arXiv subjects
Publications and source records attributed to M. Beneke.
Using the hierarchy of scales between the mass, $M$, and the width, $Γ$, of a heavy, unstable particle we construct an effective theory that allows calculations for resonant processes to be systematically expanded in powers of the coupling $α$ and $Γ/M$. We illustrate the method by computing the next-to-leading order line shape of a scalar resonance in an abelian gauge-Yukawa model.
Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of universal form factors up to hard-scattering corrections. In this paper we extend our previous investigation of heavy-to-light currents in soft-collinear effective theory to final states with invariant mass Lambda^2 as is appropriate to exclusive B meson decays. The effective theory contains soft modes and two collinear modes with virtualities of order m_b*Lambda (`hard-collinear') and Lambda^2. Integrating out the hard-collinear modes results in the hard spectator-scattering contributions to exclusive B decays. We discuss the representation of heavy-to-light currents in the effective theory after integrating out the hard-collinear scale, and show that the previously conjectured factorization formula is valid to all orders in perturbation theory. The naive factorization of matrix elements in the effective theory into collinear and soft matrix elements may be invalidated by divergences in convolution integrals. In the factorization proof we circumvent the explicit regularization of endpoint divergences by a definition of the universal form factors that includes hard-collinear, collinear and soft effects.
This report contains the results of the Workshop on the CKM Unitarity Triangle, held at CERN on 13-16 February 2002 to study the determination of the CKM matrix from the available data of K, D, and B physics. This is a coherent document with chapters covering the determination of CKM elements from tree level decays and K and B meson mixing and the global fits of the unitarity triangle parameters. The impact of future measurements is also discussed.
We investigate the factorization of different momentum modes that appear in matrix elements for exclusive B meson decays into light energetic particles for the specific case of B -> pi form factors at large pion recoil. We first integrate out hard modes with virtualities of order m_b^2 (m_b being the heavy quark mass), and then hard-collinear modes with virtualities m_b Lambda (Lambda being the strong interaction scale). The resulting effective theory contains soft and collinear fields with virtualities Lambda^2. We prove a previously conjectured factorization formula for B -> pi form factors in the heavy quark limit to all orders in alpha_s, paying particular attention to `endpoint singularities' that might have appeared in hard spectator interactions.
We compute next-to-leading order QCD corrections to the CP asymmetry a_{fs} = Im(Gamma_{12}/M_{12}) in flavour-specific B_{d,s} decays such as B_d->X l nu or B_s->D^-_s pi^+. The corrections reduce the uncertainties associated with the choice of the renormalization scheme for the quark masses significantly. In the Standard Model we predict a^d_{fs} = -(5.0 +- 1.1)*10^{-4}. As a by-product we also obtain the width difference in the B_d system at next-to-leading order in QCD.
I estimate the SU(3) flavour symmetry breaking in the ratio of penguin-to-tree ratios of the decays B_s\to K^+ K^- and B_d\toπ^+π^-, given an assumption on the flavour symmetry breaking of the hadronic input parameters. The decay amplitudes are calculated in QCD factorization. Implications for the determination of gamma are discussed.
In position space the interaction terms of soft-collinear effective theory must be multipole-expanded to obtain interaction terms with homogeneous scaling behaviour. In this note we provide a manifestly gauge-invariant formulation of the theory after this expansion in the presence of non-abelian gauge fields, extending our previous result. We give the effective Lagrangian (including the Yang-Mills Lagrangian for collinear and ultrasoft gluons) and heavy-to-light transition currents to second order in the power expansion, paying particular attention to the field redefinitions that lead to the gauge symmetries of the effective Lagrangian.
An important unresolved question in strong interaction physics concerns the parameterization of power-suppressed long-distance effects to hard processes that do not admit an operator product expansion (OPE). Recently Bauer et al.\ have developed an effective field theory framework that allows one to formulate the problem of soft-collinear factorization in terms of fields and operators. We extend the formulation of soft-collinear effective theory, previously worked out to leading order, to second order in a power series in the inverse of the hard scale. We give the effective Lagrangian and the expansion of ``currents'' that produce collinear particles in heavy quark decay. This is the first step towards a theory of power corrections to hard processes where the OPE cannot be used. We apply this framework to heavy-to-light meson transition form factors at large recoil energy.
In this talk I report recent results on hadronic B decays obtained with the QCD factorization approach. In the first part I update the fit of the Wolfenstein parameters (\barρ,\barη) to CP-averaged B -> pi pi, pi K branching fractions, and give the correlation between the time-dependent and direct CP asymmetry in B_d -> pi^+pi^- decay. In the second part I present an investigation of B decays into final states containing an eta or eta^\prime meson. I discuss the new theoretical issues that arise for flavour singlet mesons and present preliminary numerical results that appear to reproduce the pattern of experimental data reasonably well.
We compute perturbative QCD corrections to the lifetime splitting between the charged and neutral $B$ meson in the framework of the heavy quark expansion. These next-to-leading logarithmic corrections are necessary for a meaningful use of hadronic matrix elements of local operators from lattice gauge theory. We find the uncertainties associated with the choices of renormalization scale and scheme significantly reduced compared to the leading-order result. We include the full dependence on the charm-quark mass $m_c$ without any approximations. Using hadronic matrix elements estimated in the literature with lattice QCD we obtain $τ(B^+)/τ(B^0_d)=1.053\pm 0.027\pm 0.017$, where the effects of unquenching and $1/m_b$ corrections are not yet included. The lifetime difference of heavy baryons $Ξ^0_b$ and $Ξ^-_b$ is also briefly discussed.
A brief report on the QCD factorization approach to exclusive B decays and its applications is presented. In an appendix a subtle issue concerning partial integration in the parameterization of infrared-sensitive power corrections is clarified.
Several pieces of direct and indirect evidence now suggest that the Kobayashi-Maskawa mechanism plays a distinguished role for CP violation at the electroweak scale. This talk provides a general overview of CP violation in its various contexts, emphasizing CP violation in flavour-violating interactions, such as due to the Kobayashi-Maskawa mechanism. I then review a few recent theoretical developments relevant to the interpretation of CP violation.
This lecture provides a general overview of CP violation, emphasizing CP violation in flavour-violating interactions, such as due to the Kobayashi-Maskawa mechanism.
I discuss three B physics results with potential for exhibiting new flavour-changing interactions: (1) the time-dependent CP asymmetry in B\to J/ψK_S decay; (2) branching fractions and CP asymmetries in B\to ππ, πK decays; (3) inclusive and exclusive semi-hadronic b\to s transitions.
We show -- by explicit computation of first-order corrections -- that the QCD factorization approach previously applied to hadronic two-body decays and to form factor ratios also allows us to compute non-factorizable corrections to exclusive, radiative B meson decays in the heavy quark mass limit. This removes a major part of the theoretical uncertainty in the region of small invariant mass of the photon. We discuss in particular the decays B\to K^* γand B\to K^* l^+l^- and complete the calculation of corrections to the forward-backward asymmetry zero. The new correction shifts the asymmetry zero by 30%, but the result confirms our previous conclusion that the asymmetry zero provides a clean phenomenological determination of the Wilson coefficient C_9.
In the heavy-quark limit, the hadronic matrix elements entering nonleptonic $B$-meson decays into two light mesons can be calculated from first principles including ``nonfactorizable'' strong-interaction corrections. The $B\toπK,ππ$ decay amplitudes are computed including electroweak penguin contributions, SU(3) violation in the light-cone distribution amplitudes, and an estimate of power corrections from chirally-enhanced terms and annihilation graphs. The results are then used to reduce the theoretical uncertainties in determinations of the weak phases $γ$ and $α$. In that way, new constraints in the $(\barρ,\barη)$ plane are derived. Predictions for the $B\toπK, ππ$ branching ratios and CP asymmetries are also presented. A good global fit to the (in part preliminary) experimental data on the branching fractions is obtained without taking recourse to phenomenological models.
Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.
Even for short-distance dominated observables the QCD perturbation expansion is never complete. The divergence of the expansion through infrared renormalons provides formal evidence of this fact. In this article we review how this apparent failure can be turned into a useful tool to investigate power corrections to hard processes in QCD.