Georgi–Jarlskog mass relation

In grand unified theories of the SU(5) or SO(10) type, there is a mass relation predicted between the electron and the down quark, the muon and the strange quark and the tau lepton and the bottom quark called the Georgi–Jarlskog mass relations. The relations were formulated by Howard Georgi and Cecilia Jarlskog.[1]

At GUT scale, these are sometimes quoted as:

${\displaystyle m_{e}\approx {\frac {1}{3}}m_{dGUT}}$

${\displaystyle m_{\mu }\approx 3m_{sGUT}}$

${\displaystyle m_{\tau }\approx m_{bGUT}}$

In the same paper it is written that:

${\displaystyle m_{dGUT}\approx {\frac {1}{3}}m_{d}}$

${\displaystyle m_{sGUT}\approx {\frac {1}{3}}m_{s}}$

${\displaystyle m_{bGUT}\approx {\frac {1}{3}}m_{b}}$

Meaning that:

${\displaystyle m_{d}\approx 9m_{e}}$ ${\displaystyle error=5\%}$

${\displaystyle m_{s}\approx m_{\mu }}$ ${\displaystyle error=21\%}$

${\displaystyle m_{b}\approx 3m_{\tau }}$ ${\displaystyle error=26\%}$