Neutrinoless Double Beta Decay and Neutrino Mass — A Point of Principle

1. Neutrinoless Double Beta Decay and Neutrino Mass — A Point of Principle

2. e– e– Nucl’ Nucl Neutrinoless Double Beta Decay[0] This is the promising approach to testing whether neutrinos are their own antiparticles. It will be sought with greatly increased sensitivity.

3. i SM vertex e– e– i  Mixing matrix Uei Uei i W– W– Nuclear Process Nucl’ Nucl To estimate the sensitivity required — we assume that 0 is dominated by a diagram with Standard Model vertices:

4. In SM vertex i e– e– i  Mixing matrix Uei Uei i W– W– Nuclear Process Nucl’ Nucl Mass (i) the i is emitted [RH + O{mi/E}LH]. Thus, Amp [i contribution]  mi Amp[0]   miUei2 m i — Down the Garden Path —

5. The Trap This makes it look as if 0 needs  mass only because of a helicity mismatch. Suppose we had a parity-conserving world, that treats right-handed and left-handed particles in the same way. Couldn’t we then have 0 without any  mass? No!  mass is still required.

6. e– e– Nucl’ Nucl ()R L X mL Why? — manifestly does not conserve L. But the Standard Model (SM) weak interactions do conserve L. Absent any non-SM L-violating interactions, the L = 2 of 0 can only come from Majorana neutrino masses, such as — mL(LcL + LLc)

7. X mL Assuming Standard Model vertices, 0 is — e– e– ()R L W– W– Nuclear Process Nucl’ Nucl The Majorana neutrino mass term plays two roles: Violate L Flip handedness It will be needed for (1) even when not needed for (2).

8. A Parity-Conserving Toy-Model Illustration Suppose there is only one generation. Suppose the W couples to the electron and neutrino via a parity-conserving vector current: Suppose the neutrino mass term is also L  R invariant: We take mM,D real, mM > mD, and neglect the electron mass.

9. The neutrino mass eigenstates are the two Majorana particles — , with mass , and . , with mass In terms of them —

10. e– e– i  i = 1,2 W– W– Consider now the particle-physics part of 0 — If the electrons both emerge Left-Handed (LH), only the LH leptonic currents contribute. For this final state, one finds that the amplitude, ALL, obeys — The amplitude is proportional to the Majorana  mass mM.

11. Similarly, if both electrons emerge right-handed, the amplitude, ARR, obeys — If the electrons emerge with opposite handedness, both the LH and RH currents are involved, and one finds that the amplitude, ALR, obeys — The amplitude is proportional to the Majorana  mass mM.

12. eR– eL– ()R LH current RH current W– W– L R X X mD mM Why ALR is also proportional to the Dirac mass mD: BK, Petcov, and Rosen; Enqvist, Maalampi, and Mursula The process is — Two flips of handedness are needed.

13. Summary Absent L-nonconserving interactions from beyond the Standard Model, 0 requires Majorana neutrino mass. This mass is needed to introduce L-nonconservation, even if it is not needed for any other reason.