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3 a) The three neutrino mass eigenstates are labelled m1, m2 and m3. Experiments have determined that Am² = m² – mị = 7.5 x 10-5 eV² and |Am22| = |m3 – m3| 2.5 x 10-3 eV². Calculate the smallest possible values of mı, m2 and m3 for: (i) the normal mass hierarchy. (ii) the inverted mass hierarchy. b) When L is expressed in km, E, in GeV and Am2 in eV², the two-flavour mixing formula for the probability of a v neutrino appearing a distance L later as a ve neutrino is Am²[eV*] L[km] E„[GeV] P(v, → v.) = sin²(20) sin? ( 1.27 where 0 is the neutrino mixing angle, Am² is the difference in the squared masses of the neutrino eigenstates and E, is the neutrino energy. The terms in square brackets denote the parameters' units. Assuming E, = 1.3 GeV, Am² = 2.5x10-3 eV² and sin 0 = /3/2, sketch P(v, → ve) and P(v → vµ) as a function of L in the range 0< L[km] < 3000. %3D For a long baseline experiment designed to detect muon-neutrinos with the param- eters E, distance L where the muon-neutrino detector should be built? = 1.3 GeV, Am² = 2.5 × 10-3 eV² and sin 0 = v3/2, what is the optimal

3 a) The three neutrino mass eigenstates are labelled m1, m2 and m3. Experiments have determined that Am² = m² – mị = 7.5 x 10-5 eV² and |Am22| = |m3 – m3| 2.5 x 10-3 eV². Calculate the smallest possible values of mı, m2 and m3 for: (i) the normal mass hierarchy. (ii) the inverted mass hierarchy. b) When L is expressed in km, E, in GeV and Am2 in eV², the two-flavour mixing formula for the probability of a v neutrino appearing a distance L later as a ve neutrino is Am²[eV*] L[km] E„[GeV] P(v, → v.) = sin²(20) sin? ( 1.27 where 0 is the neutrino mixing angle, Am² is the difference in the squared masses of the neutrino eigenstates and E, is the neutrino energy. The terms in square brackets denote the parameters' units. Assuming E, = 1.3 GeV, Am² = 2.5x10-3 eV² and sin 0 = /3/2, sketch P(v, → ve) and P(v → vµ) as a function of L in the range 0< L[km] < 3000. %3D For a long baseline experiment designed to detect muon-neutrinos with the param- eters E, distance L where the muon-neutrino detector should be built? = 1.3 GeV, Am² = 2.5 × 10-3 eV² and sin 0 = v3/2, what is the optimal

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3 a) The three neutrino mass eigenstates are labelled m1, m2 and m3. Experiments have determined that Am² = m² – mị = 7.5 x 10-5 eV² and |Am22| = |m3 – m3| 2.5 x 10-3 eV². Calculate the smallest possible values of mı, m2 and m3 for: (i) the normal mass hierarchy. (ii) the inverted mass hierarchy. b) When L is expressed in km, E, in GeV and Am2 in eV², the two-flavour mixing formula for the probability of a v neutrino appearing a distance L later as a ve neutrino is Am²[eV*] L[km] E„[GeV] P(v, → v.) = sin²(20) sin? ( 1.27 where 0 is the neutrino mixing angle, Am² is the difference in the squared masses of the neutrino eigenstates and E, is the neutrino energy. The terms in square brackets denote the parameters' units. Assuming E, = 1.3 GeV, Am² = 2.5x10-3 eV² and sin 0 = /3/2, sketch P(v, → ve) and P(v → vµ) as a function of L in the range 0< L[km] < 3000. %3D For a long baseline experiment designed to detect muon-neutrinos with the param- eters E, distance L where the muon-neutrino detector should be built? = 1.3 GeV, Am² = 2.5 × 10-3 eV² and sin 0 = v3/2, what is the optimal
Transcribed Image Text:3 a) The three neutrino mass eigenstates are labelled m1, m2 and m3. Experiments have determined that Am² = m² – mị = 7.5 x 10-5 eV² and |Am22| = |m3 – m3| 2.5 x 10-3 eV². Calculate the smallest possible values of mı, m2 and m3 for: (i) the normal mass hierarchy. (ii) the inverted mass hierarchy. b) When L is expressed in km, E, in GeV and Am2 in eV², the two-flavour mixing formula for the probability of a v neutrino appearing a distance L later as a ve neutrino is Am²[eV*] L[km] E„[GeV] P(v, → v.) = sin²(20) sin? ( 1.27 where 0 is the neutrino mixing angle, Am² is the difference in the squared masses of the neutrino eigenstates and E, is the neutrino energy. The terms in square brackets denote the parameters' units. Assuming E, = 1.3 GeV, Am² = 2.5x10-3 eV² and sin 0 = /3/2, sketch P(v, → ve) and P(v → vµ) as a function of L in the range 0< L[km] < 3000. %3D For a long baseline experiment designed to detect muon-neutrinos with the param- eters E, distance L where the muon-neutrino detector should be built? = 1.3 GeV, Am² = 2.5 × 10-3 eV² and sin 0 = v3/2, what is the optimal
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