What is a "reggized gluon"? I'm reading a paper in which the author used these words many times assuming that the reader knows what he is talking about. Can someone please explain what it is? What is the difference between a regular gluon and a reggized gluon?
 A: After doing some research, I think this figure, from a new book by Kovchegov and Levin, illustrates it well:


Fig. 3.10. Reggeized gluon (bold corkscrew line) represented as the sum of all leading-$\ln s$ corrections to the single-gluon exchange amplitude for $qq\to qq$ scattering.

So essentially, a reggeized gluon is an "effective particle" that is actually a quantum superposition of one gluon, two gluons, three gluons, etc. but only counting the terms in the amplitude that are leading logarithmic - that is, terms proportional to $\alpha_s(\alpha_s\ln s)^n$, not $\alpha_s^2(\alpha_s\ln s)^n$ or so on.
Mathematically, here's what's going on. The amplitude for single-gluon exchange looks like this:
$$(\text{stuff})\frac{s}{k_\perp^2}$$
The amplitude for two-gluon exchange, taking into account both the straight and crossed diagrams, looks like this:
$$-(\text{stuff})\frac{s}{k_{\perp}^2}\frac{\alpha_s N_c}{4\pi^2}\ln s\int\mathrm{d}^2\mathbf{k}_{2\perp}\frac{k_{\perp}^2}{k_{1\perp}^2 k_{2\perp}^2} \equiv (\text{stuff})\frac{s}{k_{\perp}^2}\omega_G(k_{\perp})\ln s$$
where $\mathbf{k}$ (total momentum transfer) is $\mathbf{k}_1$ (momentum of one gluon) plus $\mathbf{k}_2$ (momentum of other gluon), and $(\text{stuff})$ is the same constant in both cases. If you go on to calculate the amplitude for $n$-gluon exchange for higher $n$, keeping only the leading logarithmic terms, you find a series of the form
$$\begin{multline}
(\text{stuff})\frac{s}{k_{\perp}^2} + (\text{stuff})\frac{s}{k_{\perp}^2}\omega_G(k_{\perp})\ln s + \frac{1}{2}(\text{stuff})\frac{s}{k_{\perp}^2}\biggl(\omega_G(k_{\perp})\ln s\biggr)^2 + \cdots \\
= (\text{stuff})\frac{s}{k_{\perp}^2}e^{\omega_G(k_{\perp})\ln s}
\end{multline}$$
(at least, this is what the book says; I haven't done the calculation myself). So this entire series of terms describing $n$-gluon exchanges condenses to a single term $(\text{stuff})s^{\omega_G(k_{\perp})+1}/k_\perp^2$. You can interpret this as representing the exchange of a single "effective particle" which has a propagator $ig_{\mu\nu}s^{\omega_G(k_{\perp})+1}/k_\perp^2$ (compare to a single gluon which has a propagator of just $ig_{\mu\nu}/k_\perp^2$). That effective particle is the reggeized gluon.
