Unbiased analysis of CLEO data at NLO and the pion distribution amplitude

Abstract

We discuss different QCD approaches to calculate the form factor F γ * γπ (Q 2 ) of the γ * γ → π 0 transition giving preference to the light-cone QCD sum rules (LCSR) approach as being the most adequate. In this context we revise the previous analysis of the CLEO experimental data on F γ * γπ Q 2 by Schmedding and Yakovlev. Special attention is paid to the sensitivity of the results to the (strong radiative) α s -corrections and to the value of the twist-four coupling δ 2 . We present a full analysis of the CLEO data at the NLO level of LCSRs, focusing particular attention to the extraction of the relevant parameters to determine the pion distribution amplitude, i.e., the Gegenbauer coefficients a 2 , a 4 . Our analysis confirms our previous results and also the main findings of Schmedding and Yakovlev: both the asymptotic, as well as the Chernyak-Zhitnitsky pion distribution amplitudes are completely excluded by the CLEO data. A novelty of our approach is to use the CLEO data as a means of determining the value of the QCD vacuum non-locality parameter λ 2 q = qD 2 q / qq = 0.4 GeV 2 , which specifies the average virtuality of the vacuum quarks.Recently, the CLEO collaboration [1] has measured the γ * γ → π 0 form factor F γ * γπ (Q 2 ) with high precision. This data has been processed by Schmedding and Yakovlev (SY) [2] using light-cone QCD sum rules (LCSR), taking also into account the perturbative QCD contributions in the next-to-leading order (NLO) approximation. In this way SY obtained useful constraints on the shape of the pion distribution amplitude (DA) in terms of confidence regions for the Gegenbauer coefficients a 2 and a 4 , the latter being the projection coefficients of the pion DA on the corresponding eigenfunctions. Note that SY have extended to the NLO the LCSR approach suggested before by Khodjamirian [3] for the leading order (LO) light-cone sum rule method.The present analysis gives further support to the claim, expressed by the above mentioned authors, that LCSRs provide the most appropriate basis in describing the form factor of the γ * γ → π 0 transition. This is intimately connected with peculiarities of real-photon processes in QCD [3,4]. But the method of the CLEO data processing, adopted in [2], seems to be not quite complete from our point of view. We think that an optimal analysis should take into account the correct ERBL evolution of the pion DA to the scale Q 2 exp of the process (the latter not to be fixed at some average point, µ SY = 2.4 GeV, as done in [2]) and to re-estimate the contribution δ 2 from the next twist term. The influence of both these effects appears to be important and it is examined here in detail. Furthermore, we are not satisfied with the error estimation performed in the SY analysis, for reasons to be explained later, and prefer therefore to use a more traditional treatment to determine the sensitivity to the input parameter δ 2 and the construction of the 1-σ and 2-σ error contours.Our main goal in the present work will be to obtain new constraints on the ...

Measurement of theγγ*→ηandγγ*→η′transition form factors

“…In Fig. 17 the form factor for the |n -state multiplied by 3Q 2 /5 is compared with the measured γ * γ → π 0 form factor [1] and the results of the QCD calculations performed by A. P. Bakulev, S. V. Mikhailov and N. G. Stefanis [29] for the asymptotic DA [30], the ChernyakZhitnitsky π 0 DA [31], and the π 0 DA derived from QCD sum rules with non-local condensates [32]. The horizontal dashed line indicates the asymptotic limit for the π 0 form factor.…”

“…18. The dotted curve shows the QCD prediction [29] for the asymptotic DA [30], defined by multiplying the π 0 curve in Fig. 17 by a factor of ( √ 2/3)f s /f π .…”

“…The dashed line indicates the asymptotic limit for the form factor. The dotted curve shows the prediction [29] for the asymptotic DA [30].…”

Erratum: QCD analytic perturbation theory: From integer powers to any power of the running coupling [Phys. Rev. D72, 074014 (2005)]

“…4(b) a comparison of this quantity with its counterpart in standard QCD, namely, a (2) (L) ν . For Standard QCD PT QCD FAPT the purpose of illustration, we select the value ν = γ 2 /(2b 0 ) ≈ 0.62, which corresponds to the 1-loop evolution exponent of the non-singlet quark operator of index 2, entering a number of applications in DIS and also various exclusive reactions [43,50,51].…”

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

“…While it may still be not possible to clarify all these theoretical issues conclusively, we believe that significant progress has quite recently been achieved in understanding the pion structure both from the theoretical side-perturbatively [26,27,28,29,30] and nonperturbatively [1, 31,32,33,34]-as well as from the experimental side [35,36,37] and associated data-processing techniques [38,39,40], a progress that could bring to a cleaner comparison between data and various theoretical QCD predictions [31,39,40,41,42,43,44,45,46,47,48,49]. 1 Moreover, a program to compute the electromagnetic and transition form factors of mesons on the lattice has been launched by two collaborations, [51,52] and [53], that may provide valuable insights when it is completed.…”