Infrared regulators and SCETII

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.Comment: 9 pages. Added discussion about relationship between IR regulators and messenger mode

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

Factorization and Endpoint Singularities in Heavy-to-Light decays

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.Comment: 5 pages, Added details on comparison with the literatur

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

Strong Phases and Factorization for Color Suppressed Decays

We prove a factorization theorem in QCD for the color suppressed decays B0-> D0 M0 and B0-> D*0 M0 where M is a light meson. Both the color-suppressed and W-exchange/annihilation amplitudes contribute at lowest order in LambdaQCD/Q where Q={mb, mc, Epi}, so no power suppression of annihilation contributions is found. A new mechanism is given for generating non-perturbative strong phases in the factorization framework. Model independent predictions that follow from our results include the equality of the B0 -> D0 M0 and B0 -> D*0 M0 rates, and equality of non-perturbative strong phases between isospin amplitudes, delta(DM) = delta(D*M). Relations between amplitudes and phases for M=pi,rho are also derived. These results do not follow from large Nc factorization with heavy quark symmetry.Comment: 38 pages, 6 figs, typos correcte

Testing factorization in B -> D(*)X decays

In QCD the amplitude for B0 -> D(*)+pi- factorizes in the large Nc limit or in the large energy limit Q >> Lambda_QCD where Q = {m_b, m_c, m_b-m_c}. Data also suggests factorization in exclusive processes B-> D* pi+ pi- pi- pi0 and B-> D* omega pi-, however by themselves neither large Nc nor large Q can account for this. Noting that the condition for large energy release in B0-> D+ pi- is enforced by the SV limit, m_b, m_c >> m_b-m_c >> Lambda, we propose that the combined large Nc and SV limits justify factorization in B -> D(*) X. This combined limit is tested with the inclusive decay spectrum measured by CLEO. We also give exact large Nc relations among isospin amplitudes for B -> D(*)X and B -> D(*) D-bar(*)X, which can be used to test factorization through exclusive or inclusive measurements. Predictions for the modes B-> D(*) pi pi, B-> D(*)K K-bar and B-> D(*) D-bar(*) K are discussed using available data.Comment: 15 pages, 3 included .eps figures, minor change

Reducing theoretical uncertainties in mb and lambda1

We calculate general moments of the lepton energy spectrum in inclusive semileptonic B -> X_c l \nu decay. 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 \nu decay.Comment: 8 pages, one figur

Enhanced Nonperturbative Effects in Z Decays to Hadrons

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.Comment: 17 pages. Paper reorganized, and more discussion and results include