Pion-photon transition: The new QCD frontier

Abstract

We perform a detailed analysis of all existing data (CELLO, CLEO, BABAR) on the pion-photon transition form factor by means of light-cone sum rules in which we include the next-to-leading order QCD radiative corrections and the twist-four contributions. The next-to-next-to-leading order radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients a 2 and a 4 , we show that the 1 error ellipse of all data up to 9 GeV 2 greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules-within the range of uncertainties due to twist-four. This remains valid also for the projection of the 1 error ellipsoid on the ða 2 ; a 4 Þ plane when including a 6 . We argue that it is not possible to accommodate the high-Q 2 tail of the BABAR data with the same accuracy, despite opposite claims by other authors, and conclude that the BABAR data still pose a challenge to QCD.

Pion-Photon Transition Form Factor and Pion Distribution Amplitude in QCD: Facing the Enigmatic Behavior of the BaBar Data

“…In our recent data analysis in [2] (see also [11]), we used Light-Cone Sum Rules (LCSRs) [12,13] and performed an extended calculation of the pion TFF which takes into account the next-toleading (NLO) order radiative corrections [14] and the twist-four contribution [12,15], while also including in terms of uncertainties the main next-to-next-to-leadingorder (NNLO) correction [4,16] and the twist-six term, computed in [17]. The evolution of ϕ (2) π (x; µ 2 ) with µ 2 > 1 GeV 2 was also taken into account at the NLO level with Λ (3) QCD = 370 MeV and Λ (4) QCD = 304 MeV. The main observations are listed below.…”

“…Moreover, following [20] with some refinements explained in [2], one obtains the following windows for the values of the moments:…”

“…These estimates were derived from our LCSR analysis [2,11] by combining all data of set 1 with the lattice results obtained in [21] and [22], respectively. All values were evaluated at the typ-ical lattice scale µ 2 Lat = 4 GeV 2 , using the definition…”

“…The (spacelike) transition form factors (TFFs) of pseudoscalar mesons, in particular the pion, have been extensively studied within QCD, because in leading order they are purely electromagnetic processes with the binding QCD effects being factorized out into the pion distribution amplitude (DA)-see [1] for a review and [2] for recent references. This means that for a highly virtual photon with the four-momentum transfer Q 2 and a quasi-real photon with q 2 → 0, the TFF can be cast as the convolution of the twist-two hard-scattering ampli-…”

“…, describing the elementary process γ * γ → qq, with the twist-two pion DA ϕ (2) π (x; µ 2 ) so that…”