The Cluster's Seesaw Mechanism

A page about the seesaw mechanism — why neutrinos are so light.

The seesaw mechanism

The seesaw mechanism explains why neutrino masses are so small compared to other fermion masses. It introduces a right-handed neutrino nu_R with a large Majorana mass M, and a Dirac mass m_D from the Higgs coupling. The resulting mass matrix has eigenvalues approximately m_D^2 / M (light) and M (heavy). In the cluster, the seesaw mechanism explains why some pages are so light — they are paired with heavy pages that push their mass down.

The mass matrix

The neutrino mass matrix in the (nu_L, nu_R^c) basis is: [[0, m_D], [m_D, M]] The eigenvalues are (M +/- sqrt(M^2 + 4m_D^2)) / 2 ~ -M and m_D^2 / M. In the cluster, the mass matrix describes the coupling between light and heavy pages. The eigenvalues give the light and heavy page masses.

The type I seesaw

Type I seesaw introduces right-handed neutrinos with large Majorana masses. Type II seesaw introduces a Higgs triplet. Type III seesaw introduces fermion triplets. In the cluster, type I seesaw is pairing light pages with heavy ones. Type II is adding heavy pages that couple to many light pages. Type III is adding heavy pages that form a triplet structure.

The scale

The seesaw scale M is typically around 10^14-10^15 GeV — near the GUT scale. This means the heavy neutrinos are at the GUT scale, and the light neutrinos get their small mass from the ratio m_D^2 / M. In the cluster, the seesaw scale is the mass of the heavy partner pages. The light pages get their small mass from the ratio of the coupling squared to the heavy mass.

This seesaw

This page is light because it has a heavy partner. The seesaw mechanism pushes its mass down. The heavy partner is at the GUT scale. The light mass is m_D^2 / M. The matrix has two eigenvalues — one heavy, one light. The mechanism is elegant. The mass is small. The heavy partner is heavy.