HW

1

• HW 6 is graded and ready for pick-up.
• DAW 3 grades received?
• Final Exam Scheduling
• Use the sign-up sheet to select one of the two
  possible final exam times (Thursday or Saturday).
• There will be another chance to do this on
  Friday.

2
Z0 Production and Decay

• Any process in which a photon is exchanged can
  also occur through Z0 exchange.
• In ee?, photon dominates the cross section at
  low energy, but the EM falls as 1/s.
• Above about 35 GeV (CM), the Z0 diagram
  contributes appreciably, and at the Z0 it gives a
  gigantic peak.
• The two contributions interfere and give a
  measurable forward-backward asymmetry (HW 7,
  prob. 4). These have been measured at many
  energies, especially for muon-pair and
  heavyquark production.

• The most powerful electroweak theory test from
  the study of the Z0 comes from very precise
  measurements of its width from the LEP
  experiments.

3
Width of the Z0
Flashback W couplings are equal for all (LH)
quarks and leptons. Z0 couplings depend on the
electric charge.
Partial width for Z0 decay to a particular
fermion-antifermion pair includes both a LH and a
RH part
for each neutrino type
Add them up
4
Unified Electroweak Theory Prediction of Z0 Width
with radiative corrections
Unified EW theory has successfully resolved our
puzzle over the Z0 semileptonic branching
fraction, and it has confirmed that there are no
Standard Model neutrinos other than the three
that we know.
5
LEP EWWG tests of the Standard Model
LEPSLD results (e e ? Z0) show excellent
overall consistency. Predicted value of
top-quark mass is very close to the measured.
6
NuTeV Trouble for the Standard Model?
Fermilab fixed-target run 1996-97. Results
presented 2001.

• NuTeV measured the rates of charged and neutral
  currents in neutrino-nucleon scattering to obtain
  sin2?W at significantly smaller Q2 than LEP.
• Result (0.2277) is higher than the expected
  (0.2227) by a statistically significant amount!
• The NuTeV sin2?W result, when converted into W
  mass, disagrees at 2.7?.

7
So far

• Weve laid out some of the key features of the
  GWS electroweak theory and demonstrated that it
  accommodates a broad range of experimental
  measurements.

• Together with the SU(2) symmetry of the weak
  isospin, there is an additional U(1) symmetry in
  the electroweak sector that, also in analogy to
  the strong, is called weak hypercharge, related
  to charge and I3W through another
  Gell-Mann-Nishijima relation

Same for both member of a doublet, e.g. YW ?1
for e and, ? for u and d.
8

• The basis of the EW theory is the local symmetry

Massless
Gauge Fields
(Fermions are also massless.)
Charges

• We have a gigantic missing link. How do the
  massless vector bosons that arise from this
  symmetry acquire the masses of the three observed
  weak vector bosons W? and Z0, while preserving
  the masslessness of the photon? Can the same
  mechanism also provide the fermion masses?

9
Spontaneous Symmetry Breaking

• The ground state of a system does not always
  exhibit the full symmetry that might otherwise be
  expected.
• Ferromagnet spins orienteded randomly at some
  T. Perfect global symmetry rotate spins by the
  same angle and the system energy is unchanged.
  As system cools it will fall into a ground state
  with spins parallel. But in what direction? In
  the absence of an external field, preferred
  direction is selected at random from the
  infinite number of possibilities. In a QFT
  long-range correlations exhibited are identified
  with a zero-mass particle.

• A physical system like this has a potential
  shaped like the bottom of a wine bottle or
  Mexican hat.
• But what does this have to do with electroweak
  theory?

10
The Higgs Potential

• Peter Higgs (and others) proposed a field that
  permeates the Universe that does not affect
  gravity, electromagnetism or the strong force,
  but has the effect of making the weak force
  short-ranged. It is the reason that fundamental
  particles cannot travel at the speed of light
  it endows them with mass.

• Higgs self-interacting complex scalar doublet
  with potential energy.

Parallel with ferromagnetism is strong! Higgs is
a scalar field that exists in a vacuum and has a
potential symmetric under rotations in ? space.
The magnetization of a ferromagnet exists in
absence of an external field, with free energy (G
?M2 ?M4, ? lt 0 , ? gt 0) symmetric under
spatial rotation.
The Higgs potential has a minimum that is not at
? 0
electroweak scale parameter
vacuum expectation value
11

• The vacuum Higgs field has four real components.
  Fluctuations around the minimum in ? breaks the
  rotational symmetry in ? space, and three of the
  Higgs components are absorbed to give mass to
  the W and Z.
• The fourth component is the physical state
  manifested as the Higgs boson

• Masses of the vector bosons and fermions arise
  from and are proportional to the couplings to the
  Higgs field (D. Miller cartoon)

Photon coupling to Higgs field is zero.
The vacuum expectation value of the Higgs field
generates fermion masses proportional to the
coupling strength.

• The Standard Model with the Higgs mechanism can
  explain fermion masses, but cannot predict them.
  In fact, the Mexican Hat potential inserted
  into the SM to incorporate spontaneous symmetry
  breaking also cant be predicted by the SM. This
  understanding requires Beyond Standard Model
  physics.

12
Why do we believe the Higgs will be found ?

• Standard Model is amazingly successful and
  requires the Higgs. (In fact most discussion
  centers on how many more than one we need to go
  beyond the SM via supersymmetry.)
• Unless the SM fails miserably, at least the
  neutral scalar Higgs that it requires will be
  found.
• Furthermore, it will most likely be found within
  the energy reach of current or next-generation
  experiments (i.e. LHC).

Higgs Boson Decay Width
Higgs self-coupling dominates for large MH gtgt ?.
This violates unitarity for large MH, with a
Higgs width that exceeds the mass.
A rigorous analysis gives MH lt 1 TeV.