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Etude et impact du bruit de fond corrélé pour la mesure de l'angle ...

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2.3 Neutrino oscil<strong>la</strong>tion, the theory 21<br />

in terms of the so called neutrino oscil<strong>la</strong>tion mechanism. As exp<strong>la</strong>ined with<br />

more d<strong>et</strong>ails in the following sections, the oscil<strong>la</strong>tion mechanism requires the<br />

neutrino to have non-null mass and lepton f<strong>la</strong>vour quantum numbers are no<br />

longer conserved.<br />

The SM is clearly not compl<strong>et</strong>e and requires extension to accommodate<br />

neutrino oscil<strong>la</strong>tion mechanism and its consequences.<br />

2.3 Neutrino oscil<strong>la</strong>tion, the theory<br />

tel-00821629, version 1 - 11 May 2013<br />

Neutrino oscil<strong>la</strong>tion were postu<strong>la</strong>ted in 1957 by Pontecorvo [86]. In analogy<br />

with K 0 $ K 0 oscil<strong>la</strong>tions, Pontecorvo suggested the possibility of neutrinoantineutrino<br />

oscil<strong>la</strong>tion ⌫ $ ⌫. When the second neutrino family where<br />

discovered, Maki, Nakagawa and Sakata proposed in 1962 the possibility<br />

of oscil<strong>la</strong>tion among the neutrino families intro<strong>du</strong>cing the concept of lepton<br />

f<strong>la</strong>vour mixing [101]. The neutrino oscil<strong>la</strong>tion mechanism is based on the fact<br />

that if neutrino have a non-null mass, f<strong>la</strong>vour states |⌫ ↵ i (interaction states)<br />

and mass states |⌫ i i (propagation states) could not coinci<strong>de</strong>, in analogy to<br />

the mixing in the quark sector:<br />

|⌫ ↵ i = X i<br />

U ⇤ ↵,i|⌫ i i (2.7)<br />

where ↵ represent the f<strong>la</strong>vour families (e, µ, ⌧), |⌫ i i the mass states of mass<br />

m i (with i =1, 2, 3) and U is the so called PMNS 1 unitary mixing matrix.<br />

Neutrinos are pro<strong>du</strong>ced via weak interaction in a <strong>de</strong>fined f<strong>la</strong>vour eigenstate<br />

|⌫ ↵ i tog<strong>et</strong>her with the corresponding lepton ↵. Assuming the neutrino is<br />

pro<strong>du</strong>ced at time t = 0:<br />

|⌫(t = 0; L = 0)i = |⌫ ↵ i = X i<br />

U ⇤ ↵,i|⌫ i i (2.8)<br />

and propagates as a free particle following the Schrodinger equation, after<br />

atim<strong>et</strong>:<br />

|⌫ ↵ (t, L)i = X U↵,ie ⇤ i(E it pL) |⌫ i i (2.9)<br />

i<br />

assuming the three mass eigenstates propagate with the same momentum<br />

with re<strong>la</strong>tivistic energies (p ' E m):<br />

q<br />

E i = p 2 + m 2 i ' p + m2 i<br />

2p ' E + m2 i<br />

(2.10)<br />

2E<br />

Eq. 2.9 could be written, using natural units (c = ~ = 1), as:<br />

|⌫ ↵ (t, L)i = X i<br />

U ⇤ ↵,ie i m2 i<br />

2E L |⌫ i i (2.11)<br />

1 Pontecorvo-Maki-Nakagawa-Sakata matrix

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