Large extra dimensions at the Deep Underground Neutrino Experiment

We investigate the potential of the long-baseline Deep Underground Neutrino Experiment (DUNE) to study large-extra-dimension (LED) models originally proposed to explain the smallness of neutrino masses by postulating that right-handed neutrinos, unlike all standard model fermion fields, can propagate in the bulk. The massive Kaluza-Klein (KK) modes of the right-handed neutrino fields modify the neutrino oscillation probabilities and can hence affect their propagation. We show that, as far as DUNE is concerned, the LED model is indistinguishable from a ($3+3N$)-neutrino framework for modest values of $N$; $N=1$ is usually a very good approximation. Nonetheless, there are no new sources of $CP$-invariance violation other than one $CP$-odd phase that can be easily mapped onto the $CP$-odd phase in the standard three-neutrino paradigm. We analyze the sensitivity of DUNE to the LED framework and explore the capability of DUNE to differentiate the LED model from the three-neutrino scenario and from a generic ($3+1$)-neutrino model.

Figure 1

Oscillation probabilities assuming a three-neutrino framework (dashed) and an LED hypothesis with $m_0=5\times {10}^{-2}\mathrm{eV}$ and $R_{\mathrm{ED}}^{-1}=0.38\mathrm{eV}$ ($R_{\mathrm{ED}}=5\times {10}^{-5}\mathrm{cm}$) for the normal neutrino mass hierarchy, $\mathrm{\Delta }{m}_{13}^2>0$. The values of the other oscillation parameters are tabulated in Table 1, see text for details. The top row displays appearance probabilities $P({\nu }_{\mu }\to {\nu }_e)$ (left) and $P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_e)$ (right) and has curves shown for ${\delta }_{13}=-\pi /2$ (green), ${\delta }_{13}=0$ (gray), and ${\delta }_{13}=\pi /2$ (purple). The bottom row displays disappearance probabilities $P({\nu }_{\mu }\to {\nu }_{\mu })$ (left) and $P({\overline{\nu }}_{\mu }\to {\overline{\nu }}_{\mu })$ (right).

Figure 2

Expected event yields at DUNE assuming three years of either neutrino-beam mode (left) or antineutrino-beam mode (right). The top row displays ${\nu }_e$ and ${\overline{\nu }}_e$ appearance yields, and the bottom row displays ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ disappearance yields. In each panel, we show the expected yield assuming a three-neutrino hypothesis with parameters from Table 1 for the normal hierarchy in blue, with error bars representing statistical uncertainties, and assuming a nonzero LED hypothesis with $m_0=5\times {10}^{-2}\mathrm{eV}$ and $R_{\mathrm{ED}}^{-1}=0.38\mathrm{eV}$ in black. The contribution of events associated to opposite-sign muons and electrons is included in the signal. Backgrounds are discussed in the text and shown under the expected signals.

Figure 3

Exclusion limits in the $R_{\mathrm{ED}}^{-1}-m_0$ plane, assuming either (a) a normal hierarchy or (b) an inverted hierarchy of neutrino masses. The exclusion regions are to the top left of the relevant curves. Shown are the 95% C.L. lines from DUNE (black), IceCube-40 (mauve) and Ice-Cube79 (blue) [20], and a combined analysis of T2K and Daya Bay (gold) [18]. We also include the 90% C.L. line from sensitivity analysis of KATRIN (burgundy) [16]. The shaded green regions are preferred at 95% C.L. by the reactor anomaly seen in reactor and Gallium experiments [19]. The gray shaded regions are excluded by the measurements of $\mathrm{\Delta }{m}_{i1}^2$, as explained in the text. The dotted gray lines are curves along which $\sum _i{m}_i^{(0)}=0.25\mathrm{eV}$. Higher values of $\sum _i{m}_i^{(0)}$ correspond to the regions above and to the right of the dotted gray lines.

Figure 4

Expected sensitivity to a nonzero set of LED parameters as measured by DUNE, assuming three years each of neutrino and antineutrino data collection. Figure 4 assumes the normal mass hierarchy (NH), and Fig. 4 assumes the inverted mass hierachy (IH). The LED parameters assumed here are $m_0=5\times {10}^{-2}\mathrm{eV}$ and $R_{\mathrm{ED}}^{-1}=0.38\mathrm{eV}$, while ${\delta }_{13}=\pi /3$. The input values of $\mathrm{\Delta }{m}_{i1}^2$, $i=1$, 2 are in Table 1. The input values for the mixing angles are, for the NH, ${\sin }^2{\theta }_{12}=0.322$, ${\sin }^2{\theta }_{13}=0.0247$, ${\sin }^2{\theta }_{23}=0.581$, and, for the IH, ${\sin }^2{\theta }_{12}=0.343$, ${\sin }^2{\theta }_{13}=0.0231$, ${\sin }^2{\theta }_{23}=0.541$.

Figure 5

Results of a four-neutrino fit to data generated assuming an LED hypothesis with $m_0=5\times {10}^{-2}\mathrm{eV}$ and $R_{\mathrm{ED}}^{-1}=0.38\mathrm{eV}$ assuming the normal hierarchy. Contours shown are 68.3% (blue), 95% (orange), and 99% (red) CL. All unseen parameters are marginalized over.