Non-leptonic B decays into two light mesons in soft-collinear effective theory

We consider non-leptonic B decays into two light mesons at leading order in soft-collinear effective theory, and show that the decay amplitudes are factorized at next-to-leading order in _s. The operators for non-leptonic B decays in the full theory are first matched to the operators in SCET_I, which is the effective theory appropriate for with Λ0.5 GeV. We evolve the operators and the relevant time-ordered products in SCET_I to SCET_II, which is appropriate for . Using the gauge-invariant operators in SCET_II, we compute non-leptonic B decays in SCET, including the non-factorizable spectator contributions and spectator contributions to the heavy-to-light form factor. As an application, we present the decay amplitudes for in soft-collinear effective theory.     

Factorization and the soft overlap contribution to heavy-to-light form factors

Using the formalism of soft-collinear effective theory, a complete separation of short- and long-distance contributions to heavy-to-light transition form factors at large recoil is performed. The universal functions ζ_M(E) parameterizing the “soft overlap” contributions to the form factors are defined in terms of matrix elements in the effective theory. Endpoint configurations corresponding to kinematic situations where one of the valence partons in the external mesons carries very small momentum are accounted for in terms of operators involving soft-collinear messenger fields. They contribute at leading order in Λ_QCD/E and spoil factorization. An analysis of operator mixing and renormalization-group evolution in the effective theory reveals that the intermediate scale is without significance to the soft functions ζ_M(E), and that the soft overlap contribution does not receive a significant perturbative (Sudakov) suppression.     

Light-cone sum rules for the heavy-to-light transition in the effective theory

Heavy-to-light weak form factor is calculated using the light-cone sum rule (LCSR) in the framework of soft-collinear effective theory (SCET). There are spin-symmetric and spin-nonsymmetric contributions. Leading order spin-symmetric contribution corresponds to the “soft overlap” where some of the partons carry very small momentum. The next-to-leading order spin-symmetric and spin-nonsymmetric parts are characterized by a collinear gluon exchange with the spectator quark. We reproduce the full theory LCSR results and give comments on recent LCSR in SCET.     

Calculation of the quark and gluon form factors to three loops in QCD

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading \( \mathcal{O}\left( \varepsilon \right) \) terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.     

Improving jet distributions with effective field theory

We obtain perturbative expressions for jet distributions using soft-collinear effective theory (SCET). By matching SCET onto QCD at high energy, tree level matrix elements and higher order virtual corrections can be reproduced in SCET. The resulting operators are then evolved to lower scales, with additional operators being populated by required threshold matchings in the effective theory. We show that the renormalization group evolution and threshold matchings reproduce the Sudakov factors and splitting functions of QCD, and that the effective theory naturally combines QCD matrix elements and parton showers. The effective theory calculation is systematically improvable and any higher order perturbative effects can be included by a well-defined procedure.     

Precision model independent determination of |Vub| from B --> pilnu

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.     

Constraining light colored particles with event shapes

Using recently developed techniques for computing event shapes with soft-collinear effective theory, CERN Large Electron Positron Collider event shape data are used to derive strong model-independent bounds on new colored particles. In the effective field theory computation, colored particles contribute in loops not only to the running of alphas but also to the running of hard, jet, and soft functions. Moreover, the differential distribution in the effective theory explicitly probes many energy scales, so even shapes have a strong sensitivity to new particle thresholds. Using thrust data from ALEPH and OPAL, colored adjoint fermions (such as a gluino) below 51.0 GeV are ruled out to 95% confidence. This is nearly an order-of-magnitude improvement over the previous model-independent bound of 6.3 GeV.     

Resummed photon spectrum in radiative upsilon decays

We present a theoretical prediction for the photon spectrum in radiative upsilon decay including the effects of resumming the end point region, E(gamma)-->M(upsilon)/2. Our approach is based on nonrelativistic QCD (NRQCD) and the soft-collinear effective theory. We find that our results give much better agreement with data than the leading order NRQCD prediction.     

Infrared scales and factorization in QCD

Effective field theory methods are used to study factorization of the deep inelastic scattering cross-section. The cross-section is shown to factor in QCD, even though it does not factor in perturbation theory for some choices of the infrared regulator. Messenger modes are not required in soft-collinear effective theory for deep inelastic scattering as x→1$x\to 1$.     

Threshold resummation in momentum space from effective field theory

Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function F2(x,Q2) in the end-point region x-->1 directly in momentum space. An explicit all-order formula is derived, which expresses the short-distance coefficient function C in the convolution F2 = C multiply sign in circle phi q in terms of Wilson coefficients and anomalous dimensions defined in the effective theory. Contributions associated with the physical scales Q2 and Q2(1-x) are separated from nonperturbative hadronic physics in a transparent way. A crucial ingredient to the momentum-space resummation is the exact solution to the integro-differential evolution equation for the jet function, which is derived. The methods developed in this Letter can be applied to many other hard QCD processes.     

Determining gamma from B --> pi(pi) decays without the CP-asymmetry Cpi(0)pi(0)

Factorization based on the soft-collinear effective theory (SCET) can be used to reduce the number of hadronic parameters in an isospin analysis of B --> pi(pi) decays by one. This gives a theoretically precise method for determining the CP violating phase gamma by fitting to the B --> pi(pi) data without Cpi(0)pi(0). SCET predicts that gamma lies close to the isospin bounds. With the current world averages we find gamma = 75 degrees +/- 2 degrees(+9 degrees)(-13 degrees), where the uncertainties are theoretical, then experimental.     

Applied validity of effortless method for design of sinusoidal surface microstructure

With the purpose of easily analyzing and designing the transmittance performance of a sinusoidal surface microstructure, the validity of effortless methods including scalar diffraction theory and effective medium theory has been evaluated quantitatively by the comparison of diffraction efficiencies predicted from scalar theory and effective indices theory, respectively, with exact results calculated with the rigorous vector method of Fourier modal method. Generally speaking, when the normalized period of surface microstructure is less than ten wavelengths of the incident light the scalar diffraction theory is believed to be inaccurate for designing and analyzing the diffraction efficiency of surface microstructure. But, in this paper, it is found that scalar diffraction theory can be used for predicting transmittance of the optical elements when the normalized period is more than three wavelengths of incident light within the error less than 5% at normal incidence. In addition, it is generally recognized that the effective medium theory is inaccurate for analyzing periodic surface microstructure when the normalized period is more than a tenth of the wavelength of incident light. However, the results in this study shows that effective medium theory is accurate as only zero-order waves are to propagate through the surface profiles, which the maximum difference between zero-order effective indices method and rigorous vector method reaches to 1%. Besides, the limitation of both simplified theories is dependent on not only the normalized period of a surface microstructure but also the normalized groove depth. Therefore, the range of applied validity of scalar theory and effective medium theory is expanded quantitatively compared to that of previous inaccuracy application for more easily designing and analyzing a sinusoidal surface microstructure.     

Inclusion of fermions in the locally SU(2) ⊗ U(1)-invariant model with dynamical symmetry breaking

It is shown that dynamic symmetry breaking in the locally SU(2) U(1)-invariant model with mixed inclusion of fermions in a four-fermion interaction leads to a situation in which one collective scalar field, representing the sum of all generations of fermion-antifermion pairs, acts as the total (one-loop) effective Lagrangian. Mass formulas are found for the scalar field and gauge vector fields. The effective Lagrangian obtained coincides in form with the standard Lagrangian in the Glashow-Weinberg-Salam theory of electroweak interactions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 41–45, July, 1991.     

Vacuum Stability in Kaluza-Klein Geometric Sigma Models

In Kaluza-Klein geometric sigma models, the scalar fields coupled to higher-dimensional gravity are pure gauge. The gauge fixed theory contains no matter fields, and can consistently be reduced to 4 dimensions, provided the internal space is chosen in the form of a group manifold. The effective 4-dimensional theory includes standard Einstein and Yang-Mills sectors, and is free of the classical cosmological constant problem. In this paper, the stability of the internal excitations is analyzed. It is shown that the initial Lagrangian can be modified to lead to a classically stable effective 4-dimensional theory, independently of the particular group used, and retaining all the basic features of the unmodified theory.     

Power-Law Expansion and Scalar Field Cosmology in Higher Derivative Theory

In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the scale factor. A number of evolutionary phases of the universe including the present accelerating phase are found to exist with scalar field in the higher derivative theory of gravitation. The properties of scalar field and other physical parameters are discussed in detail. We find that the equation of state parameter for matter and scalar field are same at late time in each case. We observe that a higher derivative term can hardly be a candidate to describe the presently observed accelerated expansion. It is only the hypothetical fluids, which provide the late time acceleration. It is also remarkable that the higher derivative theory does not effect the radiating model of scalar field cosmology.     

Analysis of the pion-kaon sigma term and related topics

We calculate the one-loop contributions to the difference between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor of the pion. This is related to the weaker final state interactions in the pion-kaon channel. Received: 21 March 2002 / Published online: 5 July 2002     

Vanishing scalar masses in no-scale supergravity

Radiative corrections to the effective scalar potential are studied in no-scale supergravity models with local supersymmetry spontaneously broken by a gravitino mass. A simple proof is given that gauge non-singlet scalar fields acquire no supersymmetry breaking masses at the one-loop level, and a general argument is given extending this result to all orders of perturbation theory in the effective low-energy theory, proving also that no trilinear soft supersymmetry breaking terms in the effective potential are generated. These results are applicable to the four-dimensional no-scale supergravity theory obtained from the superstring after compactification, and support suggestions that the dominant source of global supersymmetry breaking in this theory may be the gaugino mass.