Approximative two-flavor framework for neutrino oscillations with nonstandard interactions

In this paper, we develop approximative two-flavor neutrino oscillation formulas including subleading nonstandard interaction effects. Especially, the limit when the small mass-squared difference approaches zero is investigated. The approximate formulas are also tested against numerical simulations in order to determine their accuracy and they will probably be most useful in the GeV energy region, which is the energy region where most upcoming neutrino oscillation experiments will be operating. Naturally, it is important to have analytical formulas in order to interpret the physics behind the degeneracies between standard and nonstandard parameters.

Figure 1

The muon neutrino survival probability $P_{\mu \mu }$ as a function of zenith angle and energy for different values of $v$ and $\beta$. The colored regions correspond to the numerical results (darker regions for higher probability), while the solid black curves correspond to the two-flavor approximation introduced in Sec. 3. In this figure, the leptonic mixing angle ${\theta }_{13}$ is set to zero.

Figure 2

The electron neutrino survival probability $P_{ee}$ as a function of zenith angle and energy for ${\theta }_{13}=0$, $v=1$, and different values of $\beta$. The colored regions and solid black curves are constructed as in Fig. 1.

Figure 3

The same as Fig. 2, but for ${\theta }_{13}=8°$.

Figure 4

The neutrino oscillation probability $P_{e\mu }$ as a function of zenith angle and energy for different values of ${\theta }_{13}$ and $\beta$. For this figure, we have used $v=1$ and the colored regions and solid black curves are constructed as in Fig. 1.

Figure 5

The neutrino oscillation probability $P_{\mu \tau }$ as a function of zenith angle and energy for different values of ${\theta }_{13}$ and $\beta$. For this figure, we have used $v=1$ and the colored regions and solid black curves are constructed as in Fig. 1.

Figure 6

The sensitivity contours (2 d.o.f.) in the ${sin}^2(2{\theta }_{23})–\Delta m_{31}^2$ plane for the ${\nu }_{\mu }$ disappearance channel at the fictive neutrino factory experiment described in the text. The black curves correspond to the sensitivity if it is assumed that there are no NSIs present, while the colored regions correspond to the sensitivity if NSIs within current bounds are taken into account. The gray circle corresponds to the simulated parameters and the gray curve to the expected direction of the NSI degeneracy. The confidence levels are 90%, 95%, and 99%, respectively. We have assumed Gaussian priors of ${\epsilon }_{ee}<2.6$, ${\epsilon }_{e\tau }<1.9$, and ${\epsilon }_{\tau \tau }<1.9$ at a 90% confidence level.

Figure 7

The sensitivity (2 d.o.f.) to the NSI parameters $v$ and $\beta$ for the ${\nu }_{\mu }$ disappearance channel at the fictive neutrino factory experiment described in the text. The dashed curves are the systematics-only sensitivities and the solid curves include parameter correlations with the standard neutrino oscillation parameters (with errors comparable to the current errors). The contours were constructed assuming no NSIs and the $+$ corresponds to this situation.