Homework 6

1) Derive the formula:

$$\sigma(AB \rightarrow \psi X) = K \int_\tau^1 dx \tau x^{-1}... ...(x,Q^2)f_{g/B}(\tau/x,Q^2) \hat{\sigma}(gg \rightarrow \psi g)$$

with: $\tau=m^2/s$, $m$ being the mass of the $\psi$,

$$\hat{\sigma} = \hat{\sigma}_0 \delta(1-\hat{s}/m^2)$$

and:

$$\sigma_0 = \frac{9\pi^2}{8m^3(\pi^2-9)} \Gamma(\psi \rightarrow ggg) I(\hat{s}/m^2)$$

.

$\Gamma(\psi \rightarrow ggg)$ is the decay width for $\psi \rightarrow ggg$, and you can take $I(\hat{s}/m^2) \approx \delta(1-\hat{s}/m^2)$.

What physical hypotheses and/or approximations go in the derivation?

2) This assigment requires the usage of the Web. By going to the site choose one of the parametrizations (MRST, etc.), and plot the sea quark and valence quark distributions for a given flavor, at two different values of $Q^2$ (high and low), respectively. Compare your results with the Regge theory predictions discussed in class.