Problem Set #2
Ground Rules for Problem Sets
- Due in class on Feb. 3.
- Will be handed back for corrections or revisions until we're happy.
- Suggestions and hints will become available through the 880.05 web page.
- Answers to articulation problems are limited to three reasonable
length sentences. You should imagine answering a question from a
graduate student at a colloquium on the current topic. This is hard!
- Checkpoint questions should be fairly quick; if you are having a
hard time, talk to classmates or the instructors.
- For any of the problems you can use any math tool such as maple or
mathematica. Provide a printout of the session.
Problem Set 2
- Why are "hard" processes in QCD easier to deal with than
- What is the difference between a string, a quark, and a parton?
- Why is it reasonable to call
the force between quarks called the "string tension"?
- What is the empirical (experimental) evidence for a linear potential
- We have seen graphs of $1/p_T (d \sigma)/(d p_T)$,
$1/m_T (d \sigma)/(d m_T)$, and $1/m_T (d N)/(d m_T)$.
How are they related to each other and which is most
- What would you plot to get straight Regge trajectories if the
potential between quarks went like $r^2$, where $r$ is the distance
between the quarks?
- Look up the kaon resonances in the Particle Data Tables (it's
all online at http://pdg.lbl.gov/).
Identify a set of resonances that lie on a Regge trajectory and
fit a least-squares straight line
using Mathematica or Maple to extract the string tension.
- Using the model for the thickness functions at the beginning
of Section 12.3, estimate the average number of baryon-baryon collisions
in a high-energy inelastic gold on gold collision.
- Does the rapidity distribution in Fig. 13.2 imply that the
collision is closer to the ``stopping'' region or the
``pure quark-gluon-plasma'' region?
Project: Simulation of High-Energy Proton-Nucleus Scattering
Figure 12.1 in Wong shows differential cross sections for a detected
proton from the collision of 100 GeV/c protons on various
nuclear targets ranging from a proton to lead. The transverse
momentum is fixed at p_T = 0.3 GeV/c and the cross section is given
as a function of x.
We would like to reproduce, at least qualitatively, the features of
this graph based on a numerical simulation (this means
you're going to write a program!). We'd like to reproduce:
- the scaling of the cross section with the number of nucleons
A in the target
- the concentration at low x for A >1
- the increasing slope with increasing A
- an estimate for the average number of baryon-baryon collisions
for each target.
We'll apply the Glauber picture described in Chapter 12, with the
- The trajectory of an incident proton is a straight line at a
fixed impact parameter b.
- The NN inelastic cross section is energy independent and given
by \sigma_in = 30 mb = 3 fm^2.
- The incident nucleon thickness function and the baryon-baryon
collision thickness function can be taken to be delta functions
[as in the discussion above eq. (12.17)].
- Model the target thickness function as in section 12.3
[eq.(12.26) and after].
The basic procedure is:
- Generate a distribution of protons with
impact parameter b corresponding to a uniform beam.
- For each proton and corresponding b, find out how many inelastic
collisions it makes [distributed according to eq.(12.9)].
Keep track of the number of collisions (if greater than 0)
and compute the average number at the end.
- Compute the final value of x for each proton based on the number
of collisions, according to the distribution D^(n)(x_n) in
- Collect statistics for bins in x to generate relative cross
sections and discuss your results.
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Copyright © 1997,1998 Richard Furnstahl and James Steele.