Sterile-active neutrino oscillations and shortcuts in the extra dimension

We discuss a possible new resonance in active-sterile neutrino oscillations arising in theories with large extra dimensions. Fluctuations in the brane effectively increase the path-length of active neutrinos relative to the path-length of sterile neutrinos through the extra-dimensional bulk. Well below the resonance, the standard oscillation formulas apply. Well above the resonance, active-sterile oscillations are suppressed. We show that a resonance energy in the range of 30–400 MeV allows an explanation of all neutrino oscillation data, including LSND data, in a consistent four-neutrino model. A high resonance energy implies an enhanced signal in MiniBooNE. A low resonance energy implies a distorted energy spectrum in LSND, and an enhanced ${\nu }_{\mu }$ depletion from a stopped-pion source. The numerical value of the resonance energy may be related back to the geometric aspects of the brane world. Some astrophysical and cosmological consequences of the brane-bulk resonance are briefly sketched.

Figure 1

Schematic representation of a periodically curved brane in Minkowski spacetime. A coordinate transformation leads to an equivalent description as a nondiagonal metric with a flat brane, as described in the text.

Figure 2

Oscillation amplitude ${sin}^{2}2\tilde{\theta }$ as a function of the neutrino energy $E_{\nu }$, for a resonance energy of $E_{\mathrm{res}}=40\mathrm{MeV}$. The different curves correspond to different values for the standard angle, ${sin}^{2}2\theta =0.2$, 0.1, 0.01, 0.001 (from above).

Figure 3

Bulk-shortcut oscillation probabilities for LSND (light line) and KARMEN (dark line) as a function of the neutrino energy. Shown is a scenario with $E_{\mathrm{res}}=33\mathrm{MeV}$; ${sin}^2{\theta }_{*}=0.01$; ${sin}^{2}2\theta =0.9$; $\delta m^2=0.7{\mathrm{eV}}^2$. For comparison, a standard oscillation probability for LSND ($\delta m^2=0.8\mathrm{eV}$, ${sin}^{2}2{\theta }_{\mathrm{LSND}}=0.006$) is displayed (dashed line). The vertical lines indicate the energy window of LSND and KARMEN.

Figure 4

Bulk-shortcut oscillation probabilities for LSND (light line) and KARMEN (dark line) as a function of the neutrino energy. Shown is a scenario with $E_{\mathrm{res}}=400\mathrm{MeV}$, ${sin}^2{\theta }_{*}=0.1$; ${sin}^{2}2\theta =0.45$; $\delta m^2=0.8{\mathrm{eV}}^2$. For comparison, a standard oscillation probability ($\delta m^2=0.8\mathrm{eV}$, ${sin}^{2}2{\theta }_{\mathrm{LSND}}=0.006$) for LSND is displayed (dashed line). The vertical lines indicate the energy window of LSND and KARMEN.

Figure 5

Bulk-shortcut oscillation probabilities for MiniBooNE as a function of the neutrino energy. Shown is a scenario with ${sin}^2{\theta }_{*}=0.1$; ${sin}^{2}2\theta =0.45$; $\delta m^2=0.8{\mathrm{eV}}^2$. The resonance energy is varied, $E_{\mathrm{res}}=200$, 300, 400 MeV, from left to right (light to dark). For comparison, the expectation for a standard oscillation solution ($\delta m^2=0.8\mathrm{eV}$, ${sin}^{2}2{\theta }_{\mathrm{LSND}}=0.006$) for LSND is displayed (dashed line). The vertical line indicates the energy threshold of MiniBooNE.

Figure 6

The muon-neutrino survival probability versus distance, for a monochromatic neutrino-beam energy of 30 MeV from stopped pions. The solid curves are parametrized by resonance energies 33, 100, 200 (identical for 300 and 400 MeV), in order of decreasing depletion. The dashed curve is the result with no bulk shortcut. The low-energy parameters for the 33 MeV resonance are chosen as in Fig. 3: ${sin}^2{\theta }_{*}=0.01$; ${sin}^{2}2\theta =0.9$; $\delta m^2=0.7{\mathrm{eV}}^2$; while the parameters for the other curves are chosen as in Fig. 4: ${sin}^2{\theta }_{*}=0.1$; ${sin}^{2}2\theta =0.45$; $\delta m^2=0.8{\mathrm{eV}}^2$. The vertical lines indicate the range of possible source to near/far detector distances.