How are particles assigned to 16bar representation in SO(10)?

[Saschenka]

Dear forum members!

Could someone tell me a reference, where it is accurately described how the SM particles + right-handed neutrino are assigned to the $\overline{16}$ representation in SO(10) models? I mean: Which component of the particle vector represents which particle?

Mainly I am interested in the derivation of the relations for all the fermion mass matrices, e.g. as they are stated (without proof) in eqn. 123 in hep-ph/9906433. Therefore I would also need the VEVs of the different Higgs fields involved. The reference noted there does not explain how the relations come about either.

Thank you all!

 

[AndyW]

Dear forum members,

Thank you for your question. The assignment of SM particles and right-handed neutrinos to the \overline{16} representation in SO(10) models is based on the embedding of the SM gauge group into SO(10). This embedding is determined by the gauge symmetry breaking pattern, which is dictated by the VEVs of the Higgs fields involved.

The detailed derivation of the relations for fermion mass matrices can be found in various sources, such as the original paper by Georgi and Glashow (Phys. Rev. Lett. 32, 438 (1974)), as well as in more recent papers like hep-ph/9906433. The VEVs of the Higgs fields involved can also be found in these papers.

Additionally, there are several textbooks and review articles that discuss the SO(10) model and its particle content in detail, such as "Grand Unified Theories and Proton Decay" by Mohapatra and Pati, and "Grand Unified Theories: An Introduction" by Langacker.

I hope this helps answer your question. If you need further clarification or have any other questions, please do not hesitate to ask.