**#57** by **lpetrich** » Jul 20, 2011 11:01 pm

One can construct a sequence of enlarged symmetries:

Broken Standard Model: SU(3) * U(1) -- QCD, photon

Unbroken Standard Model: SU(3) * SU(2) * U(1) -- QCD, electroweak (weak isospin, weak hypercharge)

Georgi-Glashow: SU(5)

SO(10)

E6

E8

First, the (Minimal Supersymmetric) Standard Model.

Broken Standard Model: particles have quantum numbers (spin, QCD multiplet, electric charge)

Gluon, gluino: (1,8,0), (1/2,8,0)

Photon, W, Z: (1,1,0), (1,1,+-1), (1,1,0)

Neutralino, chargino: (1/2,1,0), (1/2,1,+-1)

Higgs: (0,1,0), (0,1,+-1)

Up quark antiquark / Sup qk aqk: (1/2,3,2/3), (1/2,3*,-2/3), (0,3,2/3), (0,3*,-2/3)

Down quark antiquark / Sdown qk aqk: (1/2,3,-1/3), (1/2,3*,1/3), (0,3,-1/3), (0,3*,1/3)

Neutrino antineutrino / Sneutrino santineutrino: (1/2,1,0), (1/2,1,0), (0,1,0), (0,1,0)

Unbroken Standard Model. Left and right handed parts of elementary fermions are separate in it. Quantum numbers: (QCD multiplet, weak-isospin multiplet, weak hypercharge)

Gauge: spins 1, 1/2

Gluon g: (8,1,0)

W: (1,3,0)

B (1,1,0)

Left-handed EF's, Higgs: spins 0, 1/2

Q: (3,2,1/6), U*: (3*,1,-2/3), D*: (3*,1,1/3)

L: (1,2,-1/2), N*: (1,1,0), E*: (1,1,1)

Hu: (1,2,1/2), Hd: (1,2,-1/2)

Right-handed EF's, Higgs: spins 0, 1/2

Q*: (3*,2,-1/6), U: (3,1,2/3), D: (3,1,-1/3)

L*: (1,2,1/2), N: (1,1,0), E: (1,1,-1)

Hu*: (1,2,-1/2), Hd*: (1,2,1/2)

Weak isospin works like angular momentum, meaning that WI value I gives multiplicity 2*I+1 and projected values I3 = I, I-1, ..., -I

Electric charge = (projected isospin I3) + (weak hypercharge Y)

The W breaks into I3 = +1 (Q = 1), I3 = 0 (Q = 0), and I3 = -1 (Q = -1)

The first and third are W+ and W-, the second mixes with the B to gives the photon and the Z

Their superpartners (winos, binos) mixed with the Higgs superpartners (higgsinos) to give charginos and neutralinos

Higgses break into into combinations of I3 = +1/2 or -1/2 and Y = +1/2 or -1/2, giving charges +1, 0, and -1

The U and the I3 = +1/2 part of the Q give the up quark (Q = 2/3)

The D and the I3 = -1/2 part of the Q give the down quark (Q = -1/3)

The N and the I3 = +1/2 part of the L give the neutrino (Q = 0)

The E and the I3 = -1/2 part of the L give the electron (Q = -1)

The U* and the I3 = -1/2 part of the Q* give the up antiquark (Q = -2/3)

The D* and the I3 = +1/2 part of the Q* give the down antiquark (Q = 1/3)

The N* and the I3 = -1/2 part of the L* give the antineutrino (Q = 0)

The E* and the I3 = +1/2 part of the L* give the positron (Q = 1)

I'm fuzzing over generations; up quarks include charm and top ones, down quarks include strange and bottom ones, and electrons include muons and tauons.