QCD Questions Answered by Experts

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Discussion Overview

The discussion revolves around various questions related to Quantum Chromodynamics (QCD), particularly focusing on the strong coupling constant, quark masses, gluon splitting functions, and the parton model. Participants explore theoretical concepts and their implications in the context of particle physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Andreas questions the universality of the strong coupling constant and the relevance of the relationship between the MS_bar quark mass and the quark pole mass, noting that both cannot be measured due to confinement.
  • He inquires about the renormalized gluon-gluon splitting function and its connection to collinear and soft poles, specifically asking about the origin of the flavor factor.
  • Andreas seeks clarification on the conservation of 3-momentum versus energy in parton cascades and the implications of the "probability picture" in the parton model.
  • Bob_for_short suggests that in deep inelastic scattering, energy is not conserved in the traditional sense because some energy is absorbed by the internal energy of reaction products, while momentum remains conserved.
  • Another participant expresses uncertainty about the energy nonconservation, suggesting it might be a conceptual trick and relates it to the lifetime of partons in the parton model.
  • Andreas later indicates that he resolved his question regarding energy nonconservation, attributing the issue to an approximation rather than parton branching.

Areas of Agreement / Disagreement

Participants express differing views on the nature of energy nonconservation in the context of parton cascades and deep inelastic scattering. Some aspects remain unresolved, particularly regarding the implications of the probability picture and the flavor factor in gluon splitting functions.

Contextual Notes

Participants reference specific theoretical constructs and approximations without providing complete definitions or derivations, which may limit understanding. The discussion includes assumptions about the parton model and its implications that are not fully elaborated.

hagi
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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.)

Thanks in advance to everyone answering!

Cheers

Andreas
 
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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.
 
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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.
 
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hagi said:
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.

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.
 
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.
 

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