PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

∆m 2 21(10 −5 eV 2 ) 7.59 ±0.20 ( )
+0.61
−0.69
∆m 2 31 (10 −3 eV 2 ) −2.36±0.07 (±0.36)
∆m 2 31 (10 −3 eV 2 ) +2.47±0.12 (±0.37)
( ) 0
+3.2
θ 12 34.4±1.0
−2.9
( ) 0
+11.1
θ 23 42.9 +4.1
−2.8
−7.2
θ 13 7.3 −3.2 +2.1 (≤ 13.3)◦
δ CP ∈ [0, 360]
Table 2.1: The 1σ and 3σ allowed ranges of the neutrino oscillation parameters and the
mass square differences.
TheprobabilityforaneutrinothatpropagatesinvacuumwithaenergyE tooscillate
from a flavor α to a flavor β, after having travelled a distance L, is given by
P(ν α → ν β ) =
∑
∣ U αj Uβj ∗ j
∣ L
e−im2 2E j ∣∣
2
j
= δ αβ − 4 ∑ Re ( (
)
U αi U ∗ αjU ∗ βiU βj ×sin
2 ∆m
2
)
ij L
4E
i>j
+ 2 ∑ Im ( (
U αi U ∗ αj U∗ βi U ) ∆m
2
)
ij L
βj ×sin , (2.3)
4E
i>j
where ∆m 2 ij = m2 i −m2 j . To get a non-zero probability of the standard model neutrinos
to oscillate from a flavor α to a flavor β, they should have masses and also nonzero masssquare
difference ∆m 2 ij. By measuring neutrino fluxes coming from different sources, the
mass-square differences andthe mixing parameters can bedetermined. Observation ofthe
disappearance of the atmospheric ν µ flux constrains the mixing angle θ 23 and the masssquare
difference |∆m 23 | 2 . Likewise observation of oscillations of solar neutrinos to other
active flavors constrains the mixing angle θ 12 and the solar mass-square difference ∆m 2 21 .
In addition, the CHOOZ reactor experiment [13] constrains the 3rd mixing angle θ 13 . In
Table. 2.1 we present the recent 1σ and 3σ allowed ranges of the neutrino mass square
differences and oscillation parameters [14]. From the neutrino oscillation experiments we
know that the solar mass square difference ∆m 2 21 > 0, while at present we do not yet
have any information whether the atmospheric mass square difference ∆m 2 31 is positive
or negative, characterizing the normal and inverted mass ordering respectively [15]. We
present an illustration of the two types of neutrino mass hierarchies in Fig. 2.1.
The oscillation experiments however, do not shed any light on the absolute neutrino
mass m t = ∑ i=1,2,3 m i. The absolute neutrino mass is constrained from the cosmological
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