Effects of nonstandard neutrino interactions at PINGU

Neutrino oscillation experiments in the past decades have greatly improved our knowledge on neutrinos by measuring the fundamental neutrino parameters. The ongoing and upcoming neutrino oscillation experiments are intended to pin down the neutrino mass hierarchy and to discover the leptonic $CP$ violation. By means of neutrino oscillograms, we analyze the impact of nonstandard neutrino interactions on neutrino oscillations in Earth matter. The standard neutrino oscillation probabilities may be significantly changed by nonstandard interaction parameters, and, in particular, the $CP$-violating effects in the energy range $E=1–20\mathrm{GeV}$ are greatly enhanced. In addition, the event rates of muon neutrinos in the proposed huge atmospheric neutrino experiment, PINGU at the South Pole, have been estimated in the presence of nonstandard neutrino interactions. It has been found that the PINGU experiment has very good sensitivities to the nonstandard neutrino interaction parameters.

Figure 1

Dependence of the effective mixing angle ${sin}^2{\tilde{\theta }}_{13}$ on the NSI parameters and neutrino energy, where a constant matter density profile $\rho =4.5\mathrm{g}/{\mathrm{cm}}^3$ has been assumed (i.e., Earth’s mantle density) and the dotted line corresponds to ${sin}^2{\tilde{\theta }}_{13}={sin}^2{\theta }_{13}$. In addition, the best-fit values of neutrino parameters (i.e., ${sin}^2{\theta }_{12}=0.30$, ${sin}^2{\theta }_{23}=0.41$, ${sin}^2{\theta }_{13}=0.023$, $\Delta m_{21}^2=7.50\times {10}^{-5}{\mathrm{eV}}^2$, and $\Delta m_{31}^2=2.47\times {10}^{-3}{\mathrm{eV}}^2$) from Ref. 32 have been used.

Figure 2

Standard neutrino oscillograms without NSIs (i.e., ${\epsilon }_{\alpha \beta }=0$) in the appearance channel: $P_{e\mu }^{\mathrm{SD}}=P({\nu }_e\to {\nu }_{\mu })$ for neutrino oscillations in the case of normal neutrino mass hierarchy (left panel) and ${\overline{P}}_{e\mu }^{\mathrm{SD}}=P({\overline{\nu }}_e\to {\overline{\nu }}_{\mu })$ for antineutrino oscillations in the case of inverted neutrino mass hierarchy (right panel).

Figure 3

Standard neutrino oscillograms without NSIs (i.e., ${\epsilon }_{\alpha \beta }=0$) in the disappearance channel: $P_{\mu \mu }^{\mathrm{SD}}=P({\nu }_{\mu }\to {\nu }_{\mu })$ for neutrino oscillations in the case of normal neutrino mass hierarchy (left panel) and in the case of inverted neutrino mass hierarchy (right panel).

Figure 4

Differences between the standard and nonstandard neutrino oscillograms in the ${\nu }_e\to {\nu }_{\mu }$ channel $\Delta P_{e\mu }\equiv P_{e\mu }^{\mathrm{NSI}}-P_{e\mu }^{\mathrm{SD}}$ (left column) and in the ${\nu }_{\mu }\to {\nu }_{\mu }$ channel $\Delta P_{\mu \mu }\equiv P_{\mu \mu }^{\mathrm{NSI}}-P_{\mu \mu }^{\mathrm{SD}}$ (right column), where the normal neutrino mass hierarchy and $\delta =0$ are assumed, and ${\epsilon }_{e\mu }=0.1$ (upper row), ${\epsilon }_{e\tau }=0.1$ (middle row), and ${\epsilon }_{\mu \tau }=0.1$ (lower row) are taken for illustration.

Figure 5

Oscillograms for the probability differences $\Delta P_{e\mu }(\delta )=P_{e\mu }^{\mathrm{NSI}}(\delta )-P_{e\mu }^{\mathrm{NSI}}(0)$ with $\delta =\pi /2$ in the normal neutrino mass hierarchy case (left column) and in the inverted neutrino mass hierarchy case (right column). The two plots in the first row correspond to $\Delta P_{e\mu }(\delta )$ with vanishing NSI parameters, i.e., $\Delta P_{e\mu }(\delta )=P_{e\mu }^{\mathrm{SD}}(\delta )-P_{e\mu }^{\mathrm{SD}}(0)$ with $\delta =\pi /2$.

Figure 6

The number of ${\nu }_{\mu }$-like events in the $E-\cos {\theta }_z$ plane, collected by the PINGU detector for one year, where the normal neutrino mass hierarchy is assumed. The upper left plot corresponds to the case of standard neutrino oscillations; i.e., all the NSI parameters are vanishing.

Figure 7

The SD-NSI asymmetry $\mathcal{A}\equiv (N_{\mu }^{\mathrm{SD}}-N_{\mu }^{\mathrm{NSI}})/\sqrt{N_{\mu }^{\mathrm{SD}}}$ of ${\nu }_{\mu }$-like events at the PINGU detector for one year, in the cases of normal neutrino mass hierarchy (left column) and inverted neutrino mass hierarchy (right column).