Soft and ultrasoft gluons in QCD

[petergreat]

I'm reading about factorization in QCD. The terms "soft gluons" and "ultrasoft gluons" are frequently referred to. I know how they are defined in terms of power counting, but don't understand their physical significance. In which QCD processes are soft gluons important, and in which are ultrasoft gluons significant?

 

[blechman]

It depends a great deal on what it is you are looking at, and to some extent it is just semantics. But as a rule, if $\lambda$ is your (IR) power counting parameter, then in terms of light cone momenta (and setting the hard scale to 1):

$$(p^+,p^-,p_\perp)\sim (\lambda,\lambda,\lambda)\Rightarrow{\rm soft}$$
$$(p^+,p^-,p_\perp)\sim (\lambda^2,\lambda^2,\lambda^2)\Rightarrow{\rm ultrasoft}$$

So that the "offshellness" of a soft mode is $\lambda^2$ while the usoft mode is $\lambda^4$.

When dealing with fully inclusive processes this distinction is irrelevant. The trouble comes in when you have exclusive or semi-inclusive processes. Then you have to distinguish soft from usoft.

See, for instance, Bauer, Pirjol, Stewart, hep-ph/0109045