Abstract
In this paper we calculate the power corrections to the pion transition form factor within the framework of perturbative QCD approach on the basis of $k_T$ factorization. The power suppressed contributions from higher twist pion wave functions and the hadronic structure of photon are investigated. We find that there exists strong cancellation between the two kinds contributions, thus the total power corrections considered currently are very small, and the prediction of the leading power contribution with joint resummation improved perturbative QCD approach is almost unchanged. This result confirms that the pion transition form factor is a good platform to constrain the nonperturbative parameters in pion wave functions. Moreover, our result can accommodate the anomalous data from BaBar, or agrees with results from Belle according to the choice of Gegebauer moment in the pion wave function, and the more precise experimental data from Belle-II is expected.
Highlights
The pion-photon transition process γÃγ → π0 provides a golden place to test the strong interaction dynamics of hadronic reactions in the framework of QCD [1,2,3,4,5,6,7]
The subleading power corrections start from 1=Q4, which fall down rapidly when Q2 increases, and are significant only at a small Q2 region. From this figure we can see that the contributions from twist-4 pion wave functions and hadronic structure of the photon have a different sign; the cancellation between them makes the power correction investigated in this paper minor even at a small Q2 region. This result is consistent with the investigation from light-cone sum rules [34], so that the next-to-leading power (NLP) corrections in pion transition form factor (TFF) are small, which is contrary to the leptonic radiative decay B → γlν [37], where the NLP corrections decrease the LP result over 50%
Within the framework of the PQCD approach based on kT factorization, we studied the high power corrections to the pion TFF
Summary
The pion-photon transition process γÃγ → π0 provides a golden place to test the strong interaction dynamics of hadronic reactions in the framework of QCD [1,2,3,4,5,6,7]. In [15,26,27], the light-cone sum rules (LCSR) approach is employed to calculate the soft correction to the leading twist contribution, which can effectively take the subleading power “hadronic” photon correction into account Within this method the theoretical accuracy for predicting the pion TFF is improved by including the nextto-next-to-leading order (NNLO) QCD correction to the twist-2 contribution, the contribution from twist-4 and twist-6 pion LCDAs, and the finite-width effect of the unstable vector mesons in the hadronic dispersion relation [28,29,30,31,32]. In a recent study [33], the pion TFF is considered through LCSR in combination with the renormalization group of QCD, which amounts to a certain version of fractional analytic perturbation theory Another approach to accommodate the contribution from the “hadronic photon” is to introduce the LCDAs of the photon.
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