KTII - Exercise 1

KTII - Exercise 1

Universit¨ at Z¨ urich

Due: 26 February 2020

For particle information, including hadronic quark content, particle masses, particle lifetimes, or other physical constants not given in the problem, please consult the Particle Data Group’s Review of Particle Physics. It is available for free on their website: http://pdg.lbl.gov/.

1. (2 pts) How could you observe B

− B ¯

oscillations in Υ(4S) decays? Draw the main Feynman diagrams for B

− B ¯

mixing.

2. (2 pts) Consider the decays of D

(c¯ u) meson. (a) D

→ K

π

(b) D

→ π

π

and (c) D

→ K

π

. Draw the leading order diagrams and order the decays in decreasing probabilty. Explain.

3. (2 pts) In a two-body scattering event, A + B → C + D, it is convenient to introduce the Mandelstam variables:

s = (p

+ p

)

/c

t = (p

− p

)

/c

u = (p

− p

)

/c

Show that s + t + u = m

+ m

+ m

+ m

.

4. (2 pts) Draw the lowest-order Feynman diagram for the decay K

→ µ

ν

γ and deduce the form of the overall effective coupling (i.e. give the powers of the strong, weak, and electromagnetic couplings associated with this diagram).

5. (2 pts) Find the mass and width of the J/ψ particle. A specific J/ψ is made with momentum 100 GeV/c and subsequently decays according to J/ψ → e

e

. Find the mean distance traveled by the J/ψ in the laboratory before decaying.

Assume that electron and positron from the J/ψ decay have the same energy. What is the energy of the decay electron in the laboratory. Find the laboratory angle of the electron with respect to the direction of the J/ψ.

1