Ultrasoft Renormalization in Non-Relativistic QCD

For Non-Relativistic QCD the velocity renormalization group correlates the renormalization scales for ultrasoft, potential and soft degrees of freedom. Here we discuss the renormalization of operators by ultrasoft gluons. We show that renormalization of soft vertices can induce new operators, and also present a procedure for correctly subtracting divergences in mixed potential-ultrasoft graphs. Our results affect the running of the spin-independent potentials in QCD. The change for the NNLL t-tbar cross section near threshold is very small, being at the 1% level and essentially independent of the energy. We also discuss implications for analyzing situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig

Power Counting in the Soft-Collinear Effective Theory

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.Comment: 12 pages, 1 fig, journal versio

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

Hard Scattering Factorization from Effective Field Theory

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).Comment: 35 pages, 4 figures, typos corrected, journal versio

Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories

We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with the gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations like massive/massless collisionless particles and the photon with the accompanying polarizations. We also include direct interactions among fluids and fields. The background FLRW model includes the general spatial curvature and the cosmological constant. We consider three different types of perturbations, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can implement easily the convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions solved separately in different gauge conditions we can naturally check the numerical accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.

Order alpha_s^2 beta_0 Correction to the Charged Lepton Spectrum in b \to c \ell \bar\nu_\ell decays

We compute the \alpha_s^2\beta_0 part of the two-loop QCD corrections to the charged lepton spectrum in b \to c \ell \bar\nu_\ell decays and find them to be about 50\% of the first order corrections at all lepton energies, except those close to the end point. Including these corrections we extract the central values \bar\Lambda=0.33 GeV and \lambda_1=-0.17 GeV^2 for the HQET matrix elements and use them to determine the $\overline{\rm MS}$ b and c quark masses, and |V_{cb}|.Comment: 15 pages, 1 Postscript figur

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

Physical interpretation of gauge invariant perturbations of spherically symmetric space-times

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.Comment: 6 pages. To appear in PR

Electronic Structure and Heavy Fermion Behavior in LiV_2O_4

First principles density functional calculations of the electronic and magnetic properties of spinel-structure LiV$_{2}$O$_{4}$ have been performed using the full potential linearized augmented planewave method. The calculations show that the electronic structure near the Fermi energy consists of a manifold of 12 bands derived from V $t_{2g}$ states, weakly hybridized with O p states. While the total width of this active manifold is approximately 2 eV, it may be roughly decomposed into two groups: high velocity bands and flatter bands, although these mix in density functional calculations. The flat bands, which are the more atomic-like lead to a high density of states and magnetic instability of local moment character. The value of the on-site exchange energy is sensitive to the exact exchange correlation parameterization used in the calculations, but is much larger than the interaction between neighboring spins, reflecting the weak coupling of the magnetic system with the high velocity bands. A scenario for the observed heavy fermion behavior is discussed in which conduction electrons in the dispersive bands are weakly scattered by local moments associated with strongly correlated electrons in the heavy bands.This is analogous to that in conventional Kondo type heavy fermions, but is unusual in that both the local moments and conduction electrons come from the same d-manifold.Comment: 6 Revtex pages, Postscript figs embedded. Revision: figure 4 replaced with a better version, showing the band character explicitel