Constraining astrophysical neutrino flavor composition from leptonic unitarity

Xun-Jie Xu,Hong-Jian He,Werner Rodejohann

doi:10.1088/1475-7516/2014/12/039

Abstract

The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of lepton mixing. We apply our unitarity bounds to derive general constraints on the flavor compositions for three types of astrophysical neutrino sources (and their general mixture), and compare them with the IceCube measurements. Furthermore, we prove that for any sources without ντ neutrinos, a detected νμ flux ratio < 1/4 will require the initial flavor composition with more νe neutrinos than νμ neutrinos.

Highlights

ArXiv ePrint: 1407.3736 these bounds would call for new physics, such as active-sterile neutrino mixing, neutrino decays, pseudo-Dirac neutrinos, or other exotic effects [10]
We will prove that for any astrophysical sources without ντ neutrinos, if the detected νμ neutrinos have a flux ratio T < 1/4, the source must generate more νe neutrinos than νμ neutrinos. These results demonstrate the importance of our general unitarity constraints
We find that the extremum equation ∂x,z,wG|x=1−y = 0 has no solution by direct calculation

Summary

Connecting Astrophysical Neutrinos to Leptonic Unitarity Triangle

The leptonic mixing in charged currents is described by the 3 × 3 unitary matrix U of Pontecorvo-Maki-Nakagawa-Sakata (PMNS) [7]. The flavor transition probability for astrophysical neutrinos ν → ν is given by. For an initial flux from a remote astrophysical neutrino source, let us denote its initial flavor compositions as (Φe0, Φμ0, Φτ0). Inspecting the formulas (2.4), we find that under the exchange νe ↔ νμ , the transition probabilities (X, Y, Z) change as follows: X ↔ Y and Z ↔ Z. Let us consider a general source with mixture [5] from all three types of sources above In this case, the initial flavor composition can be written as, (η : 1−η : 0), with the parameter η ∈ [0, 1].

Unitarity Constraints on Flavor Transitions of Astrophysical Neutrinos

Unitarity Constraints on Flavor Ratios of Astrophysical Neutrinos

Conclusions