Measurement of neutrino CP violating angle (2)
Figure 1 : The reconstructed energy spectra of muon neutrinos and muon anti-neutrinos obtained at Super-Kamiokande. The back dots represent the obtained data and the red histogram shows the best fit.
The T2K international research collaborative collaboration, which includes Osaka City University High Energy Physics Laboratory, has successfully excluded nearly half of the possible values for the neutrino CP phase angle δCP at a statistical confidence level of 3σ. As previously introduced in the High Energy Physics Laboratory News “Measurement of the Neutrino CP Phase Angle,” CP symmetry breaking is a crucial condition for explaining the current matter dominated universe. There is an increasing possibility that CP symmetry breaking in the neutrino sector also contributes to this phenomenon.
Figure 2 :The allowed regions of Δm232 and sin2(θ23)．The blue cross point corresponds to the bet fit value obtained from the T2K experiment, and the blue solid line represents the allowed region with 90% confidence level.
The results this time are based on statistical data of 1.49×10²¹ POT for the neutrino mode and 1.64×10²¹ POT for the antineutrino mode. Compared to previous announcements, the data for the antineutrino mode has doubled. Along with this, the precision of each oscillation parameter has been improved, not only δCP. We’ll start by introducing those improvements.
Figure 3 : The reconstructed energy spectra of electron neutrinos (upper plot) and electron anti-neutrinos (lower plot) observed at Super-Kamiokande.
In the phenomenon of muon neutrino disappearance, Figure 1 shows the reconstructed energy distribution of muon neutrinos and anti-muon neutrinos obtained at Super-Kamiokande. When compared to the case without oscillation, the disappearance phenomenon of muon neutrinos due to oscillation is clearly seen around 0.6 GeV. The value of θ23 can be obtained from the magnitude of the disappearance, and \(\varDelta m^2_{32}\) can be obtained from the energy at which the disappearance is maximum. Figure 2 shows the situation for the neutrino normal mass hierarchy. The best fit values and errors are \(\sin^2θ_{23}=0.536^{+0.031}_{-0.046}\)，\(|\varDelta m^2_{32}|=(2.434 \pm 0.064)×10^{-3}\)
Values obtained from other experiments are also illustrated, but the T2K experiment provides the most precise measurement of θ23 in the world.
Regarding the phenomenon of electron neutrino appearance, Figure 3 shows the reconstructed energy distribution. With the increase in antineutrino mode data, the number of anti-electron neutrino appearance events has increased compared to the previous result. From this data, the value of θ13 is obtained as \(\sin^2\theta_{13}=0.0268^{+0.0051}_{-0.0046}\) for the neutrino normal mass hierarchy and \(\sin^2\theta_{13}=0.0305^{+0.0064}_{-0.0052}\) for the inverted mass hierarchy.
Figure 4 : The allowed regions of sin2(θ13) and δCP (upper plot), and the allowed regions of sin2(θ23) and δCP (lower plot). The white dotted line shows the 1σ(68.27%) confidence level, and the white solid line corresponds to the 3σ (99.73%) confidence level.
Now, let’s move on to the measurement of δCP. This is obtained from the asymmetry of the oscillation probabilities of \(\nu_{\mu}\rightarrow\nu_e\) and \(\bar{\nu}_{\mu}\rightarrow\bar{\nu}_e\) as follows:
\[ \sin\delta_{CP} \propto \frac{P(\nu_{\mu}\rightarrow\nu_{e}) – P(\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{e})}{P(\nu_{\mu}\rightarrow\nu_{e}) + P(\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{e}) }\] Figure 4 illustrates the results. Particularly, the middle plot shows sin²θ23 and δCP. The region inside the white dotted line represents the 1σ (68.27%) confidence level, and the region inside the white solid line represents the 3σ (99.73%) confidence level. The best fit values are \(-1.89^{+0.70}_{-0.58}\) for the normal mass hierarchy and \(-1.38^{+0.48}_{-0.54}\) for the inverted mass hierarchy, with the 3σ allowed regions being [-3.41, 0.03] for the normal mass hierarchy and [-2.54, -0.32] for the inverted mass hierarchy. This is the first time in the world that a closed region has been obtained at the 3σ confidence level, which is considered an important research achievement. Additionally, since the CP symmetry breaking of neutrinos is proportional to sinδCP, it is noteworthy that the value of δCP is close to -π/2, indicating the possibility of maximum breaking. With more data to be collected in the future, the focus will be on where the value of δCP will settle.