P780.02 Spring 2003 L12 Richard Kass

The properties of the Z0

For about ten years the Z0 was studied in great detail at two accelerator complexes: LEP at CERN and SLC at SLACBoth of these accelerators were able to produce millions of Z’s using the reaction:

ffZee 0

The fermions could be charged leptons, neutrinos, and quarks. The mass the fermion has to be < MZ/2. (MZ=91.18820.0022 GeV) Both accelerators collided e+e- beams with energy MZ/2. The standard model makes many predictions about the decay modes of the Z.

f

e+

Z0

e-

ff

e+

e-

f

At center of mass energies close to MZ the reaction with the Z dominates over thereaction with the .

e+e- cross section vs CM energy

dominates

P780.02 Spring 2003 L12 Richard Kass

The Decay of the Z0

]|||[|48

)( 2222

0 fA

fV

ZZ cccMg

KffZ

The standard model predicts that the decay rate into fermion anti-fermion pairs is:

f

Z0

f

With K=1 for leptons and K=3 (color factor) for quarks.cV

f and cAf are the vertex factors listed in lecture 11.

Predicted Standard Model Z decay Widths (first order)fermion predicted (MeV)e, , 84

e, , 167u, c 300d ,s ,b 380

Comparison of experiment and standard model (from PDG2000)quantity experiment standard model(hadrons) 1743.92.0 1742.21.5 MeV(neutrinos) 498.81.5 501.650.15 MeV(l+l-) 83.960.09 84.000.03 MeV

Z cannot decay into thetop quark since Mt>MZ.

excellentagreement

See Griffithspage 327

P780.02 Spring 2003 L12 Richard Kass

Z Decay and the Number of NeutrinosThe standard model predicts the following cross section:

M&S 9.1.422222

00

2

20

)(

)()(12)(

ZZZcmcm

Z

MME

XZeeZ

E

MXZee

In this equation Z is the “total width” of the Z, the sum of all the partial widths listed on the previous page. The “X” refers to the final state and is usuallythe sum of all measured hadronic (quark) final states. What is of interest here is that while the height of the curve depends on X the shape of the curve depends onZ, the full width. The full width depends on the number of neutrino species:

)()(2)(3)(3 0000 ZnuuZddZllZZ

Each neutrino species contributes 167 MeV to Z.By varying the energy of the beams (e+e-ZX) can be mapped out and Z determined.

Excellent agreement with only 3 (light) neutrino families!

Data from the four LEP experiments.All experiments are measuring the cross sectionfor e+e-hadrons (“X”) as a function ofcenter of mass energy.

P780.02 Spring 2003 L12 Richard Kass

How Good is the Standard Model ?

The standard model of particle physics (Glashow, Weinberg, Salam) is verysuccessful in explaining electro-weak phenomena. But we may be seeingsome cracks in the model!

Summary of standard model measurements compared withpredictions. Taken from a talkby Kevin McFarland (Prof. at U of Rochester and memberof NuTeV).

P780.02 Spring 2003 L12 Richard KassLimits of Standard ModelWhat’s in the standard model+QCD?Quantum field theory based on SU(3)xSU(2)xU(1) symmetry containing:a) spin ½ point-like objects: quarks and leptonsb) spin 1 objects: force carriers (W, Z, , gluons)c) spin 0 (scaler) object(s): Higgs Boson(s) (M&S 9.2.2)The minimal standard model has been very successful in describing known phenomena and predicting new physics.The minimal standard model has a), b), massless neutrinos, and one massiveneutral Higgs boson.

What’s wrong with the standard model?There are (at least) 18 parameters that must be put into the standard model: masses of quarks (6) masses of charged leptons (3) CKM matrix (4) coupling constants, EM, stong, weak (3) Fermi constant (GF) or vacuum expectation value of Higgs field (1) mass of Higgs (or masses if more than one Higgs boson) (1+?)neutrinos have mass!electroweak data might not fit together….based on point particles (idea breaks down at very very high energies, Planck scale).

“The 18 arbitrary parameters of the standard model in your life”, R. Cahn, RMP V68, No. 3, 1996

P780.02 Spring 2003 L12 Richard Kass

The Higgs BosonThe standard model requires that at least one scalar particle exist.This particle, known as the “Higgs” (after Peter Higgs) does two things:a) makes the theory renormalizableb) “generates” the masses of the W, Z, and fermions

Renormalizable means that (e.g.) that scattering amplitudes and cross sectionswill be finite at high energy. Diagrams with the exchange of a virtual Higgs cancelother diagrams with virtual W’s and Z’s.

ZZ

For example the cross section for W+W-W+W- grows as Ecm2! At a few TeV the

cross section grows so large that is would violate unitarity (probability >1)! The cross section can be made to be finite by adding diagrams (amplitudes) of the form:

Adding the Higgs amplitudes makes the total amplitude for W+W-W+W- finite.

P780.02 Spring 2003 L12 Richard KassThe Higgs Boson and MassIn the minimal standard model the Higgs field is a scalar in an SU(2) doublet. Only one component of the doublet has to have mass. Thus there is onlyone massive Higgs particle in this model. The mass of this particle is given by:

MH2=2v2

Both and v are constants.But only one of them can be calculated from already measured quantities!

2GeV/c246sin

WWMv

The mass of the fermions are related to the Higgs field. The standard model Lagrangian contains terms of the form:

Hffv

mffmL f

f int

The strength of the Higgs coupling to a fermion anti-fermion pair depends on the mass of the fermion.Thus we would expect Higgs to decay preferentially to the fermion with mass closest to MH/2.

)()()()( eeHBRccHBRHBRbbHBR

P780.02 Spring 2003 L12 Richard Kass

Where is the Higgs Boson?Present experimental limits on the Higgs suggest MH >110 GeV/c2. Constraints from theory predict a low mass Higgs (MH < 110 GeV/c2).

Higgs may be discovered at Fermilab in next 3-5 years.Will definitely be discovered (or ruled out) at LHC/CERN in 5-7 years.

excluded by experiment

confusing?

Mass of Higgsmust be < 1TeVotherwise higherorder correctionscause problems withthe model.