Rare radiative exclusive B decays in soft-collinear effective theory

We consider rare radiative B decays such as B -> K^* gamma or B -> rho gamma in soft-collinear effective theory, and show that the decay amplitudes are factorized to all orders in alpha_s and at leading order in Lambda/m_b.By employing two-step matching, we classify the operators for radiative B decays in powers of a small parameter lambda(~ \sqrt{Lambda/m_b}) and obtain the relevant operators to order lambda in SCET_I. These operators are constructed with or without spectator quarks including the four-quark operators contributing to annihilation and W-exchange channels. And we employ SCET_II where the small parameter becomes of order Lambda/m_b, and evolve the operators in order to compute the decay amplitudes for rare radiative decays in soft-collinear effective theory. We show explictly that the contributions from the annihilation channels and the W-exchange channels vanish at leading order in SCET. We present the factorized result for the decay amplitudes in rare radiative B decays at leading order in SCET, and at next-to-leading order in alpha_s.Comment: v2: 31 pages, 11 figures. An appendix is added about the quark mass effects on radiative B decay

On Power Suppressed Operators and Gauge Invariance in SCET

The form of collinear gauge invariance for power suppressed operators in the soft-collinear effective theory is discussed. Using a field redefinition we show that it is possible to make any power suppressed ultrasoft-collinear operators invariant under the original leading order gauge transformations. Our manipulations avoid gauge fixing. The Lagrangians to O(lambda^2) are given in terms of these new fields. We then give a simple procedure for constructing power suppressed soft-collinear operators in SCET_II by using an intermediate theory SCET_I.Comment: 15 pages, journal versio

External Operators and Anomalous Dimensions in Soft-Collinear Effective Theory

It has recently been argued that soft-collinear effective theory for processes involving both soft and collinear partons contains a new soft-collinear mode, which can communicate between the soft and collinear sectors of the theory. The formalism incorporating the corresponding fields into the effective Lagrangian is extended to include external current and four-quark operators relevant to weak interactions. An explicit calculation of the anomalous dimensions of these operators reveals that soft-collinear modes are needed for correctly describing the ultraviolet behavior of the effective theory.Comment: 15 pages, 2 figure

Constraining the Unitarity Triangle with B -> V gamma

We discuss the exclusive radiative decays $B\to K^{*}\gamma$, $B \to\rho\gamma$, and $B\to\omega\gamma$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\to\rho l\nu$ decay spectrum to the branching fraction of $B\to\rho\gamma$. The method is based on the cancellation of soft hadronic form factors in the large energy limit, which occurs in a suitable region of phase space. The ratio of the $B\to\rho\gamma$ and $B\to K^{*}\gamma$ branching fractions determines the side $R_{t}$ of the standard unitarity triangle with reduced hadronic uncertainties. The recent Babar bound on $B(B^0\to\rho^0\gamma)$ implies $R_t < 0.81 (\xi/1.3)$, with the limiting uncertainty coming only from the SU(3) breaking form factor ratio $\xi$. This constraint is already getting competitive with the constraint from $B_{s}$-$\bar B_{s}$ mixing. Phenomenological implications from isospin-breaking effects are briefly discussed.Comment: 23 pages, 8 figure

Factorization and Shape-Function Effects in Inclusive B-Meson Decays

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.Comment: 51 pages, 10 figures; minor corrections, version to appear in Nuclear Physics

Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors

The hard-scattering contributions to heavy-to-light form factors at large recoil are studied systematically in soft-collinear effective theory (SCET). Large logarithms arising from multiple energy scales are resummed by matching QCD onto SCET in two stages via an intermediate effective theory. Anomalous dimensions in the intermediate theory are computed, and their form is shown to be constrained by conformal symmetry. Renormalization-group evolution equations are solved to give a complete leading-order analysis of the hard-scattering contributions, in which all single and double logarithms are resummed. In two cases, spin-symmetry relations for the soft-overlap contributions to form factors are shown not to be broken at any order in perturbation theory by hard-scattering corrections. One-loop matching calculations in the two effective theories are performed in sample cases, for which the relative importance of renormalization-group evolution and matching corrections is investigated. The asymptotic behavior of Sudakov logarithms appearing in the coefficient functions of the soft-overlap and hard-scattering contributions to form factors is analyzed.Comment: 50 pages, 10 figures; minor corrections, version to appear in JHE

Non-factorizable Contributions to B→ππB \to \pi\pi Decays

We investigate to what extent the experimental information on $B \to \pi\pi$ branching fractions and CP asymmetries can be used to better understand the QCD dynamics in these decays. For this purpose we decompose the independent isospin amplitudes into factorizable and non-factorizable contributions. The former can be estimated within the framework of QCD factorization for exclusive $B$ decays. The latter vanish in the heavy-quark limit, $m_b \to \infty$, and are treated as unknown hadronic parameters. We discuss at some length in which way the non-factorizable contributions are treated in different theoretical and phenomenological frameworks. We point out the potential differences between the phenomenological treatment of power-corrections in the ``BBNS approach'', and the appearance of power -suppressed operators in soft-collinear effective theory (SCET). On that basis we define a handful of different (but generic) scenarios where the non-factorizable part of isospin amplitudes is parametrized in terms of three or four unknowns, which can be constrained by data. We also give some short discussion on the implications of our analysis for $B \to \pi K$ decays. In particular, since non-factorizable QCD effects in $B \to \pi \pi$ may be large, we cannot exclude sizeable non-factorizable effects, which violate $SU(3)_F$ flavour symmetry, or even isospin symmetry (via long-distance QED effects). This may help to explain certain puzzles in connection with isospin-violating observables in $B \to \pi K$ decays.Comment: published version, minor correction

Inclusive Measure of |V_ub| with the Analytic Coupling Model

By analyzing B -> X_u l nu_l spectra with a model based on soft-gluon resummation and an analytic time-like QCD coupling, we obtain |V_ub| = (3.76 +-0.13 +- 0.22)*10^(-3), where the first and the second error refers to experimental and theoretical errors, respectively. The V_ub value is obtained from the available measured semileptonic branching fractions in limited regions of the phase-space. The distributions in the lepton energy E_l, the hadron invariant mass m_X, the light-cone momentum P_+ = E_X - p_X, together with the double distributions in (m_X,q^2) and (E_l,s_h^max), are used to select the phase-space regions. The q^2 is the dilepton squared momentum and s_h^max is the maximal m_X^2 at fixed q^2 and E_l. The V_ub value obtained is in complete agreement with the value coming from exclusive B decays and from an over-all fit to the Standard Model parameters. We show that the slight disagreement (up to +2 sigma) with respect to previous inclusive measurements is not related to different choices for the b (and c) masses but to a different modelling of the threshold (Sudakov) region.Comment: 19 pages, 2 figures, revised version accepted in Eur.Phys.J.

The B-Meson Distribution Amplitude in QCD

The B-meson distribution amplitude is calculated using QCD sum rules. In particular we obtain an estimate for the integral relevant to exclusive B-decays \lambda_B = 460 \pm 110 MeV at the scale 1 GeV. A simple QCD-motivated parametrization of the distribution amplitude is suggested.Comment: 17 pages, 8 figures, Latex styl

Rare Decays of \Lambda_b->\Lambda + \gamma and \Lambda_b ->\Lambda + l^{+} l^{-} in the Light-cone Sum Rules

Within the Standard Model, we investigate the weak decays of $\Lambda_b \to \Lambda + \gamma$ and $\Lambda_b \to \Lambda + l^{+} l^{-}$ with the light-cone sum rules approach. The higher twist distribution amplitudes of $\Lambda$ baryon to the leading conformal spin are included in the sum rules for transition form factors. Our results indicate that the higher twist distribution amplitudes almost have no influences on the transition form factors retaining the heavy quark spin symmetry, while such corrections can result in significant impacts on the form factors breaking the heavy quark spin symmetry. Two phenomenological models (COZ and FZOZ) for the wave function of $\Lambda$ baryon are also employed in the sum rules for a comparison, which can give rise to the form factors approximately 5 times larger than that in terms of conformal expansion. Utilizing the form factors calculated in LCSR, we then perform a careful study on the decay rate, polarization asymmetry and forward-backward asymmetry, with respect to the decays of $\Lambda_b \to \Lambda \gamma$, $\Lambda l^{+}l^{-}$.Comment: 38 pages, 15 figures, some typos are corrected and more references are adde