HW #1 (129A), due Sep 13, 4pm
So-called B-factory experiments are looking for subtle difference between
properties of matter and anti-matter, hopefully getting insight into the ques-
tion why there exists only matter but no anti-matter in our Universe. There
are two of them running, one called BABAR (http://www.slac.stanford.
edu/BFROOT/) at Stanford Linear Accelerator Center (SLAC) and the other
called Belle (http://belle.kek.jp/) at KEK Laboratory in Japan. Both
of them collide beams of electrons and positrons (anti-particle of electron)
of different energies and produce a particle called Υ(4S), a bound state of
a bottom quark and an anti-bottom quark in 4Sstate with total spin 1, of
mass 10.580 GeV/c2. In this process, there is no other particle produced.
Answer the following questions.
1. SLAC experiment collides an electron of energy 9.0 GeV, while the
KEK experiment uses 8.0 GeV electron. What is the energy of positron
in each experiment?
2. Υ(4S) quickly decays into a pair of B-mesons, of mass 5279 MeV/c2.
In the rest frame of Υ(4S), what are their energies and momenta?
3. B-mesons live 1.54 ×10−12 sec on average. How far do they go on
average in the rest frame of Υ(4S) before they decay?
4. When a Υ(4S) decays, it produces B-meson (and also anti-B-meson)
at different angles each time. Using the angle θdefined relative to
the beam axis in the rest frame of Υ(4S), give the analytic expres-
sion of four-momentum of the B-meson in the laboratory frame (not
numbers!).
5. Using the probability distribution
dP
dcos θ=3
8(1 + cos2θ),(1)
work out the average distance a B-meson can go in the laboratory
frame for each experiment (a number for each).
Note These experiments collide electrons and positrons of different energies
so that B-mesons go over longer distance. They determine the points
of their decays for detailed studies of their properties.