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

A Fourth Generation?

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.

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.

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.

Grand Unification

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.

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.

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