Hao-Chung Hu, Hsiang-nan Li
We calculate the time-like pion-photon transition form factor and the pion electromagnetic form factor up to next-to-leading order (NLO) of the strong coupling constant in the leading-twist $k_T$ factorization theorem. It is found that the NLO corrections to the magnitudes (phases) of the above form factors are smaller than 10% (10 degrees) at large invariant mass squared $Q^2$ of the virtual photons. The increase of the strong phases with $Q^2$ is obtained, consistent with the tendency indicated by experimental data. This behavior is attributed to the inclusion of parton transverse momenta $k_T$, implying that the $k_T$ factorization theorem is an appropriate framework for analyzing complex time-like form factors. Potential extensions of our formalism to two-body and three-body hadronic $B$ meson decays are pointed out.
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http://arxiv.org/abs/1204.6708
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