5 Neutrinos Come in at Least Three Flavors The known neutrino flavors: e, Each of these is associated with the corresponding charged-lepton flavor: e
6 The Meaning of this Association e Detector e e W boson Short Journey e W W
7 Over short distances, neutrinos do not change flavor. W Short Journey Does Not Occur But if neutrinos have masses, and leptons mix, neutrino flavor changes do occur during long journeys.
8 Let Us Assume Neutrino Masses and Leptonic Mixing Neutrino mass — There is some spectrum of 3 or more neutrino mass eigenstates i : (Mass) 2 1 2 3 4 Mass ( i ) m i
9 Leptonic mixing — When W + + + , the produced neutrino state | > is | > = U* i | i >. Neutrino offlavor Neutrino of definite mass m i Leptonic Mixing Matrix e e, , e, , or i
10 Another way to look at W decay: A given + can be accompanied by any i. Amp(W + + + i ) = U* i is | > = U* i | i >. The neutrino state | > produced together with + i
11 According to the Standard Model, extended to include neutrino mass and leptonic mixing — The number of different i is the same as the number of different . The mixing matrix U is 3 x 3 and unitary: UU † = U † U = 1. Some models include “sterile” neutrinos — neutrinos that experience none of the known forces of nature except gravity. In such models, there are N > 3 i, and U is N x N, but still unitary.
12 Just as each neutrino of definite flavor is a superposition of mass eigenstates i, so each mass eigenstate is a superposition of flavors. From | > = i U* i | i > and the unitarity of U, | i > = U i | >. The flavor- fraction of i is — | | 2 = |U i | 2.
13 The Standard Model (SM) description of neutrino interactions (not masses or leptonic mixing) is well-confirmed. We will assume it is true, and extend it to include mixing. For the lepton couplings to the W boson, we then have — Left-handed Taking mixing into account
16 Evidence For Flavor Change Neutrinos Solar Reactor (L ~ 180 km) Atmospheric Accelerator (L = 250 and 735 km) Stopped Decay LSND L 30 m Evidence of Flavor Change Compelling Unconfirmed ( )
17 Solar e is now well established. The mechanism for this flavor conversion is the — Large Mixing Angle version of the — Mikheyev Smirnov Wolfenstein — Effect. This occurs as the neutrinos stream outward through solar material. It requires both interactions with matter and neutrino mass and mixing. What Happens To Solar Neutrinos
18 How Does the Large Mixing Angle MSW Effect Work? The solar matter effect is important for the high- energy 8 B neutrinos, not the low-energy pp neutrinos. Since 3 couples at most feebly to electrons (to be discussed), and solar neutrinos are born e, the solar neutrinos are mixtures of just 1 and 2. (Convention: 2 heavier than 1 ). This is a 2-neutrino system. Solar neutrino flavor change is e x, where x is some combination of and .
19 In the sun, At the center of the sun, √2G F N e ≈ 0.75 × 10 -5 eV 2 / MeV. For Δ m 2 sol ≈ 8 × 10 -5 eV 2 and typical 8 B neutrino energy of ~ 8 MeV, Δ m 2 sol / 4E ≈ 0.25 × 10 -5 eV 2 / MeV. The interaction term in H dominates, and e is approximately an eigenstate of H.* e x e x *For the (E ~ 0.2MeV) pp neutrinos, H Vac dominates.
20 8 The 8 B solar neutrino propagates outward adiabatically. It remains the slowly - changing heavier eigenstate of the slowly - changing H. It emerges from the sun as the heavier eigenstate of H Vac, 2.* It stays 2 until it reaches the earth. Nothing “oscillates”! Since 2 = e sin sol + x cos sol, ( See 2 2 U matrix ) Prob[See e at earth] = sin 2 sol. *Good to 91% (Nunokawa, Parke, Zukanovich-Funchal)