Teorías Sobre Estilos de aprendizaje:

Imagine we have a source of only LH neutrinos fromπ+ decays. These neutrinos may either be either Dirac or LH Majorana neutrinos. Let’s assume that we can flip the helicity of the

neutrinos produced. If the helicity-flipped neutrinos are Majorana particles and they would behave like anti-neutrinos when they interact. On the other hand, if the helicity-flipped neutrinos were Dirac, then only sterile RH neutrinos would be emitted. They do not interact at all. In an ideal world, we would be able to build the experiment described above, however it is currently impossible. Instead, we are pursuing another route: neutrinoless double-β decay (0νββ), which is a beyond the standard model analogue to singleβ-decay.

Neutrinoless double-beta decay

Single-β decay is energetically forbidden for many even-even nuclei. However, a second order process that changes a nucleus atomic number, Z, by two units is possible. In this process, two electrons are emitted along with two anti-neutrinos. This process is called two-neutrino double-β decay (2νββ). A more interesting process is neutrinoless double-beta decay (0νββ)7, which as the name states emits zero anti-neutrinos,

M(A,Z)→D(A,Z+2) + 2e−. (1.32)

This equation shows us that this process violates lepton number, but there is nothing in the SM that says lepton number must be conserved. This process can be visualized as an exchange of a virtual neutrino between two neutrons within a nucleus, see Figure 1.7. In the SM of weak interactions, the first neutron will emit a right-handed anti-neutrino. But, the second neutron requires the absorption of a left-handed neutrino. Several things need to happen for this to occur, (1) the neutrino must have mass (and we know it does) so that it is not in a pure helicity state and (2) the neutrino and anti-neutrino would have to be indistinguishable, hence a Majorana particle. Neutrinoless double-beta decay is the only viable way to show that neutrinos are either Majorana or Dirac. The discovery of this decay would signal that the neutrino is a Majorana fermion (its own anti-particle) and that lepton number is violated, having significant implications for our understanding of the nature of the neutrino and fundamental interactions. Also, since the decay rate (Equation 1.33) is

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proportional to the effective Majorana mass (Equation 1.34) of the electron neutrino, the scale and hierarchy of the masses could potentially be set.

(T₁0_/ν₂)−1 =G0ν|hmββi|2 M_F0ν− gA gV 2 M_GT0ν 2 (1.33) hmββi= X i U_ei2mi = c 2 13c212m1+c213s212m2ei2φ2 +s213m2ei2φ3 (1.34)

In Equation 1.33 G0ν is the two-body phase-space factor including coupling constant,M_F0ν

Figure 1.7: The Feynman diagrams for 0νββdecay (left) and 2νββdecay (right). 0νββoccurs with the exchange of a virtual Majorana neutrino, which is only possible if the neutrino is its own anti-particle. Figure from Ref. [64].

and M_GT0ν are the Fermi and Gamow-Teller matrix elements, respectively. The constantsgA and gV are the axial-vector and vector relative weak coupling constants, respectively. The quantity hmββi is the effective Majorana mass, which is given in Equation 1.34 where eiφi are the unknown Majorana phases. The termhmββicontains all of the interesting physics of 0νββ and is equivalent to zero if the neutrino is a Dirac particle. However, the presence of these unknown phases adds a bit of uncertainty to the determination of hmββi since terms may cancel. Furthermore, the nuclear matrix elements, M0ν

F and MGT0ν , must be calculated and the current literature values have a spread of a roughly a factor of two [7]. Finally, there may be other processes that may contribute to 0νββ. However, if 0νββ is observed,

independent measurements with several isotopes would allow for the extraction ofhmββi[65].

Experimental Aspects of 0νββ

The signal for 0νββ would be a peak in the kinetic energy spectrum corresponding to the two electrons. This peak is located at the endpoint energy as determined by the mass differences of the parent and daughter nuclei (the Q-value), see Figure 1.8. This is sharp contrast to the 2νββ energy spectrum, which would be a continuous spectrum since the energy of the decay is shared between four particles, the two neutrinos and two electrons. Experimental searches for 0νββ have been carried out using several nuclei, including but not limited to,

48_Ca,76_Ge,82_Se, 96_Zr,100_Mo,116_Cd, 128_Te, 130_Te, 136_{Xe and} 150_{Nd. In addition, a subset of}

the Heidelberg-Moscow collaboration claim to have measuredT₁0_/ν₂ = (1.19+2_−0..99₅₀)×1025 years andhmββi= 0.22−0.35 eV in76Ge [66]. Since there is such a large uncertainty in the nuclear matrix elements, convincing evidence of the Majorana nature of the neutrino will require several experiments to have observed 0νββ. A number of experiments are coming online in the near future which can either confirm or refute the claim of an observation made by [66]. One of which is the Majorana Experiment [67–69], which will be discussed briefly in the

next section and in more detail in Chapter 3.