Factorization in Exclusive and Seminclusive Decays and Effective Theories for Massless Particles

Abstract

We prove rigorously factorization in the seminclusive decay $B\to D^{(\ast )}+jet$ using the large energy effective theory. It is also shown that this effective theory is unable to consistently describe completely exclusive processes, such as the decay $B\to D^{(\ast )}+\pi (\rho )$, and therefore also related properties such as factorization. This is due to an oversimplification of transverse momentum dynamics. We present a variant of the large energy effective theory, i.e. a new effective theory for massless particles, which properly takes into account transverse momentum dynamics and is therefore the natural framework to study exclusive non-leptonic decays. Finally, it is shown that the collinear instability of the large energy effective theory disappears when seminclusive observables are considered.

Latex file, 34 pages, no figures. There is a more detailed discussion about pinch singularities; some typos are corrected

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