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 3m_{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
m_e	Electron mass		511 keV
m_d	Down quark mass	μ_MS = 2 GeV	4.4 MeV
m_u	Up quark mass	μ_MS = 2 GeV	1.9 MeV
m_μ	Muon mass		105.7 MeV
m_s	Strange quark mass	μ_MS = 2 GeV	87 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

Inserting values from the table above for comparison:

m_{e}\approx {\frac {1}{3}}m_{d}

→

0.511MeV\approx 1.5MeV

m_{{\mu }}\approx 3m_{s}

→

105.7MeV\approx 261MeV

m_{{\tau }}\approx m_{b}

→

1.78GeV\approx 4.24GeV

{\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. Bibcode:1979PhLB...86..297G. doi:10.1016/0370-2693(79)90842-6.

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