arXiv subjects
Publications and source records attributed to Christian W. Bauer.
We discuss the relationship between the graphical amplitudes T, C, P, ... used to parameterize nonleptonic B decay amplitudes, and matrix elements of operators in the soft-collinear effective theory (SCET) at leading order in Λ/m_b. Using the SU(3) flavor symmetry of the weak Hamiltonian we derive all-order constraints on the electroweak penguin contributions to the Wilson coefficients of SCET operators.
In light of the large amount of new experimental data, we revisit the determination of V_{cb} and m_b from inclusive semileptonic and radiative B decays. We study shape variables to order lqcd^3/m_b^3 and alpha_s^2β_0, and include the order alpha_s, lqcd/m_b correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the 1S and kinetic mass schemes for the b quark, with and without expanding m_b-m_c in HQET. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find V_{cb} = (41.4 +- 0.6 +- 0.1) x 10^{-3} and m_b^{1S} = 4.68 +- 0.03 GeV, including our estimate of the theoretical uncertainty in the fit.
Using the soft-collinear effective theory we derive the factorization theorem for the decays B-> M1 M2 with M{1,2}= pi,K, rho,K*, at leading order in Lambda/E_M and Lambda/mb. The results derived here apply even if alpha_s(E_M Lambda) is not perturbative, and we prove that the physics sensitive to the E*Lambda scale is the same in B-> M1 M2 and B-> M form factors. We argue that c-cbar penguins could give long-distance effects at leading order. Decays to two transversely polarized vector mesons are discussed. Analyzing B-> pi pi we find predictions for B^0 -> pi^0 pi^0 and |V_{ub}| f_+(0) as a function of gamma.
We use soft collinear effective field theory (SCET) to study nonperturbative strong interaction effects in Z decays to hadronic final states that are enhanced in corners of phase space. These occur, for example, in the jet energy distribution for two jet events near E_J=M_Z/2, the thrust distribution near unity and the jet invariant mass distribution near zero. The extent to which such nonperturbative effects for different observables are related is discussed.
We consider matching from SCETI, which includes ultrasoft and collinear particles, onto SCETII with soft and collinear particles at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. We give a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in SCETII are sufficient to reproduce all the infrared divergences of SCETI. We explain the relationship between IR regulators and an additional mode proposed for SCETII.
We calculate the decay distributions for inclusive B -> X_s gamma and B -> X_u l nu decays in the endpoint region, where radiative corrections are large. The computation is done using effective field theory methods. The matching coefficients are computed to O(alpha_s), and the anomalous dimensions to next-to-leading order. The final expressions for the differential decay spectra include the complete O(alpha_s) corrections, and sum the leading and next-to-leading Sudakov series. We present results for regions of phase space where the shape function can be expanded in local operators, and give the matching coefficients of the resulting enhanced non-perturbative effects to order alpha_s. We show that moments of the shape function {\it are not} given by moments of local operators once perturbative effects are included, explain why the shape function and its moments satisfy different renormalization group equations, and contrast this with the situation for deep inelastic scattering. We show that there are large perturbative corrections in the usual definition of the shape function. This renders incorrect previous prescriptions for combining radiative corrections with the shape function.
We show how to relate moments of the reconstructed hadronic invariant mass distribution to the moments of the physical spectrum in a model independent way. The only information needed on detector resolution functions are their first few moments. Theoretical predictions for the first three moments as functions of non-perturbative parameters are given for various lepton energy cuts.
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.
We consider the triple differential distribution dΓ/(dE_J)(dm_J^2)(dΩ_J) for two-jet events at center of mass energy M, smeared over the endpoint region m_J^2 << M^2, |2 E_J -M| ~ Δ, \lqcd << Δ<< M. The leading nonperturbative correction, suppressed by \lqcd/Δ, is given by the matrix element of a single operator. A similar analysis is performed for three jet events, and the generalization to any number of jets is discussed. At order \lqcd/Δ, non-perturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two and three jet events.
We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of endpoint singularities. A general procedure is described for including soft effects usually associated with the tail of wavefunctions in hard exclusive processes. We give an operator formulation of these soft effects using the soft-collinear effective theory, and show that they appear at the same order in the power counting as the hard spectator contribution.
We present expressions for shape variables of B decay distributions in several different mass schemes, to order $α_s^2β_0$ and (Lambda_{QCD}/mb)^3. Such observables are sensitive to the b quark mass and matrix elements in the heavy quark effective theory, and recent measurements allow precision determinations of some of these parameters. We perform a combined fit to recent experimental results from CLEO, BABAR, and DELPHI, and discuss the theoretical uncertainties due to nonperturbative and perturbative effects. We discuss the possible discrepancy between the OPE prediction, recent BABAR results and the measured branching fraction to D and D* states. We find |Vcb| = (40.8 +- 0.9) x 10^{-3} and mb^{1S} = 4.74 +- 0.10 GeV, where the errors are dominated by experimental uncertainties.
We describe in some detail the derivation of a power counting formula for the soft-collinear effective theory (SCET). This formula constrains which operators are required to correctly describe the infrared at any order in the Lambda_QCD/Q expansion (lambda expansion). The result assigns a unique lambda-dimension to graphs in SCET solely from vertices, is gauge independent, and can be applied independent of the process. For processes with an OPE the lambda-dimension has a correspondence with dynamical twist.
In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with back-to-back jets of collinear particles. Our proofs do not depend on the choice of a particular gauge, and the formalism is applicable to both exclusive and inclusive factorization. As examples we treat the pi-gamma form factor (gamma gamma* -> pi^0), light meson form factors (gamma* M -> M), as well as deep inelastic scattering (e- p -> e- X), Drell-Yan (p pbar -> X l+ l-), and deeply virtual Compton scattering (gamma* p -> gamma(*) p).
We calculate the subleading twist contributions to the endpoint of the inclusive lepton energy spectrum in B -> X_u l ν. We show that the same two subleading twist functions that appear in the decay B -> X_s γgovern the subleading effects in this decay. Using these results we find large O(Lambda/mB) corrections to the determination of |Vub| from the endpoint of the charged lepton spectrum. Using a simple model for the relevant subleading shape functions, we estimate the uncertainty in |Vub| from Lambda/mb corrections to be at the ~ 15% level for a lower lepton energy cut of 2.2 GeV.
We calculate general moments of the lepton energy spectrum in inclusive semileptonic B -> X_c l νdecay. Moments which allow the determination of mb^{1S} and lambda1 with theoretical uncertainties Delta(mb^{1S}) ~ 0.04 GeV and Delta(lambda1) ~ 0.05 GeV^2 are presented. The short distance 1S mass is used to extract a mass parameter free of renormalon ambiguities. Moments which are insensitive to mb and lambda1 and therefore test the size of the 1/mb^3 matrix elements and the validity of the OPE are also presented. Finally, we give an expression for the total branching ratio with a lower cut on the lepton energy, which allows one to eliminate a source of model dependence in current determinations of |Vcb| from B -> X_c l νdecay.
The factorization of soft and ultrasoft gluons from collinear particles is shown at the level of operators in an effective field theory. Exclusive hadronic factorization and inclusive partonic factorization follow as special cases. The leading order Lagrangian is derived using power counting and gauge invariance in the effective theory. Several species of gluons are required, and softer gluons appear as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in B->D pi, and the soft-collinear convolution for the B->Xs gamma spectrum.
We review how to determine |Vub| from inclusive semileptonic B decay using combined cuts on the leptonic and hadronic invariant masses to eliminate the b -> c background. This leads to a determination of |Vub| with theoretical uncertainty at the 5 -10% level.
In this talk I review the status of our ability to extract the CKM matrix elements |Vub| and |Vcb| from semileptonic decays. I will review both exclusive and inclusive methods and put a strong emphasis on how to ensure keeping the extractions model independent.