# Rutgers Physics 418 Nuclei & Particles (Somalwar)

## Homework 9 - Due December 1, 2017

Das & Ferbel refers to the textbook *Introduction to Nuclear and
Particle Physics, ***2nd **
Edition, by A. Das and T. Ferbel

Syllabus

Read entire Chapter 11

1) Das & Ferbel, Problem 11.2.

2) Das & Ferbel, Problem 11.3. In each case, comment on the preferred
direction of the pions, i.e., along or perpendicular to the Z-axis. By taking
into account all the spin projections (0, +1 and -1), show that the
distribution is spherically symmetric for unpolarized rho's.

3) Das & Ferbel, Problem 11.4. (A trick question? Note that the
decay is weak.)

4) Das & Ferbel, Problem 11.5. For part (d), don't forget that both
symmetric and antisymmetric combinations are possible for the final
state.

5)
The running QCD coupling constant
α_{s} can written as α_{s} =
12π/(33-2f)ln(Q^{2}/Λ ^{2}) , where Λ
is a parameter which is chosen to fit experiments and takes a value of
about 500 MeV. In this formula f is the available number of quark
flavors which increases from 3 (u,d,s) at Q^{2} = (1GeV)^{2} to
5 at Q^{2} = (10GeV)^{2} (all but the top quark). Use this formula to
calculate α_{s} at these two values of
Q^{2}.