I am getting confused regarding $U(1)$ normalization while trying to check unification of gauge coupling constants in a class of models. For $ U(1)_Y $ the normalization constant square is $ \surd{3/5} $ if we take the GUT group SU(5) . For $ U(1)_{B-L} $ its according to some convention $ \surd{3/8} $ and according to some others $ \surd{3/2} $ if we take the GUT group $ SO(10) $. Initially I was following a paper by Manfred Lindner where he has taken $ \surd{3/8 } $. Today I have seen a paper by R. Mohapatra where he has taken $ \surd{3/2} $. I am not being able to derive any one of them from the $ SO(10) $ multiplets. Depending on the normalization the boundary condition for intermediate symmetry breaking also changes and that is going to affect the running. My calculations are giving some nonsense results now where the U(1) coupling is hitting the Landau Pole much before the preferred unification scale. May be I have to do all the calculations more carefully.
Monday, February 22, 2010
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