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_d0.511 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

  1. 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.


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