^T \sigma_2 \ell) $ as a dimension-5 effective operator that generates Majorana masses.
• Derives the Majorana mass term $ \frac{1}{2} m_{\ell\ell'} \nu_\ell C^{-1} \nu_{\ell'} + \text{h.c.} $, showing its invariance under Standard Model gauge symmetries.
• Analyzes the implications of the Weinberg operator, including lepton number violation and the possibility of neutrinoless double beta decay.

Experimental results

Research questions

• RQ1 How do neutrino masses arise in the Standard Model, and what is the role of the Weinberg operator in generating them?
• RQ2 What are the observable consequences of neutrino masses, such as neutrino oscillations and lepton number violation?
• RQ3 How do matter effects (MSW effect) modify neutrino oscillation probabilities in dense media like the Sun or Earth?
• RQ4 What is the connection between neutrino oscillations and neutrinoless double beta decay in the context of Majorana neutrinos?
• RQ5 What are the implications of the Weinberg operator's non-renormalizability, and how can it be embedded in a more complete theory of new physics?

Key findings

• The Fermi coupling constant $ G_F $ is related to the $ W $-boson mass and coupling via $ G_F / \sqrt{2} = g^2 / (8M_W^2) $, with $ G_F^2 = 5.297 \times 10^{-44} \, \text{cm}^2/\text{MeV}^2 $.
• Neutrino flavor is defined by the charged-current interaction: $ \nu_\mu $ is produced in $ \pi^+ \to \mu^+ + \nu_\mu $, and $ \bar{\nu}_e $ in neutron beta decay.
• Neutrino oscillations are described by the Pontecorvo formalism, with mixing governed by the PMNS matrix, and matter effects accounted for by the MSW mechanism.
• The Weinberg operator $ \frac{1}{M} (H^T \sigma_2 \ell)(H^T \sigma_2 \ell) $ generates Majorana masses, with $ m \sim \langle H^0 \rangle^2 / M $, where $ M $ is a high-energy scale.
• The resulting Majorana mass term leads to lepton number violation, enabling the neutrinoless double beta decay process $ (A,Z) \to (A,Z+2) + 2e^- $, which is forbidden in the Standard Model.
• The operator is non-renormalizable (dimension 5), but consistent with low-energy phenomenology, and its origin must be explained by a UV-complete theory at a scale $ M \sim 10^{14} \, \text{GeV} $ to match observed neutrino masses.