Another possible way to determine the neutrino mass hierarchy

Abstract

We show that by combining high precision measurements of the atmospheric δm 2 in both the electron and muon neutrino (or anti-neutrino) disappearance channels one can determine the neutrino mass hierarchy. The required precision is a very challenging fraction of one per cent for both measurements. At even higher precision, sensitivity to the cosine of the CP violating phase is also possible. This method for determining the mass hierarchy of the neutrino sector does not depend on matter effects. Typeset by REVT E XNeutrino flavor transitions have been observed in atmospheric, solar, reactor and accelerator neutrino experiments. Transitions for at least two different E/L's (neutrino energy divided by baseline) are seen. To explain these transitions, extensions to the Standard Model of particle physics are required. The simplest and most widely accepted extension is to allow the neutrinos to have masses and mixings, similar to the quark sector, then these flavor transitions can be explained by neutrino oscillations. This picture of neutrino masses and mixings has recently come into sharper focus with the latest salt data presented by the SNO collaboration[1]. When combined with the latest KamLAND experiment[2] and other solar neutrino experiments[4, 5] the range of allowed values for the solar mass squared difference, δm 2 21 , and the mixing angle, θ 12 , are 1 + 7.3 × 10 −5 eV 2 < δm 2 21

Recent results from Daya Bay experiment

“…First is Δm 2 21 and second is Δm 2 μμ which is a flavour mixture of Δm 2 31 and Δm 2 32 since current experiments have little sensitivity to the mass hierarchy. Atmospheric and accelerator neutrino experiments measure Δm 2 μμ sin 2 θ 12 Δm 2 31 + cos 2 θ 12 Δm 2 32 + 2Δm 2 21 sin θ 12 cos θ 12 sin θ 13 tan θ 23 cos δ [17]. Till 2012 the value of θ 13 was unknown.…”

Study of muon neutrino disappearance using the Fermilab Main Injector neutrino beam

“…The analysis reported here is conducted in the two-neutrino framework, and we can tentatively identify m 2 m 2 atm m 2 32 and sin 2 32 where effects of order sin 2 13 have been neglected [12]. The Main Injector Neutrino Oscillation Search (MINOS) is a long-baseline, two-detector neutrino oscillation experiment that uses a muon-neutrino beam produced by the Neutrinos at the Main Injector [13,14] (NuMI) facility at Fermi National Accelerator Laboratory (FNAL).…”

Impact of hierarchy upon the values of neutrino mixing parameters

“…(1), but does make the transformation of the mass-squared differences. Given that the octant of θ 12 is known from matter effects, it is, in principle, possible to distinguish hierarchy through the precision measurement of vacuum oscillation channels [50][51][52][53]; however, for θ 13 ∼ 0, hierarchy is difficult to discern in part because of the large separation between mass-squared differences, ∆ 21 ≪ |∆ 32 |. …”