A. Problems from Perkins:
B. Prepare for the in-class Written Exam Monday, March 29th:
Lectures + Homework
+ Perkins chapters 1-4.
Exclude sections: 1.5, 1.9, 2.5, 2.6,
2.9, 2.11.2, 3.1, 3.3-5, 3.7-11, 4.2.1, 4.9-13
C. Note on Perkins 4.1
I only just realized how little there is in the textbook to guide you on this problem and that a web search has hints embedded in impenetrable papers involving Reggeons and Pomerons! This is not what I want you to learn about, so here is the lead up to this problem with an example.
The primary reason to assign this problem is to demonstrate that physically observable quantities like the total cross section s can be largely determined by just the quark content, without delving into all the other details (like energy, angular momentum etc.). The simple additive quark model tells you that the total cross section is proportional to all the possible quark on quark scattering possibilities for similar kinematic conditions (e.g. same center of mass energy). For example, in section 4.8.1 (p. 123) the ratio s(pN)/s(NN) = 2/3 comes from counting the number of quark pair combinations 2x3=6 for pN and 3x3=9 for the NN.
In more detail, write out the actual quark/quark scattering combinations:
E.g.
pN = p-p -> (ubar d) (uud) = 2 uu + ud + 2 u dbar + d dbar
NN = pp -> (uud) (uud) = 4 uu + 4 ud + dd
The 2/3 ratio we got depends on the assumption that all the different combinations uu, u dbar, dd contribute the same amount to the cross section. This would not be the case if the interactions were primarily electromagnetic because then we would get factors related to the different charges on the u and d quarks. The strong interaction doesn't care about the charge, and in this case not even quark flavor (u vs. d) because these are in the same isodoublet.
For problem 4.1 you are asked to confirm various total cross section relations in this model. You should multiply out the particle quark content for each pair of particles (e.g. Lp -> (uds)(uud) = .....) as we did above and attempt to verify the equations given. To get the equations to balance you will have to make some assertions about the equivalence (or not) of different quark pair terms - the main goal of this problem is for you to think about how you can just the assertions in terms of the interactions. You need to be consistent for all three examples.
These cross sections relationship are reasonably well matched by the data, giving support to the idea that the fundamental features of these interactions is quite well described by considering quark content assigned in the static quark model.