Do right-handed neutrinos provide more anomaly-free U(1) solutions?

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Breo
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If we consider de right-handed neutrino there would be more anomaly-free solutions than hypercharge for a U(1)?
 
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Thank you.

If we would assign one hypercharge to a field that would determine the value of all others hypercharges? Are those predicted, also, by only one anomaly-free solution?
 
If you guys could tell me a good textbook about the open problems in SM I would be very grateful.