Two-parton twist-3 factorization in perturbative QCD
Department of Physics, Ochanomizu University, Bunkyo-ku, 112-8610, Tokyo, Japan
2 Institute of Physics, Academia Sinica, Taipei, Taiwan 115, Republic of China
3 Department of Physics, National Cheng-Kung University, Tainan, Taiwan 701, Republic of China
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We prove the collinear factorization theorem for the process at the twist-3 level in the covariant gauge by means of the Ward identity, concentrating on the two-parton case. It is shown that soft divergences cancel and collinear divergences are grouped into the pseudo-scalar and pseudo-tensor two-parton twist-3 pion distribution amplitudes. The delicate summation of a complete set of diagrams for achieving factorization in momentum, spin, and color spaces is emphasized. The proof is then extended to the exclusive semileptonic decay , assuming the hard scale to be of , where is a hadronic scale and M B the B meson mass. We explain the distinction between the factorization of collinear divergences for a pion distribution amplitude and of soft divergences for a B meson distribution amplitude. The gauge invariance and universality of the two-parton twist-3 pion distribution amplitudes are confirmed. The proof presented here can accommodate the leading twist-2 case. We then compare our proof with that performed in the framework of soft-collinear effective theory.
© Springer-Verlag, 2005