Abstract
We reconsider QCD factorization for the leading power contribution to the γ*γ → π0 form factor Fγ*γ→π0(Q2) at one loop using the evanescent operator approach, and demonstrate the equivalence of the resulting factorization formulae derived with distinct prescriptions of γ5 in dimensional regularization. Applying the light-cone QCD sum rules (LCSRs) with photon distribution amplitudes (DAs) we further compute the subleading power contribution to the pion-photon form factor induced by the “hadronic” component of the real photon at the next-to-leading-order in mathcal{O}left({alpha}_sright) , with both naive dimensional regularization and ’t Hooft-Veltman schemes of γ5. Confronting our theoretical predictions of Fγ*γ→π0 (Q2) with the experimental measurements from the BaBar and the Belle Collaborations implies that a reasonable agreement can be achieved without introducing an “exotic” end-point behaviour for the twist-2 pion DA.
Highlights
Dimensional regularization was resolved by adjusting the way of manipulating γ5 in each diagram to preserve the axial-vector Ward identity [6]
Computing these effective diagrams with dimensional regularization applied to the UV divergences and with the IR singularities regularized by the fictitious gluon mass, we find that ME(11)off vanishes at one loop with the naive dimensional regularization (NDR) scheme of γ5 and it receives a nonvanishing contribution of O( ) with the HV scheme of γ5 from the effective diagram with a collinear gluon exchange between two external quarks
To understand the phenomenological impact of the QCD resummation for the large logarithms appearing in the factorization formula for the leading power contribution and in the light-cone QCD sum rules (LCSRs) for the hadronic photon correction, we further present in figure 7 our predictions for the π0γ∗γ form factor, at LL, next-to-leading order (NLO) and NLL accuracy, with the BMS model
Summary
The one-loop contribution to the matrix element of the evanescent operator OE, μν depends on the renormalization prescription of γ5 in the D-dimensional space We will employ both the NDR and HV schemes of γ5 below for the illustration of the prescription independence of the factorization formula of Fγ∗γ→π0(Q2) at O(αs) and at leading power in 1/Q2. We emphasize again that the γ5-prescription independence of the leading power factorization formula for Fγ∗γ→π0(Q2) stems from the fact that the QCD matrix element q(x p) q(xp)|jμem|γ(p ) itself is free of the γ5 ambiguity in dimensional regularization and both the NDR and HV prescriptions can be employed to construct QCD factorization theorems for hard processes provided that the corresponding matching coefficients are computed in an appropriate way without overlooking the potential evanescent operators.
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