# Perturbative QCD and NRQCD

1. Aug 23, 2006

### BuckeyePhysicist

What is the relationship between pQCD and NRQCD?

Is it that pQCD is for high energy/short-distance regime, e.g. quark gluon plasma? And NRQCD is for low energy/long-distance regime, e.g. quarkonium ?

And what is relation between heavy quark effective theory and pQCD and that between heavy quark effective theory and NRQCD ?

2. Aug 25, 2006

### Red5

pQCD works in the perturbitive region where \alpha_s the strong coupling constant is small, Matrix elements for physical processes are obtained from expansion in this parameter. NRQCD works as an effective field theory for quarks with velocities much less than the speed of light and the results obtained are expansions in the parameter (\alpha/v)^n. pNRQCD is obtained from the low velocity limit of the QCD Lagrangian. The NRQCD effective theory is useful when heavy quarks are produced near threshold and hence have small velocites, whereas in the high energy regieme pQCD is used.

3. Aug 27, 2006

### BuckeyePhysicist

NRQCD expends in powers of (\alpha/v)^n but not \beta ? \beta = v/c where
v is the relative velocity of the two heavy quark constituents for quarkonium. \beta ~ 0.3 for charmonium and \beta ~0.1 for bottomonium, right?