# Some QCD questions

1. Jul 1, 2009

### hagi

Hi @ all,

during tmy exam preparation I stumbled upon some facts that I couldn't explain to myself.

1. Strong coupling constant $$g_s$$ is universal -> colour charge is quantised

2. The MS_bar quark mass $$\bar{m} = m_0 + \delta \bar{m}$$ can be given as a function of the quark pole mass $$m = m_0 + \delta m$$,
$$\bar{m}(m^2) = \frac{m}{1 + 2\alpha_s}$$,
but neither can be measured because of confinement. What is the purpose of giving such an equation? Is any relevance therein?

3. The renormalized gluon-gluon splitting function contains a term proportional to $$N_F P_{qg}$$. Is this just a consequence of the collinear and soft poles of the unrenormalized gluon-gluon splitting function? Whence does the flavour factor comes?

4. Does anybody know something about parton cascade/parton branching/probability picture and why 3-momentum is conserved, but energy not? (This topic showed up during the heuristic justification of the parton model.)

Cheers

Andreas

2. Jul 1, 2009

### Bob_for_short

4) If it is about deep inelastic scattering, then the energy is "not conserved" in the sense that its part goes to the "internal" energy of the reaction products (breaking a target in pieces takes some energy). The momentum is always conserved.

Bob_for_short.

Last edited: Jul 1, 2009
3. Jul 1, 2009

### hagi

I think it is not a specific DIS question. The energy nonconservation should imho be a trick but that's exactly my problem, why this trick is allowed. The problem is that I had to ask the prof so much things that I couldn't ask everything and his notes are not selfexplaining.

He called the whole thing "probability picture" and his conclusion was that in the parton model (infinite momentum frame) the life time for partons with
Bjorken 0<x<1 is much longer than for partons with x<0 or x>1 corresponding to a backward directed motion of a daugher parton.

Last edited: Jul 1, 2009
4. Jul 1, 2009

### Bob_for_short

I am not good at it but I remember that the energy is somewhat distributed between partons and this repartition is described with a probability function.

5. Jul 2, 2009

### hagi

Thanks but I solved question 4 now. The energy nonconservation is just due to an approximation of a square root, to be able to compute the answer but it has nothing to do with the parton branching as such. Quigg helped me here.