Part VII: Neutrino Physics
Introduction
Neutrinos are the most abundant massive particles in the universe, yet the least understood. Originally thought to be massless in the Standard Model, the discovery of neutrino oscillations proved they have tiny non-zero masses.
Nobel Prize 2015: Kajita and McDonald for discovering neutrino oscillations
Neutrino Oscillations
PMNS Matrix
Flavor eigenstates $(\nu_e, \nu_\mu, \nu_\tau)$ are superpositions of mass eigenstates $(\nu_1, \nu_2, \nu_3)$:
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix
Contains 3 mixing angles $(\theta_{12}, \theta_{23}, \theta_{13})$ and CP-violating phase $\delta_{CP}$
Oscillation Probability
For two-flavor approximation:
where $\Delta m^2 = m_2^2 - m_1^2$, $L$ = baseline, $E$ = neutrino energy
Experimental Results
Mass Splittings
Solar Neutrinos (KamLAND, SNO):
$\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$
$\sin^2\theta_{12} = 0.307 \pm 0.013$
Atmospheric Neutrinos (Super-K, MINOS, NOvA):
$|\Delta m^2_{32}| = (2.51 \pm 0.05) \times 10^{-3}$ eV$^2$
$\sin^2\theta_{23} = 0.546 \pm 0.021$ (near maximal mixing)
$\sin^2\theta_{13} = 0.0220 \pm 0.0007$ (reactor experiments)
Key Experiments
Super-Kamiokande:
50 kton water Cherenkov detector
Atmospheric neutrino oscillations (1998)
SNO (Sudbury):
Heavy water detector
Solar neutrino problem resolution
Daya Bay / RENO:
Reactor neutrinos
Measured $\theta_{13}$ (2012)
T2K / NOvA:
Long-baseline accelerator
Measuring $\delta_{CP}$
Open Questions
Unsolved Mysteries
1. Mass Hierarchy:
Normal ($m_1 < m_2 < m_3$) or Inverted ($m_3 < m_1 < m_2$)?
JUNO, DUNE, Hyper-K will resolve this
2. Absolute Mass Scale:
Oscillations only measure $\Delta m^2$, not absolute masses
Cosmology: $\sum m_\nu < 0.12$ eV (Planck)
KATRIN: $m_{\nu_e} < 0.8$ eV (direct measurement)
3. Dirac or Majorana?
Are neutrinos their own antiparticles (Majorana)?
Neutrinoless double-beta decay: $(A,Z) \to (A,Z+2) + 2e^-$
Current limit: $T_{1/2} > 10^{26}$ years (no signal yet)
4. CP Violation in Leptons:
Is $\delta_{CP} \neq 0$?
Current hint: $\delta_{CP} \approx -90°$ (T2K, NOvA)
Could explain matter-antimatter asymmetry (leptogenesis)
Key Takeaways
- •Neutrino oscillations prove non-zero neutrino masses (beyond SM)
- •Three mass splittings: $\Delta m^2_{21} \sim 10^{-5}$ eV$^2$, $\Delta m^2_{32} \sim 10^{-3}$ eV$^2$
- •PMNS mixing: $\theta_{12} \approx 34°$, $\theta_{23} \approx 47°$, $\theta_{13} \approx 8.5°$
- •Open questions: mass hierarchy, absolute scale, Dirac vs Majorana, CP violation
- •Future experiments: DUNE, Hyper-K, JUNO (hierarchy), KATRIN (mass), KamLAND-Zen (0νββ)