Problem Set #2

Ground Rules for Problem Sets

Problem Set 2

Articulation Questions

  1. Why are "hard" processes in QCD easier to deal with than "soft" processes?
  2. What is the difference between a string, a quark, and a parton?
  3. Why is it reasonable to call the force between quarks called the "string tension"?
  4. What is the empirical (experimental) evidence for a linear potential between quarks?

Checkpoint Questions

  1. 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 useful?
  2. 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?
  3. Look up the kaon resonances in the Particle Data Tables (it's all online at 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.
  4. 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.
  5. 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:

  1. the scaling of the cross section with the number of nucleons A in the target
  2. the concentration at low x for A >1
  3. the increasing slope with increasing A
  4. 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 following assumptions:

The basic procedure is:

  1. Generate a distribution of protons with impact parameter b corresponding to a uniform beam.
  2. 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.
  3. Compute the final value of x for each proton based on the number of collisions, according to the distribution D^(n)(x_n) in Supplement 13.1.
  4. 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.