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

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

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

Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium

We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We discuss the interplay of the scales arising in the Soft-Collinear Effective Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2. For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for 1-z << alpha_s^2. The S- and P-wave octet shape functions are calculated. When they are included in the analysis of the photon spectrum of the Upsilon (1S) system, the agreement with data in the end-point region becomes excellent. The NRQCD matrix elements and are also obtained.Comment: Revtex, 11 pages, 6 figures. Minor improvements and references added. Journal versio

Subleading Shape Functions in Inclusive B Decays

The contributions of subleading shape functions to inclusive decay distributions of B mesons are derived from a systematic two-step matching of QCD current correlators onto soft-collinear and heavy-quark effective theory. At tree-level, the results can be expressed in terms of forward matrix elements of bi-local light-cone operators. Four-quark operators, which arise at O(g^2), are included. Their effects can be absorbed entirely into a redefinition of other shape functions. Our results are in disagreement with some previous studies of subleading shape-function effects in the literature. A numerical analysis of B->X_u+l+nu decay distributions suggests that power corrections are small, with the possible exception of the endpoint region of the charged-lepton energy spectrum.Comment: 22 pages, 2 figures; several typos corrected; version published in JHE

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

Assessing hazards and disaster risk on the coast for Pacific small island developing States: The need for a data-driven approach

Small island developing States, such as those in the Pacific, are often prone to multiple hazards that have potential to result in disaster and / or restrict development. Hazard data can be limited in resolution or omitted in or near SIDS’ coasts, but a growing and improved range of datasets are becoming available. Through an analysis of approximately 100 policy documents on hazards and disaster risk management in Pacific island nations, we found: limited information on hazards and how they manifest to disasters at local levels, thus not fully connecting driver and subsequent risk; at times a non-specific multi-hazard approach prompting needs to address more specific hazards; and restricted temporal and spatial scales of analysis that potentially limit continuity of actions where mitigation methods evolve. These limitations suggest that appropriate and timely high resolution hazard data, is needed from the top-down to underpin the design and development of local disaster risk management plans, simultaneous to local, bottom-up knowledge and interpretation to bring the realities of such hazard data to life. Developing and ensuring openly available hazard data will enable island States to develop more robust, inclusive disaster risk management plans and mitigation policies, plus aid inter-island comparison for communal learning