When semantics turns to substance: reformulating QCD analysis of F₂^γ(x,Q²)

Abstract

QCD analysis of F γ 2 (x, Q 2 ) is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies important difference in the way factorization mechanism works in photon-hadron and photon-photon collisions as compared to the hadronic ones. Moreover, a careful definitions of the very concepts of the "leading order" and "next-to-leading order" QCD analysis of F γ 2 are needed in order to separate genuine QCD effects from those of pure QED origin. After presenting such definitions, I show that all existing allegedly LO, as well as NLO analyses of F γ 2 (x, Q 2 ) are incomplete. The source of this incompleteness of the conventional approach is traced back to the lack of clear identification of QCD effects and to the misinterpretation of the behaviour of q γ (x, M ) as a function of α s (M ). Complete LO and NLO QCD analyses of F γ 2 (x, Q 2 ) are shown to differ substantially from the conventional ones. Whereas complete NLO analysis requires the knowledge of two so far uncalculated quantities, a complete LO one is currently possible, but compared to the conventional formulation requires the inclusion of four known, but in the existing LO analyses unused quantities. The arguments recently advanced in favour of the conventional approach are analyzed and shown to contain a serious flaw. If corrected, they actually lend support to my claim.

QCD analysis of F[sub 2][sup γ](x,Q[sup 2]): an unconventional view

“…As all these functions are known, there is, however, no obstacle to performing such an analysis. As shown in [1] for the pointlike part of F γ 2 (x, Q 2 ) in the nonsinglet channel, the results in these two approaches are numerically significantly different, the single most important contribution to this difference coming from C (1) γ . The coefficient function C (1) q enters F γ 2 already at the LO 4 due to the fact that it does so in the convolution with purely QED part of quark distribution function of the photon, which has no analogue in hadronic collisions.…”

“…• As shown in [1] the LO QCD expression for F γ 2 contains in addition to terms included in the conventional LO analysis of F γ 2 (i.e. those proportional to k (0) q and P (0) ij ), also terms involving k (1) q , C (1) q , C (0) γ and C (1) γ .…”

“…Note, that in the conventional approach C (0) γ , which has nothing to do with QCD, appears only at the "NLO", and C (1) γ , which involves evaluation of Feynman diagrams with a single QCD vertex is not used even there! For clear and unambiguous definition of the terms "LO" ("NLO") it is thus vital to agree on the basic criterion, namely that they refer to perturbative expansions of physical quantities retaining the first (first two) nontrivial powers of α s .…”

“…In [1] I have proposed an alternative approach to QCD analysis of F γ 2 (x, Q 2 ), and by implication to any hard process involving initial photon, which differs substantially from the conventional one. It builds in part on arguments advocated for a long time by the authors of [2] and agrees with the approach to calculations of direct photon production at HERA pursued in [3].…”

“…It is their presence what distinguishes hard collisions of photons from those of hadrons. In [1] I have discussed conceptual as well as numerical differences between the results obtained within the conventional and alternative approaches for the pointlike part of F γ 2 in the nonsinglet channel and under the simplifying assumption β 1 = 0. In this talk I will concentrate on proper definitions of the concepts "leading order" (LO) and "next-to-leading order" (NLO) of QCD and on the discussion of their implications for charm contribution F γ 2,c (x, Q 2 ) to photon structure function, recently measured at LEP [4,5].…”