PHOTO : The E9

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where [LAMBDA] is the new physics scale responsible for the existence of the excited leptons, [[??].sub.[mu]v] and [B.sub.[mu]v] are the field strength tensors, g and g are the gauge couplings, f and f' are the scaling factors for the gauge couplings of SU(2) and U(1), [[sigma].sup.[mu]v] = i([[gamma].sup.[mu]][[gamma].sup.v] - [[gamma].sup.v][[gamma].sup.[mu]])/2 where [[gamma].sup.[mu]] are the Dirac matrices, [??] denotes the Pauli matrices, and Y is

hypercharge.

The group U[(1).sub.Y] for weak

hypercharge Y then reduces the symmetry to being gauge equivalent so that particles and antiparticles have the same positive mass.

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The resulting vertex takes the form bino-sfermion-fermion, L [contains] -[X.sub.L][[??].sub.L][bar.[chi]][P.sub.L]f - [X.sub.R][[??].sub.R][bar.[chi]][P.sub.R]f, where tree-level couplings, [X.sub.L,R] = [square root of 2] g'[Y.sub.L,R], are expressed in terms of the

hypercharge assignment [Y.sub.L,R] of the fermion Weyl spinors.

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The gauge boson coupling to Higgs and [eta] (the equivalent of (4)) will be (neglecting

hypercharge)

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We also add an [SU(3).sub.c] (color) triplet, [SU(2).sub.L] singlet, [U(1).sub.Y]

hypercharge 2/3, and vector-like quark (VLQ) U.

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There are broadly three classes of such models, namely, type I, type II, and type III seesaw models requiring involvement of right-handed neutrinos, a [SU(2).sub.L] triplet scalar with

hypercharge Y = 2 and [SU(2).sub.L] hyperchargeless triplet fermions, respectively.

where [LAMBDA] is the new physics scale, [W.sub.[mu]v] and [B.sub.[mu]v] are the field strength tensors, [??] denotes the Pauli matrices, Y is the

hypercharge, g and g' are the gauge couplings, and f and f' are the scaling factors for the gauge couplings of SU(2) and U(1); [[sigma].sup.[mu]v] = i([[gamma].sup.[mu]][[gamma].sup.v]- [[gamma].sup.v][[gamma].sup.[mu]])/2 with [[gamma].sup.[mu]] being the Dirac matrices.