Double neutrino production and detection in neutrino detectors

Large, high-energy ($E>100\mathrm{GeV}$) cosmic neutrino telescopes are now quite mature. IceCube, for example, observes about 50 000 well-reconstructed single atmospheric neutrino events/year, with energies above 100 GeV. Although the neutrino detection probability is small, current detectors are large enough so that it is possible to detect two neutrinos from the same cosmic-ray interaction. In this paper, we calculate the expected rate of double-neutrino interactions from a single cosmic-ray air shower. The rate is small, about $0.07\mathrm{events}/\mathrm{year}$ for a $1{\mathrm{km}}^3$ detector like IceCube, with only a small dependence on the assumed cosmic-ray composition and hadronic interaction model. For a larger detector, like the proposed KM3Net, the rate is about $0.8\mathrm{events}/\mathrm{year}$, high enough to be easily observable. These double neutrino interactions are the major irreducible background to searches for pairs of supersymmetric particles produced in neutrino or cosmic-ray air-shower interactions. Other standard model backgrounds are considered, and found to be small.

Figure 1

The geometry used in the calculation for an incident cosmic ray at zenith angle $\theta$. The parameters used are $R_{\mathrm{obs}}$ for the radius from the center of the Earth to the observation height, at which the particles are saved, $R_{\mathrm{atm}}$ for the radius from the center of the Earth to the top of the atmosphere, $D$ for the distance between the cosmic-ray source and the detector, and $S$ for the neutrino-neutrino separation in the detector.

Figure 2

The zenith-angle distribution of pairs that would be detected in the IceCube-model detector. Most of the pairs come from just below the horizon.

Figure 3

The primary energy of the cosmic-ray progenitor of the pairs that would be detected in the IceCube-model detector. The solid black line shows the result of a fit to the detection probability distribution, weighted with the flux $\Phi (E_p)$.

Figure 4

The neutrino energies of the pairs that would be detected in the IceCube-model detector (two entries/pair).

Figure 5

The predicted pair-detection rate as a function of detector diameter, $D_{\max }$. This is for an assumed roughly spherical detector. IceCube fits this model fairly well. KM3NeT is likely to be wider than it is high, so the KM3NeT rates determined here may be slight overestimates.