Abstract: We study the generation of primordial perturbations in a (single-field) slow-roll inflationary Universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a nonzero variance Delta(2) (k, t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize Delta(2) (k, t). This can (and should) be achieved by proper renormalization in an expanding Universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the cosmic microwave background anisotropies is significantly altered. We find a nontrivial change in the consistency condition that relates the tensor-to-scalar ratio r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n(t) = 0, is now compatible with a nonzero ratio r approximate to 0.12 +/- 0.06, which is forbidden by the standard prediction (r = -8n(t)). The influence of relic gravitational waves on the cosmic microwave background may soon come within the range of planned measurements, offering a nontrivial test of the new predictions.

Abstract: We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the "2 + 1'' flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a approximate to 0.11 fm (a(-1) = 1.729 GeV) and a lattice spatial volume of approximately (1.8 fm)(3). We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the b-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B-meson decay constant to O(alpha(s)pa) using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios f(Bs)/f(Bd) and xi = f(Bs)root B-Bs/f(Bd)root B-Bd, thereby demonstrating the viability of the method. For the ratio of decay constants, we find f(Bs)/f(Bd) = 1.15(12) and for the ratio of mixing matrix elements, we find xi = 1.13(12), where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected O(1/m(b)) effects.

Abstract: We qualitatively corroborate the results of [W. Roberts, M. Pervin, Int. J. Mod. Phys. A 24 (2009) 2401] according to which hyperfine mixing greatly affects the decay widths of b -> c semileptonic decays involving doubly heavy bc baryons. However, our predictions for the decay widths of the unmixed states differ from those reported in the work of Roberts and Pervin by a factor of 2, and this discrepancy translates to the mixed case. We further show that the predictions of heavy quark spin symmetry, might be used in the future to experimentally extract information on the admixtures in the actual physical bc baryons, in a model independent manner.