- #1
Max
[[Mod. note -- I have "repaired" various non-ASCII characters as best
as I can, but it's *much* safer if postings are submitted in 7-bit-ASCII
only. In particular, Microsoft Windows "smart quotes" tend to get
quite mangled before they arrive at s.p.r moderstors' mailboxes... :(
-- jt]]
In the SU(5) grand unified theory, there are two sets of Higgs fields.
They are the {5} and {24} representations (we don't consider {45}
here). {24} breaks SU(5) down to SU(3)c*SU(2)l*U(1)y, and gives mass
to X gauge bosons via Higgs mechanism. {5} breaks SU(3)c*SU(2)l*U(1)y
further down to SU(3)c*U(1)em, and gives mass to W+- and Z gauge
bosons.
However, only {5} gives mass directly to the fermions via a Yukawa
type coupling. The conventional wisdom is that the "Higgs
representation must appear in the tensor product of the SU(5)
representations in which the fermion and its antifermion
appear." (H.Georgi's Lie Algebras in Particle Physics, Page 234-235).
This reasoning sounds empirical to me, because it's based on the way
fermion and its antifermion are assigned to different representations
of SU(5). Is there any first principle which explains why {24} is not
mass generating for fermions?
as I can, but it's *much* safer if postings are submitted in 7-bit-ASCII
only. In particular, Microsoft Windows "smart quotes" tend to get
quite mangled before they arrive at s.p.r moderstors' mailboxes... :(
-- jt]]
In the SU(5) grand unified theory, there are two sets of Higgs fields.
They are the {5} and {24} representations (we don't consider {45}
here). {24} breaks SU(5) down to SU(3)c*SU(2)l*U(1)y, and gives mass
to X gauge bosons via Higgs mechanism. {5} breaks SU(3)c*SU(2)l*U(1)y
further down to SU(3)c*U(1)em, and gives mass to W+- and Z gauge
bosons.
However, only {5} gives mass directly to the fermions via a Yukawa
type coupling. The conventional wisdom is that the "Higgs
representation must appear in the tensor product of the SU(5)
representations in which the fermion and its antifermion
appear." (H.Georgi's Lie Algebras in Particle Physics, Page 234-235).
This reasoning sounds empirical to me, because it's based on the way
fermion and its antifermion are assigned to different representations
of SU(5). Is there any first principle which explains why {24} is not
mass generating for fermions?