For a relativistic picture of charge e moving
in a circular orbit of radius r in uniform magnetic
field B, show that the momentum in GeV of the
praticle is given by
p = 0.3 B r
if B is expressed in Tesla and r is measured in meters.
Time of Flight
Two particles of masses M1 and M2, and common momentum p,
travel between two scintillation counters which are a
distance L apart.
What is the difference in their flight times between the
two counters if their momentum is much greater
than their masses ?
What is the minimum flight path needed to distinguish
a pi+ from a K+ if they have momentum of 3 GeV
and the flight time can be measured to an accurace of
200 ps ?
Search for Higgs particles :
In the Standard Model, it is the Higgs boson that gives
masses to the weak gauge bosons (W, Z) and to the leptons
and quarks.
The predicted Higgs scalar would couple most strongly to
the heaviest particles :
the couple strength between the Higgs boson and fermion
is proportional to square of the fermion mass.
Pick the three most dominant decay modes of the Higgs if the
Higgs boson mass is less than 110 GeV.
Higgs Production at LEP II
Since the couplings between Higgs bosons and electrons
(tiny mass) are very weak,
the LEP electron-position collider searched for
the Higgs particles produced in association with the
gauge bosons.
Question:
Draw Feynman diagram for the most dominant channel.
Question:
Using the most dominant channel,
plot the number of Higgs bosons produced (if the
Standard Model Higgs bosons exist) at Higgs mass
= 70 GeV, 90 GeV and 110 GeV from LEP II in year 2000.
For this calculation, you will need following information:
In 2000, LEP-II ran at the center-of-mass
between 200 GeV and 208 GeV. Take 204 GeV
for the calculations.
The integrated luminosity in 2000 per
experiment can be found from
The production cross-sections can be found
from Figure 11.4 in
"QCD and Collider Physics" by
Keith Ellis, James Stirling, and Bryan
Webber. URL for the figure is
Fig.4 : e+e- -> ZH cross sections for
various Higgs masses
Fig.5 : Higgs production mechanisms at
hadron colliders
Fig.6: cross section of pp -> H + anything
at cm = 14 TeV
Fig.7: cross sections of gg -> H,
qq-bar -> WH as a function of cm energy
(pp or pp-bar colliders)
Fig.9: cross section of pp -> H + anything
where H -> gamma gamma at cm = 14 TeV
Higgs Production at the Tevatron
Between 1992 and 1995 (called "Run I"),
the Tevatron delivered
about 110 pb-1 to both CDF and D0 experiments.
If Higgs mass is ~100 GeV, the best stretage to
search Higgs bosons is through production in
association with gauge bosons.
Question:
Draw Feynman diagram of the most dominant
channel.
Question:
Using Fig.1, 2, and 7, calculate the number of
Higgs bosons the Tevatron would have
produced in this channel
during Run I.
Higgs Production at LHC
If Higgs mass is ~100 GeV, the best
stretage at LHC is using the
H -> gamma gamma channel.
Question:
Draw Feynman diagram for this.
Question:
Using Fig.9, calculate the total number of
Higgs bosons in this channel after three years of
collisions. Note that the expected luminosity per
year is 100 fb-1, and there are two experiments,
ATLAS and CMS.
Symmetry Principles :
Parity and Charge conjugation
The eta0 (549) meson has spin 0 and is observed to decay to
3 pion final states by the electromagnetic processes
eta0 -> pi0 pi0 pi0 and
eta0 -> pi+ pi- pi0
Using this information, deduce the parity of the
eta0 and hence explain why the decays
eta0 -> pi+ pi- and
eta0 -> pi0 pi0
have never been observed.
More generally, considering the quark content of
mesons, why do mesons with J^(pc) = 0--, 0+-, 1-+
not exist ?
Muon Decay
Consider muons decaying in their rest frame :
mu- -> e- + nu_e-bar + nu_mu.
The distribution becomes
(1 / Gamma) (d Gamma / d x) = 2x^2 (3 - 2x),
where x = 2 E_e / M_mu,
E_e = electron energy and M_mu = muon mass,
and Gamma is the total (or full) width
Gamma = (G_F^2 M_mu^5) / (192 pi^3).
d Gamma / d x peaks at x = 1 (the electron mass is neglected).
When x=1, i.e. the electron has its maximum energy,
sketch the momentum of the electron, and the momentum and
spin of nu_e-bar and nu_mu.
Sketch the previous process when P operation
(the parity inversion) is applied, and when CP operation
is applied.
Experimentally (Phys. Rev. 119, 1400 (1960))
it is easier to study mu+ decays than
mu- decays. Explain the reason.
Using the measured muon lifetime is 2.2 x 10^(-6) sec and
the total width of muon (above),
estimate the tau lifetime.
Note that unlike muon, tau can decay into various channels.