In the seesaw mechanism

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Flavour, neutrinos and CP violation · Flavour, neutrinos and CP violation

Symmetry and Flavour, Ch Neutrino masses, mixing and oscillations

Problem

In the seesaw mechanism, a Dirac mass

m_D

and a heavy right-handed Majorana mass

M_R

combine, for

m_D \ll M_R

, to give a light neutrino mass

m_\nu \approx m_D^2/M_R

, and the light neutrino is then its own antiparticle. ((a)) A model puts the heavy partner at

M_R = 1\times10^{15}\,\mathrm{GeV}

and must reproduce

m_\nu = 0.05\,\mathrm{eV}

. Find the Dirac mass

m_D

it needs, in GeV, and say whether it is closer to the electron mass (

0.511\,\mathrm{MeV}

) or to the masses of the

W

and

Z

. ((b)) For a Majorana neutrino, neutrinoless double beta decay has an amplitude proportional to

m_{\beta\beta}=\big|\sum_iU_{ei}^2m_i\big|

. Take the normal ordering with

m_1=0

, so that

m_2=\sqrt{\Delta m^2_{21}}

and

m_3=\sqrt{\Delta m^2_{31}}

, with

\Delta m^2_{21}=7.49\times10^{-5}\,\mathrm{eV^2}

\Delta m^2_{31}=2.513\times10^{-3}\,\mathrm{eV^2}

|U_{e2}|^2=0.301

and

|U_{e3}|^2=0.0222

. The relative phase between the two surviving terms is unknown. Find the largest and the smallest possible

m_{\beta\beta}

. ((c)) Compare your range with KamLAND-Zen's bound, which lies somewhere between

0.028

and

0.122\,\mathrm{eV}

, and explain why an observed neutrinoless decay, at any rate, would show that neutrinos are their own antiparticles.

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