Atmospheric neutrinos with three flavor mixing

Abstract

We analyze the atmospheric neutrino data in the context of three flavor neutrino oscillations taking account of the matter effects in the Earth. With the hierarchy among the vacuum mass eigenvalues 3 2 ӷ 2 2 у 1 2 , the solution of the atmospheric neutrino problem depends on ␦ 31 ϭ 3 2 Ϫ 1 2 and the 13 and 23 mixing angles and . Whereas the sub-GeV atmospheric neutrino data imposes only a lower limit on ␦ 31 Ͼ10 Ϫ3 eV 2 , the zenithangle-dependent suppression observed in the multi-GeV data limits ␦ 31 from above also. The allowed regions of the parameter space are strongly constrained by the multi-GeV data. Combined with our earlier solution to the solar neutrino problem which depends on ␦ 21 ϭ 2 2 Ϫ 1 2 and the 12 and 13 mixing angles and , we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric neutrino problems simultaneously. ͓S0556-2821͑97͒05411-8͔ PACS number͑s͒: 14.60.Pq, 95.85.Ry

Constraints on three flavor neutrino mixing

“…The broken lines enclose regions whose predictions fall within the range given by ½ uncertainties. These results have been presented in [23].…”

“…We can now estimate the maximum contribution of the channel to the atmospheric neutrino anomaly using the CHOOZ result. Since the relevant AE ¿½ is about ½¼ ¾ Î ¾ , matter effects are negligible for the problem [23]. Hence the relevant probability is the vacuum ° oscillation probability,…”

Phenomenology of neutrino oscillations

“…(1), one can show that the solar neutrino problem depends only on δm 2 21 , ω and φ while the atmospheric neutrino problem depends only on δm 2 32 , ψ and φ. It is this simplification that allows us to analyse the two problems within a 3 − ν framework under reasonable control and one gets a fairly broad and stable set of allowed regions in the 5-parameter space [4,5]. If we temporarily put φ as zero, then the two problems decouple and the results are the following :-There are three solutions of the solar neutrino problem : [6] turns out to be a crucial result.…”

“…Extensive literature exists on the solar [4,10] and atmospheric neutrinos [5,11]. So, we shall be brief.…”

“…All these are consistent with ν µ oscillating into ν τ over the distance scale of about 10,000 km ; so it is for the upward-going ν µ travelling through the earth that the effect is most dominant. The effect of earth matter in the atmospheric neutrino problem is not significant [5] at the present level of accuracy and hence one can use Eq.(3). The resulting neutrino prameters were given in Sec 2.…”