Georgi–Jarlskog mass relation
# 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.

At GUT scale, these are sometimes quoted as:

    $m_{e}\approx {\frac {1}{3}}m_{dGUT}$
    $m_{\mu }\approx 3m_{sGUT}$
    $m_{\tau }\approx m_{bGUT}$

In the same paper it is written that:

    $m_{dGUT}\approx {\frac {1}{3}}m_{d}$
    $m_{sGUT}\approx {\frac {1}{3}}m_{s}$
    $m_{bGUT}\approx {\frac {1}{3}}m_{b}$

Meaning that:

    $m_{d}\approx 9m_{e}$ $error=5\%$
    $m_{s}\approx m_{\mu }$ $error=21\%$
    $m_{b}\approx 3m_{\tau }$ $error=26\%$

Current values for Lepton and Quark masses :

| Symbol | Description | Renormalization scheme (point) | Value |
| - | - | - | - |
| $m_e$ | Electron mass | | 0.511 MeV |
| $m_u$ | Up quark mass | $μ_{MS}$ = 2 GeV | 1.9 MeV |
| $m_d$ | Down quark mass | $μ_{MS}$ = 2 GeV | 4.4 MeV |
| $m_s$ | Strange quark mass | $μ_{MS}$ = 2 GeV | 87 MeV |
| $m_μ$ | Muon mass | | 105.7 MeV |
| $m_c$ | Charm quark mass | $μ_{MS}$ = $m_c$ | 1.32 GeV |
| $m_τ$ | Tau mass | | 1.78 GeV |
| $m_b$ | Bottom quark mass | $μ_{MS}$ = $m_b$ | 4.24 GeV |
| $m_t$ | Top quark mass | On-shell scheme | 172.7 GeV |
