Posted: 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.
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.