ABSTRACT
Neutrino physics has gone through a revolution in the last ten years. Now it is beyond doubt that neutrinos have a non-vanishing rest mass. All the evidence stems from neutrino oscillation experiments, proving that neutrinos can change their flavour if travelling from a source to a detector. Oscillations violate the concept of single lepton number conservation but total lepton number is still conserved. Furthermore, the oscillation experiments are not able to measure absolute neutrino masses, because their results depend only on the differences of masses-squared, Δm2 = m2i −m2j , with mi,mj as the masses of two neutrino mass eigenstates. In the full three neutrino mixing framework the weak eigenstates νe, νμ and ντ can be expressed as superpositions of three neutrino mass eigenstates ν1,ν2 and ν3 linked via a unitary matrix U:
⎛
⎜ ⎜ ⎝
⎞
⎟ ⎟ ⎠
=
⎛
⎜ ⎜ ⎝
⎞
⎟ ⎟ ⎠
⎛
⎜ ⎜ ⎝
⎞
⎟ ⎟ ⎠
(1)
This kind of mixing has been known in the quark sector for decades and the analogous matrix U is called Cabbibo-Kobayashi-Maskawa matrix. The corresponding mixing matrix in the lepton sector is named Pontecorvo-Maki-Nakagawa-Sato (PMNS)-matrix [?]. The unitary matrix U in eq. 1 can be parametrised in the following form
U =
⎛
⎜ ⎜ ⎝
−s12c23− c12s23s13eiδ c12c23− s12s23s13eiδ s23c13 s12s23− c12s23s13eiδ −c12s23− s12c23s13eiδ c23c13
⎞
⎟ ⎟ ⎠
(2)
where si j = sinθi j,ci j = cosθi j (i, j = 1,2,3). The phase δ is a source for CP-violation and like in the quark sector cannot be removed by rephasing the neutrino fields. The Majorana case, ie. the requirement of particle and antiparticle to be identical, restricts the freedom to redefine the
fundamental fields even further. The net effect is the appearance of a CP-violating phase even for two flavours. For three flavours two additional phases have to be introduced resulting in a mixing matrix of the form
U =UPMNSdiag(1,eiα2,eiα3) (3)
with the two new Majorana phases α2 and α3. These phases again might only be accessible in double beta decay, they are not accessible in neutrino oscillation experiments. They are a further source of CP-violation. Based on the observations from neutrino oscillations (see (Kayser 2006)), various neutrino mass models have been proposed. These can be categorized as normal hierarchy (m3 m2 ≈ m1), inverted hierarchy (m2 ≈ m1 m3) and almost degenerate (m3 ≈ m2 ≈ m1) neutrinos (Fig. 1). A key result, based on the observed Δm2 in atmospheric neutrinos, is the existence of a neutrino mass eigenstate in the region around 10-50 meV. This is the minimal value neccessary, because it corresponds to the square root of the measured Δm2 in case one of the mass eigenstates is zero. Fixing the absolute mass scale is of outmost importance, because it will fix the mixing matrix and various other important quantities will then be determined, like the contribution of neutrinos to the mass density in the Universe. Traditionally, laboratory experiments search for a finite neutrino rest mass by exploring the endpoint energy of the electron spectrum in tritium beta decay. Currently a limit for the electron neutrino mass of less than 2.2 eV has been achieved (Bornschein 2006). A similar limit is obtained by analysing recent cosmic microwave background measurements using the WMAP satellite combined with large scale galaxy surveys and Lyman-α systems, see e.g. (Lesgourges 2006). However, there are about two orders of magnitude difference with respect to the region below 50 meV and even the next generation beta decay experiment, called KATRIN, can at best lead to an improvement of a factor ten. However it should be noticed, that beta decay and double beta decay are measuring slightly different observables and are rather complementary than competitive. Therefore, very likely double beta decay is the only way to explore the region below 100 meV.
