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The colour-suppressed tree amplitude in non-leptonic B decays is particularly sensitive to perturbative and non-perturbative corrections. We calculate the two-loop (NNLO) vertex corrections to the colour-suppressed and colour-allowed tree amplitudes in QCD factorization. Our results are given completely analytically, including the full dependence on the charm quark mass. We then update theoretical predictions for a range of interesting observables derived from pi pi, pi rho, and rho rho final states that do not depend (significantly) on penguin contributions, and hence are now available with NNLO accuracy. We observe good agreement with experimental data within experimental and theoretical errors, except for observables involving the pi^0 pi^0 branching fraction.

We perform a perturbative (near-critical) analysis of the stability of an asymptotically Schroedinger Reissner-Nordstrom black hole with respect to generation of charged scalar hair. We find that apart from the expected instability at low temperatures typical of holographic models of superconductivity, in the presence of certain operators a similar instability appears as well at high temperatures. We propose that the reason for such a phase diagram could be due to peculiar features of the dual gauge theory or the failure of the model to provide a consistent holographic dual of a non-relativistic superconductor.

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of stationary universes.

We discuss the universal relation between density and size of Dark Matter halos.This relation was recently shown to hold on a wide range of scales, from dwarf galaxies to galaxy clusters, both in astronomical observations and numerical simulations of structure formation in the Universe. The nature of this relation has not been previously understood. We demonstrate that this relation can be derived analytically in a "secondary infall" model of structure formation. Qualitative understanding given by this model provides a new tool to observationally constrain the properties of DM and large scale modifications of gravity.

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.

Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined.
To overcome this obstacle, the Master Constraint Method has been proposed which replaces the individual constraints by a weighted sum of absolute squares of the constraints. Now the direct integral decomposition methods (DID), which are closely related to Rigged Hilbert spaces, become available and have been successfully tested in various situations.
It is relatively straightforward to relate the Rigging Inner Product to the path integral that one obtains via reduced phase space methods. However, for the Master Constraint this is not at all obvious. In this paper we find sufficient conditions under which such a relation can be established. Key to our analysis is the possibility to pass to equivalent, Abelian constraints, at least locally in phase space. Then the Master Constraint DID for those Abelian constraints can be directly related to the Rigging Map and therefore has a path integral formulation.

In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator. By the standard technique of skeletonization and the coherent state path-integral, we derive a path-integral formula from the group averaging for the master constraint operator. Our derivation in the present paper suggests there exists a direct link connecting the canonical Loop quantum gravity with a path-integral quantization or a spin-foam model of General Relativity.

An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure" usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed.
In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element.
From this path integral for the Holst formulation of GR we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical LQG and the spin foam approach.

This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory.

Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the quantum inequalities which limit its magnitude and duration. However, these inequalities allow the possibility that negative energy and related effects might be observable. Some recent proposals for experiments to search for sub-vacuum phenomena will be discussed. Fluctuations of the energy density around its mean value will also be considered, and some recent results on a probability distribution for the energy density in two dimensional spacetime are summarized.

Leading models of galaxy formation require large-scale energetic outflows to regulate the growth of distant galaxies and their central black holes. However, current observational support for this hypothesis at high redshift is mostly limited to rare z>2 radio galaxies. Here we present Gemini-North NIFS Intregral Field Unit (IFU) observations of the [O III]5007 emission from a z~2 ultraluminous infrared galaxy (ULIRG; L_IR>10^12 L_sol) with an optically identified Active Galactic Nucleus (AGN). The spatial extent (~4-8 kpc) of the high velocity and broad [O III] emission are consistent with that found in z>2 radio galaxies, indicating the presence of a large-scale energetic outflow in a galaxy population potentially orders of magnitude more common than distant radio galaxies. The low radio luminosity of this system indicates that radio-bright jets are unlikely to be responsible for driving the outflow. However, the estimated energy input required to produce the large-scale outflow signatures (of order ~10^59 ergs over ~30 Myrs) could be delivered by a wind radiatively driven by the AGN and/or supernovae winds from intense star formation. The energy injection required to drive the outflow is comparable to the estimated binding energy of the galaxy spheroid, suggesting that it can have a significant impact on the evolution of the galaxy. We argue that the outflow observed in this system is likely to be comparatively typical of the high-redshift ULIRG population and discuss the implications of these observations for galaxy formation models.

Recent X-ray observations of hot gas in the galaxy cluster MS 0735.6+7421 reveal huge radio-bright, quasi-bipolar X-ray cavities having a total energy ~10^{62} ergs, the most energetic AGN outburst currently known. We investigate the evolution of this outburst with two-dimensional axisymmetric gasdynamical calculations in which the cavities are inflated by relativistic cosmic rays. Many key observational features of the cavities and associated shocks are successfully reproduced. The radial elongation of the cavities indicates that cosmic rays were injected into the cluster gas by a (jet) source moving out from the central AGN. AGN jets of this magnitude must be almost perfectly identically bipolar. The relativistic momentum of a single jet would cause a central AGN black hole of mass 10^9 M_{sun} to recoil at ~6000 km s^{-1}, exceeding kick velocities during black hole mergers, and be ejected from the cluster-center galaxy. When the cavity inflation is complete, 4PV underestimates the total energy received by the cluster gas. Deviations of the cluster gas from hydrostatic equilibrium are most pronounced during the early cavity evolution when the integrated cluster mass found from the observed gas pressure gradient can have systematic errors near the cavities of ~10-30%. The creation of the cavity with cosmic rays generates a long-lasting global cluster expansion that reduces the total gas thermal energy below that received from the cavity shock. One Gyr after this single outburst, a gas mass of ~ 6 \times 10^{11} M_{sun} is transported out beyond a cluster radius of 500 kpc. Such post-cavity outflows can naturally produce the discrepancy observed between the cluster gas mass fraction and the universal baryon fraction inferred from WMAP observations. (Abridged)

The velocity of the inner ejecta of stripped-envelope core-collapse supernovae (CC-SNe) is studied by means of an analysis of their nebular spectra. Stripped-envelope CC-SNe are the result of the explosion of bare cores of massive stars ($\geq 8$ M$_{\odot}$), and their late-time spectra are typically dominated by a strong [O {\sc i}] $\lambda\lambda$6300, 6363 emission line produced by the innermost, slow-moving ejecta which are not visible at earlier times as they are located below the photosphere. A characteristic velocity of the inner ejecta is obtained for a sample of 56 stripped-envelope CC-SNe of different spectral types (IIb, Ib, Ic) using direct measurements of the line width as well as spectral fitting. For most SNe, this value shows a small scatter around 4500 km s$^{-1}$. Observations ($< 100$ days) of stripped-envelope CC-SNe have revealed a subclass of very energetic SNe, termed broad-lined SNe (BL-SNe) or hypernovae, which are characterised by broad absorption lines in the early-time spectra, indicative of outer ejecta moving at very high velocity ($v \geq 0.1 c$). SNe identified as BL in the early phase show large variations of core velocities at late phases, with some having much higher and some having similar velocities with respect to regular CC-SNe. This might indicate asphericity of the inner ejecta of BL-SNe, a possibility we investigate using synthetic three-dimensional nebular spectra.

An XMM-Mewton observation performed in May 2008 has confirmed that the 13 seconds pulsations in the X-ray binary HD 49798/RX J0648.0-4418 are due to a rapidly rotating white dwarf. From the pulse time delays induced by the 1.55 days orbital motion, and the system's inclination, constrained by the duration of the X-ray eclipse discovered in this observation, we could derive a mass of 1.28+/-0.05 M_sun for the white dwarf. The future evolution of this post common envelope binary system will likely involve a new phase of mass accretion through Roche-lobe overflow that could drive the already massive white dwarf above the Chandrasekhar limit and produce a Type Ia supernova.

Recent X-ray observations of hot gas in the galaxy cluster MS 0735.6+7421 reveal huge radio-bright, quasi-bipolar X-ray cavities having a total energy ~10^{62} ergs, the most energetic AGN outburst currently known. We investigate the evolution of this outburst with two-dimensional axisymmetric gasdynamical calculations in which the cavities are inflated by relativistic cosmic rays. Many key observational features of the cavities and associated shocks are successfully reproduced. The radial elongation of the cavities indicates that cosmic rays were injected into the cluster gas by a (jet) source moving out from the central AGN. AGN jets of this magnitude must be almost perfectly identically bipolar. The relativistic momentum of a single jet would cause a central AGN black hole of mass 10^9 M_{sun} to recoil at ~6000 km s^{-1}, exceeding kick velocities during black hole mergers, and be ejected from the cluster-center galaxy. When the cavity inflation is complete, 4PV underestimates the total energy received by the cluster gas. Deviations of the cluster gas from hydrostatic equilibrium are most pronounced during the early cavity evolution when the integrated cluster mass found from the observed gas pressure gradient can have systematic errors near the cavities of ~10-30%. The creation of the cavity with cosmic rays generates a long-lasting global cluster expansion that reduces the total gas thermal energy below that received from the cavity shock. One Gyr after this single outburst, a gas mass of ~ 6 \times 10^{11} M_{sun} is transported out beyond a cluster radius of 500 kpc. Such post-cavity outflows can naturally produce the discrepancy observed between the cluster gas mass fraction and the universal baryon fraction inferred from WMAP observations. (Abridged)