SU(6)

The Lie group SU(6) occurs in both the Standard Model and in some grand unified theories.

In the Standard Model

SU(6) is an approximate symmetry that classifies lighter baryons and mesons, explaining many patterns in the particle zoo. It combines SU(3) flavour and SU(2) spin. Quarks u,d,s, with spin up and down belong to the fundamental representation 6. Mesons belong to the 35 representation and baryons to the 56 representation obtained from the product quark-antiquark and quark-quark-quark, respectively.

In Grand Unified Theories

The SU(6) grand unified theory includes the Georgi–Glashow SU(5) gauge group.

The fermionic matter content of this model comes in three generations (copies) of

[math]\displaystyle{ 15\oplus \bar{6}\oplus \bar{6} }[/math]

as SU(6) representations.

This gauge group is broken down to the Georgi–Glashow model by a pair of 6_H/[math]\displaystyle{ \bar{6}_H }[/math] Higgs fields.

[math]\displaystyle{ SU(6)\begin{matrix}6_H/\bar{6}_H\\ \longrightarrow \end{matrix} SU(5)\times U(1) }[/math]

The fermions decompose as

[math]\displaystyle{ 15\rightarrow 10\oplus 5 }[/math]

[math]\displaystyle{ \bar{6}\rightarrow \bar{5}\oplus 1 }[/math]

The Yukawa coupling [math]\displaystyle{ \bar{6} \bar{6}_H 15 }[/math] causes 5 and a [math]\displaystyle{ \bar{5} }[/math] SU(5)-rep of fermions to pair up and acquire GUT scale masses for each generation.

An adjoint Higgs 35_H breaks the model down further to the standard model.

Recently, a new type of grand unified theory based on SU(6) group has been proposed to realize a unification of strong and electroweak interactions.^[1] The work provides a complete form of 35 generators in SU(6) group.

References

0.00 (0 votes)