Talk:Introduction to Parton Distribution Functions

I have made several small changes throughout the text. In addition, I would like to point out some more general issues, which the author might want to consider.

- I think that the author should also mention asymptotic freedom of QCD. This could be done, for example, after saying that "... the theory that describes .... is called Quantum Chromodynamics" or in the following paragraph.

- I know it is common in the literature, but, to be precise, the PDFs represent number densities (rather than probability densities), as they are normalized to the number of partons (and not to 1).

- Is it true that QCD predicts that half the proton momentum is carried by gluons? If so, a reference should be given.

- When listing the non DIS experiments (jet production, Drell-Yan and W production) one should add RHIC experiments. In particular large P_T pion production at RHIC is in excellent agreement with pQCD computation (and I believe it has been used for extracting PDFs). Also W production will be measured at RHIC.

Reviewer B:

Report of second referee

The article is a good consise outline of the state of parton distributions at present. I do however believe a few changes or additions are desirable (and in some cases necessary).

I have made numerous small edits in the text, which either (in my opinion) make the english more clear, or add in a few words a little more information. For instance I have slightly changed the comments on the gluon distribution carrying half the momentum of the proton which was queried by the first referee. I also have a number of suggestions which I will list below. In most cases I feel that these may add clarity, and are perhaps absent at the moment due to the clash with required brevity.

In "Definition of PDFs", the comment that at low Q^2 the nucleon is seen as containing 3 valence quarks seems far too simplistic to me. At lower Q^2 the valence quarks become more and more dominant, but at all scales where the concept of PDFs make sense there are still significant sea and gluon distributions and a wide distribution in x of valence quarks.

In this section I feel a bit more mention of the concept of factorisation of physical cross-sections into partonic cross-sections and parton distributions, up to higher-twist power-like corrections, is really vital, since this factorisation theorem is the whole bvasis for being able to use PDFs. Indeed, the term "higher twist" is used in "Theory uncertainties" without having been defined. On similar lines the definition of scheme of the parton distributions is probably more important in terms of factorisation scheme. The PDFs in use are always defined in the MS-bar renormalisation scheme (up to subtleties for heavy quarks), but different factorisation schemes, e.g. DIS-scheme PDFs are in use.

At the end of "Examples of PDFs" it might be worth noting that to first approximation all groups ignore theoretical errors, though this is commented on later in "Theoretical uncertainties".

Even though I understand the desire to keep "Data sets in fit" short, various improvements could be made with very little addition in length. I have added the comment that Z as well as W bosons are produced at the Tevatron, but constraints also come from virtual photon production in fixed target pp collisions. Regarding DIS it is worth noting that different targets, e.g. deuterium and nuclear targets, and probes, i.e. neutrinos, give information on flavour decomposition, and that the gluon is only probed via the rate of evolution in DIS (or more recently, and to a small extent, the longitudinal structure function). A liitle more clarity can be added to the list of data fit by different groups, by at least pointing out that CTEQ, MSTW, NNPDF and GJR have differences in exactly which data they fit, and e.g. GJR has no W and Z production data, which is also true for ABKM.

In "Treatment of experimental errors and estimation of uncertainties" I think it is only fair to note in some manner that NNPDF do have some ambiguity in their central values and uncertainties from procedural uncertainties. For instance, the different method for stopping theit fits (in which data are split into training and validation sets, rather than the best fit to all data being found) led to significant differences between their recent analyses even with the same data (as noted in section 5.4 and figure 24 of the NNPDF article referenced by the author). This does not alter the conclusions of this section though.

In "Model uncertainties", the part on "input distributions" is perhaps the least satisfactory part of the article for me. A bit more should be said on NNPDF here, even if it is lifted from the previous section. I personally feel the comment at the beginning is misleading since the study in Aaron et al. uses far fewer parameters than any of the other groups in the first place. Hence, the statement that varying the analytic form can give dominant uncertainties should be accompanied by the caveat that this depends on how restricted the analytic form is in the first place. The example of GJR is then an extreme, though more specific example of this. In this case the analytic form is specified quite precisely using a particulat theoretical assumption leading to a much narrower uncertainty at small x than other groups. What the author has written is correct, and worthwhile pointing out, but I am not sure how it can be considered as an approach to consider the size of the uncertainty due to the choice of input distribution. It seems rather to be an extreme example of a limitation of uncertainty from this source, i.e. the opposite of the NNPDF idea. Perhaps this is what the author meant to convey, but some rewriting seems appropriate here.

In "Flavour symmetry", the assumption that s is quarter the average of the sum of ubar and dbar is only a rather approximate assumption for most grouos at present. MSTW do assume that strange has the same shape at small x as the other light quarks, but not at high x (perhaps this was a typo). NNPDF make no asumption on the shape, and CTEQ are somewhere between the two. Perhaps some comment on the study of s not equal to sbar is apprpriate, but not is space is a premium. There is no experimental information on the difference between dbar and ubar below x=0.01. They are not the same above this value, but the best information on this comes from the E866 Drell-Yan ratio data, not DIS experiments, so the end of this paragraph should be corrected.

In "heavy quark treatments" a reference would be welcome, and similarly in "Coupling constant" a reference to the LEP values would be useful.

In "Theory uncertianties" I have added a comment that cross-sections as well as evolution have theory uncertainties, and already noted that higher twist has not previously been mentioned. I also note that NNLO corrections are fully known for vector boson production in hadronic collisions. Of the data used in global fits only jet cross-sections are not fully calculated at NNLO.

Perhaps RHIC could be mentioned in the final "Applications and prospects" section. I do not agree with the previous referee that much reference need be made of RHIC elsewhere. Currently no group makes use of RHIC data in their extraction of PDFs. Of course, most of the data is in nuclear collisions, which is less attractive due to having to model nuclear corrections. There is data from proton collisions which is potentially useful, but so far has not had sufficient precision to make it necessary for inclusion in PDF fits.

I will be happy to liase further with the author about any of these points.

Report of Referee B on revised version

I am very mainly happy with the revised version but still have a number of small remaining points which I would ideally like to be addressed.

- Near the end of "Method of Determinations", I think it would be very helpful to point out that the "remainder", or "higher twist" terms are formally of order 1/Q^2.

- In order to be precise it should be made clear at the end of "Data Sets in fit" that ABKM uses fixed target Drell Yan data (i.e. not Tevatron Drell-Yan data).

- In "Model Uncertainties", not only MSTW have used more sophisticated parameterisations for the strange distribution. In fact, CTEQ were first, and NNPDF have a very flexible strange parameterisation at small x.

With these small number of minor revisions I will be very happy to accept the article.