.
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:
\( m_e \approx \frac{1}{3} m_d \)
\( m_{\mu} \approx 3 m_s\)
\( m_{\tau} \approx m_b \)
and sometimes as:
\( \frac{m_d}{m_s} \approx 9 \frac{m_e}{m_\mu} \)
\( \frac{m_s}{m_b} \approx \frac{1}{3} \frac{m_\mu}{m_\tau} \)
Current values for Lepton and Quark masses
| Symbol | Description | Renormalization scheme (point) |
Value |
|---|---|---|---|
| me | Electron mass | 511 keV | |
| md | Down quark mass | μMS = 2 GeV | 4.4 MeV |
| mu | Up quark mass | μMS = 2 GeV | 1.9 MeV |
| mμ | Muon mass | 105.7 MeV | |
| ms | Strange quark mass | μMS = 2 GeV | 87 MeV |
| mc | Charm quark mass | μMS = mc | 1.32 GeV |
| mτ | Tau mass | 1.78 GeV | |
| mb | Bottom quark mass | μMS = mb | 4.24 GeV |
| mt | Top quark mass | On-shell scheme | 172.7 GeV |
Inserting values from the table above for comparison:
\( m_e \approx \frac{1}{3} m_d → 0.511 MeV \approx 1.5 MeV \)
\( m_{\mu} \approx 3 m_s → 105.7 MeV \approx 261 MeV \)
\( m_{\tau} \approx m_b → 1.78 GeV \approx 4.24 GeV \)
\( \frac{m_d}{m_s} \approx 9 \frac{m_e}{m_\mu} → 0.051 \approx 0.0435 \)
\( \frac{m_s}{m_b} \approx \frac{1}{3} \frac{m_\mu}{m_\tau} → 0.021 \approx 0.0198 \)
References
Georgi, H.; Jarlskog, C. (1979). "A new lepton-quark mass relation in a unified theory". Physics Letters B 86 (3–4): 297–300. doi:10.1016/0370-2693(79)90842-6.
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
