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Register a new userUnraveling Soft Components in the Shape Function for Inclusive B Decays
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Authors
Hiroyuki Kawamura n RIKEN
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We present a systematic study of the shape function for inclusive B-meson decays in the heavy-quark limit, which is based on the QCD equations of motion and heavy-quark symmetry, and takes into account the cusp divergence due to radiative corrections.
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Using methods of effective field theory, factorized expressions for arbitrary B -> X_u l nu decay distributions in the shape-function region of large hadronic energy and moderate hadronic invariant mass are derived. Large logarithms are resummed at next-to-leading order in renormalization-group improved perturbation theory. The operator product expansion is employed to relate moments of the renormalized shape function with HQET parameters such as m_b, Lambda(bar) and lambda_1 defined in a new physical subtraction scheme. An analytic expression for the asymptotic behavior of the shape function is obtained, which reveals that it is not positive definite. Explicit expressions are presented for the charged-lepton energy spectrum, the hadronic invariant mass distribution, and the spectrum in the hadronic light-cone momentum P_+ = E_H - P_H. A new method for a precision measurement of |V_{ub}| is proposed, which combines good theoretical control with high efficiency and a powerful discrimination against charm background.
The inclusive semileptonic branching ratio is often employed to normalize other inclusive B decays. Using recent determinations of the non-perturbative parameters of the Operator Product Expansion we compute the normalization factor for the branching ratio of B->X_s gamma and find a few percent enhancement with respect to previous determinations.
The combination of collinear factorization with effective field theory originally developed for soft interactions of heavy quarks provides the foundations of the theory of exclusive and semi-inclusive B decays. In this article I summarize some of the later conceptual developments of the so-called QCD factorization approach that make use of soft-collinear effective theory. Then I discuss the status and results of the calculation of the hard-scattering functions at the next order, and review very briefly some of the phenomenology, covering aspects of charmless, electroweak penguin and radiative (semi-leptonic) decays.
We propose a method for a QCD based calculation of one-particle inclusive decays of the form B to bar D X or B to bar D^* X. It is based on the heavy mass limit and a short distance expansion of the amplitudes, which yield a power series in the parameter 1/M^2_X for the spectra and in Lambda_QCD m_b/(m_b - m_c)^2 for the rates. We study the leading term of this expansion for the case of the semi--leptonic decays B to bar D X l^+ u.
We present preliminary results on two analyses performed by the SLD Collaboration using inclusive B decays: a search for CP violation and a search for the b --> sg transition.
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