Talk:QCD evolution equations for parton densities

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    Reviewer A

    here are my remarks. 1. The paper in its present form gives a perfect and exhaustive introduction into the subject of parton densities and corresponding evolution equations. 2. At the same time, I would not recommend changing its title from "Parton densities" to a more general one addressing "Partons" or "Parton Dynamics. The point is, the notion of "partons" is being (rightfully) applied to time-like particle multiplication as well, which manifests itself in the physics of Jets. At the same time, Guido's text deals with the space-like processes (parton densities) only.

    Reviewer B

    It would be useful if after eq (17), when evolution equations for moments are mentioned, a reference to the entry "Operator Product Expansion" were added (this entry is currently being written). Even though the OPE will be treated elsewhere, when referring to it the author could elaborate a little more on the relation between the OPE and the parton approach. It would be useful top then refer back to this point when discussing factorization in sect6: indeed, the present reference to the oprator expansion in this section is a bit obscure given that the OPE was not mentioned before.

    This said, I agree with referee C that a better title for this contribution would be "Perturbative QCD and the parton model" or something of that sort, and the entry QCD evolution equations could then simply refer back to this: I don't think that a separate treatment of evolution equations disconnected from the rest would be deirable.

    Reviewer C:

    Professor Altarelli has written an authoritative article. It is much more general than the title "QCD evolution equations for parton densities" suggests. In fact, it is a general introduction to the general topic of Perturbative Quantum Chromodynamics and the QCD parton formalism, encompassing a number of topics---QCD, Hard Processes, DIS and hadron-hadron collisions, Factorization, Parton Distributions, Evolution equations---more or less corresponding to the various sections of the article. This is understandable, since all the topics preceding the one on evolution equations are necessary to discuss the latter; and I assume this is the first article being written up in the general area of high energy physics in Scholarpedia. (I only see one (dummy) link to related topics---the one on "Bjorken scaling".)

    This raises a fundamental question: shouldn't this article be more generally titled, such as "Perturbative Quantum Chromodynamics and the QCD parton formalism", if the topics covered in the various sections preceding QCD evolution do not appear independently in the Scholarpedia? This is an important question, since these latter topics (listed above) are important on their own right, and need to be referred to by less general topic that may be entered later in the Scholarpedia. I think Professor Altarelli and the editors should discuss this matter and reach a sensible resolution to this problem.

    In fact, as the designated author of the Bjorken scaling article, I can't help but to note that, aside from the origin of Bjorken scaling, the main part of the intended article (on how Bjorken scaling is actually broken in contemporary high energy physics, in particular in QCD) strongly overlaps with this one, hence, to some extent, it seems to be a bit redundant. This is another problem that needs to be sorted out. It is also one particular example of the general problem pointed out in the previous paragraph.

    I have a list of many minor suggestions for improvements (and corrections) on the text. I will enumerate them in a later session, after the bigger issues have come to a resolution.

    Wu-Ki Tung


    On Reviewer C question

    "...Coming to your specific question, certainly there is ample space to do much better on QCD, on the parton model and Bj scaling (this is what Wu-Ki could do) etc. ... "

    Editor (RG)

    My point of view is that Altarelli contribution is a good introduction to parton techniques in QCD, but each separate section reviewer C mentioned deserves an entry, even if there will be some overlap. The goal of Scholarpedia is of being useful to readers, so if Altarelli introduced --as I asked-- all the concepts required to understand DGLAP, that is reasonable. Even more we should be a little tolerant with the first article of a new section as is the case for High Energy (Phenomenology).

    Concerning the title of the article. I agree with reviewer B that the article can be seen as a nice introduction to parton techniques in perturbative QCD, I hesitate to change it for two reasons:

    1. - The "abstract" of each article contains a short definition and the one Altarelli wrote is pertinent for DGLAP.
    2. - "Perturbative Quantum Chromodynamics and the QCD parton formalism" is quite long.

    The tendency is to have short encyclopedic titles (the article was originally called DGLAP equations but Altarelli asked to change as it is in his present form). This because we have an autolinker that automatically links words matching titles in other articles.

    Moreover reviewer A seems not favorable to the change of the title for the article does not deal with the notion of partons in jet physics.

    My proposal is to keep the main title. When this category will have more articles and will have a real editor (I'm just helping and waiting for some real expert) he will add secondary dummy articles that redirect to it. RG

    Reviewer C:

    Here are a few suggested modifications:

    1. Since color charges are not numerical quantum numbers, it is slightly misleading to say "they average to zero" or "with net zero color charge". If possible, "zero" might be replaced by "singlet" or "neutral".

    2. "In the QCD theory there are no constants with the dimension of mass ...": perhaps better to replace "constants" by "fundamental parameters"?

    3. After Eq.(3), perhaps needs something like "where c_i are calculable constants (in a given renormalization scheme)."

    4. Eq.(4) is confusing: (i) normally q^2 = (q.q) by definition (in any metric), but here a negative sign appears on the left side; and (ii) (k.k') appears, but k and k' are not explained (as the lepton momenta), furthermore, the diagram shows ell and ell' as the lepton momenta!

    5. "an unlimited number of hadrons species,": should be "hadron" rather than "hadrons".

    6. "The early measurements at SLAC (Stanford Linear Accelerator Centre) of DIS dissipated all doubts": perhaps "dissipated" --> "dispelled"?

    7. "and the success of the "naive" (not so much after all) parton model of Feynman imposed quarks as the basic fields": perhaps "imposed quarks as" --> "helped to establish quarks as"

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