1. The Standard Model Lecture III
Thomas J. LeCompte
High Energy Physics Division Argonne National Laboratory

2. A Fourth Generation?

3. A Fourth Generation
There are severe electroweak constraints on such a generation.
First, the neutrino must be heavy (>45 GeV)
Otherwise the Z would decay to these neutrinos, which would be visible in the Z width and branching fractions (20% invisible).
Next, the quark and lepton doublets need to be almost degenerate:
The W mass loops are sensitive to the mass differences between doublet members
The top and bottom already have “saturated” this.

4. Peskin-Takeuchi Parameters
Peskin and Takeuchi attempted to parameterize all of the EWK data in terms of three values:
S: (“stuff”) related to the number of fermion families
T: (“isospin”) related to the mass differences in doublets
U: (“useless”) includes dimension-8 operators, and usually set to 0.
This framework allows easy comparison between data and different theories.
For example, a degenerate 4th generation increases S by 1/(6p) and leaves T and U unchanged
The SM has S=T=U=0
A 4th generation is barely allowed – a conspiracy between S and T could still fit with some difficulty.
The new doublets need to be almost degenerate.

5. A Tight Fit
In addition to precision EWK, there are other difficulties a 4th generation faces:
Neutral K’s and B’s mix quickly, but neutral D’s mix slowly.
With 3 generations, this is because the heaviest u-type quark (top) is much heavier than the heaviest d-type quark (bottom)
With a heavy, degenerate 4th generation, this is no longer true: it would have to be due to CKM suppression
Adds 3 new angles and 2 new phases: enough to do this.
It’s possible to have a 4th generation, but all of the parameters associated with it have to conspire to make it look like there are exactly 3 generations.

6. Grand Unification

7. Grand Unification
Face it: SU(3)QCD x SU(2)L x U(1)Y is not the obvious first choice for the symmetry group of the SM.
Perhaps these are subgroups of a larger group
The “smallest” such group is SU(5)
The fact that the coupling constants seem to reach a common value at 1016 GeV or so suggests some sort of unification.
This naturally explains why atoms are neutral:
Quarks and leptons are in the same multiplets.
The theory is naturally anomaly-free if there are only complete SU(5) multiplets.

8. SU(5) Multiplets
This theory has 24 gauge bosons. (Remember, every multiplet has to be complete) The Standard Model has 12 (8 gluons, 2 W’s, a Z and a photon), so there must be 12 new ones. These new ones, the X+4/3 and Y-1/3 carry color in addition to electroweak charges.
Quarks and leptons live in the same SU(5) multiplet. (e.g.)
Proton decay
is mediated by the X:
The X has to have mass less than the GUT scale: 1016 GeV
That sets a limit on the proton lifetime t(p) < 1028 – 1031 years.

9. Experimental Limits
Super-Kamiokande has measured the proton lifetime (in the pe+ channel) at >1031 years.
Minimal SU(5) is in trouble
One can play tricks to stretch this
What evidence do we have that the family assignments are:
More commonly, people look at other gauge groups: SO(10), U(1)xSU(5)…
and not