Effective Theory Description of Weak Annihilation in B Xu l nu Decays.pdf

Effective Theory Description of Weak Annihilation in B → X ℓν Decays u 6 0 J.J. Sanz-Cilleroa∗ 0 2 a Groupe Physique Th´eorique, IPN Orsay, Universit´e Paris-Sud XI, 91406 Orsay, France p e-mail: cillero@ipno.in2p3.fr e S The semileptonic B → Xuℓν decays allow a pretty clean determination of the CKM matrix element |Vub |. Nev- ertheless, the presence of weak annihilation effects near the end-point of the q2 spectrum introduces uncertainties 1 in the inclusive calculation, requiring the use of non-perturbative techniques like heavy meson chiral perturbation 1 theory and large NC limit. v 2 0 0 1. Introduction l 9 0 The B ∼ bq¯ meson decay through the inclusive 6 q 0 semileptonic channel Bq → Xuℓν has been shown / to be a very clean way to determine |Vub | [2]. h p The inclusive Bq analysis makes use of the op- - erator product expansion (OPE) [2,3]. The first l p difference between the B− and B0 decays arises e u d,s 3 h at next-to-next-to-next-to-leading order (N LO) : in the 1/mb expansion. It is due to the topolo- v i gies where the incoming bq¯ pair annihilates into X a W –boson (Fig. (1)), giving away an infinites- r imal amount of momentum through soft gluon Figure 1. Examples of a) non-annihilating topolo- a radiation. These contributions are known as gies; b) WA diagrams. weak-annihilation (WA) [4]. They appear as a with Bq = 0 in the factorisatio