ON THE THEORETICAL ANALYSIS OF THE SMALL x DATA IN RECENT HERA PAPERS

A number of internal inconsistencies, misleading conclusions and lack of completeness in the analyses of the small x deep inelastic data in recent papers of HERA physicists, particularly in a very recent one by the H1 collaboration are pointed out. It is also shown that, when an analysis without prejudice is carried over, the situation is very different from the one claimed there in what respects checks of theoretical expectations. The so-called H1 Collaboration has recently produced a preprint concerning deep inelastic data at small x, that we will henceforth call HERA2. The work constitutes an improvement of the former HERA analysis of the structure function F2, to be denoted by HERA1, extending it to wider x, Q 2 ranges and greatly diminishing the errors. There is not much to be argued about the experimental obtaining of the data. The machine and the detectors worked wonderfully. The quality of the data is excellent. It is therefore more of a pity that the physicists in the collaboration have not been more careful with the subsequent theoretical analysis which shows features that, to put it as mildly as possible, are difficult to justify. Because the second paper HERA2 (ref.2) is so much superior in the quality of the data, I will mostly discuss it here. Regarding it, I will address myself to a number of separate (but related) questions which I will now ennumerate: 1) Parametrizations of the data. 2) Behaviour of structure functions as x → 0. 3) Theoretical analysis with so-called “Double scaling limit”. 4) Connection with various theoretical models. This is the central part of the present note, which will then be finished with some comments. 1.-The theory of strong interactions is QCD. On this practically everybody is agreed, so, when presenting parametrizations of data one should try to, at least, not violate grossly standard QCD features. In this, I think, it is no excuse that the parametrization is merely “a phenomenological ansatz”, as is described the parametrization of p. 20 of HERA2, Eq. (8). As should be by now widely known, the structure function F2 may be split in a singlet and a nonsinglet piece, F2 = FS + FNS . For small x, FNS ≃ BNSx . No matter what, the fact that both FS and FNS are proportional to cross sections implies that BNS > 0: “phenomenological ansatz” or not. A measure of the quality of the fit is obtained by noting that the corresponding coefficient in (8), denoted by e in the table underneath this Eq. (8) in HERA2 is negative. Really. But there is more. It may perhaps be argued that Eq.(8) was not meant to have anything to do with a QCD description: at least it should be compatible with the rest of the paper HERA2. In the same page 20, the authors state that the wide range of Q covered by their experiment allows them to study the behaviour at small x, and its variation with Q. So they write F2(x,Q ) ≃ x→0 x (1)