Semi-inclusive hadronicBdecays in the endpoint region

Abstract

We consider in the soft-collinear effective theory semi-inclusive hadronic B decays, B ! XM, in which an energetic light meson M near the endpoint recoils against an inclusive jet X. We focus on a subset of decays where the spectator quark from the B meson ends up in the jet. The branching ratios and direct CP asymmetries are computed to next-to-leading order accuracy in s and to leading order in 1=m b . The contribution of charming penguins is extensively discussed, and a method to extract it in semi-inclusive decays is suggested. Subleading 1=m b corrections and SU3 breaking effects are discussed.

Semiinclusive hadronicBdecays as null tests of the standard model

“…For simplicity we concentrate on the ∆S = 1 decay B − →K 0 X − d , while the results will be easy to extend to the ∆S = 0 decay B − → K 0 X − s , as well as to the decays involving K * vector mesons. More importantly, the results will also apply to theB 0 →K 0 X 0 , K 0 X 0 s decays, since the contributions where the spectator ends up in the energetic K 0 meson are 1/m 2 b suppressed [12]. The relevant part of the SCET I effective weak Hamiltonian is…”

“…The view of BBNS [23] is that the phase space suppression of the threshold region is strong enough so that nonperturbative contributions are subleading, while Bauer et al [22] argue that the phase space suppression is not effective as numerically 2m c /m b ∼ O(1). For semiinclusive hadronic decays the factorization of charming penguin contributions into soft and collinear parts has been shown in [21]. We will first proceed as though charm quarks can be perturbatively integrated out leading to C 1 term in (15) for p = c. The effect of nonperturbative charming penguins will then be discussed at the end of present subsection.…”

“…with the ellipses denoting an order of magnitude smaller terms that can be found in Appendix A of [21]. In the matching of full QCD effective weak Hamiltonian to SCET I weak Hamiltonian the strong phases are generated at the order α S (m b ) from the configurations with on-shell intermediate quarks carrying a collective momentum p 2 ∼ m 2 b .…”

“…We restrict the discussion to the endpoint region of the decay phase space with energetic neutral kaon going in then = (1, 0, 0, 1) direction, and the particles in X − s,d forming an energetic jet with invariant mass p 2 X ∼ Λ QCD m B going in the n = (1, 0, 0, −1) direction. For this kinematic setup SCET [19,20] offers a theoretical framework [21] that will allow us to assess the size of U-spin breaking using already available nonperturbative input from lattice QCD (in the limit of perturbative charming penguins). For simplicity we concentrate on the ∆S = 1 decay B − →K 0 X − d , while the results will be easy to extend to the ∆S = 0 decay B − → K 0 X − s , as well as to the decays involving K * vector mesons.…”

“…Also, since untagged final states are used no separation of X d from X s is required, rendering PWDs in (1) rather powerful null test observables. Finally, if M 0 is a light meson (for instance K S , η ′ ) the partial decay widths in the endpoint region where M 0 is very energetic, with E M ∼ M B /2 + O(Λ), do not depend on the spectator quark at LO and NLO in 1/m b [12]. Thus the PWD for both charged and neutral semiinclusive B meson decays (2) vanish in the endpoint region up to U-spin breaking and corrections of higher order in 1/m b .…”