Experimental Status - GDR Neutrino

Working Group 4 : Accelerators, Research and Development, detection techniques

The recent measurements on neutrino oscillation probability open new research field for fundamental research and request new facilities and sophisticated detectors to probe new physics. This working group (WG4) focus on new and innovative detection techniques in neutrino physics and will try to make the state of art in these field.

Experimental status in three active neutrino oscillation framework
Most the parameters of the PMNS matrix are measured

$\underbrace{ \left( \begin{array}{c} \textcolor{red}{\nu_e}\\ \textcolor{green}{\nu_\mu}\\ \textcolor{blue}{\nu_\tau} \end{array} \right)}_{Flavor Eigenstates} = \textcolor{blue}{ \underbrace{ \left( \begin{array}{ccc} c_{12} & s_{12} & 0\\ -s_{12} & c_{12} & 0\\ 0 & 0 & 1 \end{array} \right) }_{Solar, Reactors}} \textcolor{green}{ \underbrace{ \left( \begin{array}{ccc} 1 & 0 & 0\\ 0 & c_{12} & s_{12} \\ 0 & -s_{12} & c_{12} \\ \end{array} \right) }_{Atmospheric, Accelerator}} \textcolor{red}{ \underbrace{ \left( \begin{array}{ccc} c_{13} & 0 &s_{13}.e^{i\delta}\\ 0 & 1 & 0\\ -s_{13}.e^{-i\delta} & 0 & 1 \end{array} \right)}_{CP Violation}} \underbrace{ \left( \begin{array}{ccc} 1 & 0 & 0\\ 0 & e^{\alpha/2} & 0\\ 0 & 0 & e^{\alpha/2+\beta/2} \end{array} \right)}_{Majorana Terms} \underbrace{ \left( \begin{array}{c} \nu_1\\ \nu_2\\ \nu_3 \end{array} \right)}_{Mass Eigenstates}$

with $c_{ij} = cos (\theta_{ij})$ and $s_{ij} = sin (\theta_{ij})$

The neutrino oscillation probability from flavor $\alpha$ to $\beta$ is given by:

$P_{\alpha - \beta} = \delta_{\alpha \beta} - 4 \sum_{i>j}^{3} Re[ U^{*}_{\alpha i}.U_{\beta i}.U_{\alpha j}.U^{*}_{\beta j}].sin\left(\frac{\Delta m^2_{ij}}{4}.\frac{L}{E}\right) + 2 \sum_{i>j}^{3} Im[ U^{*}_{\alpha i}.U_{\beta i}.U_{\alpha j}.U^{*}_{\beta j}].sin\left(\frac{\Delta m^2_{ij}}{2}.\frac{L}{E}\right)$

Neutrino Parameter Status

$\begin{array}{|c|c|} \hline Parameter & Value \\ \hline \hline sin^2 \theta_{12} & 0.312^{+0.052}_{-0.047} \\ \hline sin^2 \theta_{23} & 0.42^{+0.22}_{-0.08} \\ \hline sin^2 \theta_{13} & 0.0251^{+0.0109}_{-0.0101} \\ \hline \Delta m^2_{12} & (7.58)^{+0.60}_{-0.59} \time 10^{-5} eV^2 \\ \hline | \Delta m^2_{32} | & (2.35)^{+0.32}_{-0.29} \time 10^{-3} eV^2 \\ \hline \text{Sign of } \Delta m^2_{32} & unknown \\ \hline \delta_{CP} & unknown \\ \hline \end{array}$

Next challenges in neutrino physics

Dirac/Majorana neutrino
Absolute mass Scale
Three active neutrino ?
$\delta_{CP}$ discovery in leptonic sector
Mass hierarchy determination…