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The Standard Model Lecture III

This lecture discusses the challenges and constraints faced by a fourth generation model in high energy physics, including the need for heavy neutrinos, almost degenerate quark and lepton doublets, and the parameters related to Fermion families. It also explores the possibility of grand unification and experimental limits on proton lifetime.

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The Standard Model Lecture III

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  1. The Standard ModelLecture III Thomas J. LeCompte High Energy Physics DivisionArgonne 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 Zwidth and branching fractions (20% invisible). • Next, the quark and lepton doublets need to bealmost degenerate: • The W mass loops are sensitive to the massdifferences between doublet members • The top and bottom already have“saturated” this.

  4. Peskin-Takeuchi Parameters • Peskin and Takeuchi attempted to parameterize all of the EWKdata 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 areother difficulties a 4th generation faces: • Neutral K’s and B’s mix quickly, butneutral 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 seemto reach a common value at 1016 GeVor so suggests some sort of unification. • This naturally explains why atoms areneutral: • Quarks and leptons are in the samemultiplets. • 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. • 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. Quarks and leptons live in the same SU(5) multiplet. (e.g.) Proton decay is mediated by the X:

  9. Experimental Limits • Super-Kamiokande has measured the protonlifetime (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 familyassignments are: • More commonly, people look at other gauge groups: SO(10), U(1)xSU(5)… and not

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