B->gamma e nu Transitions from QCD Sum Rules

B->gamma e nu transitions have recently been studied in the framework of QCD factorization. The attractiveness of this channel for such an analysis lies in the fact that, at least in the heavy quark limit, the only hadron involved is the B meson itself, so one expects a very simple description of the form factor in terms of a convolution of the B meson distribution amplitude with a perturbative kernel. This description, however, does not include contributions suppressed by powers of the b quark mass. In this letter, we calculate corrections to the factorized expression which are induced by the ``soft'' hadronic component of the photon. We demonstrate that the power-suppression of these terms is numerically not effective for physical values of the $b$ quark mass and that they increase the form factor by about 30% at zero momentum transfer. We also derive a sum rule for lambda_B, the first negative moment of the B meson distribution amplitude, and find lambda_B = 0.6 GeV (to leading order in QCD).Comment: 13 pages, 5 figure

Dynamical Systems, Stability, and Chaos

In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective we show how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. We discuss stability and bifurcations in three simple model problems, and conclude with a survey of recent extensions of stability theory to complex networks.Comment: 28 pages, 10 figures. 26/04/2007: The book title was changed at the last minute. No other changes have been made. Chapter 1 in: J.P. Denier and J.S. Frederiksen (editors), Frontiers in Turbulence and Coherent Structures. World Scientific Singapore 2007 (in press

Liberating the NHS; commissioning, outsourcing and a new politics debate

In the short months following the result of the UK 2010 General election, a new Government White Paper has been released entitled: Equity and Excellence: Liberating the NHS (Department of Health (DH), 2010a). It strives to distance itself from previous health-care proposals (DH, 2009), yet if the initiatives of this latest paper are combined against previous initiatives, also using high impact declarative terms, such as competition and choice, it is clear that little has changed and more important principles than saving money are at risk

Light-cone sum rules for B→πB \to \pi form factors revisited

We reconsider and update the QCD light-cone sum rules for $B\to \pi$ form factors. The gluon radiative corrections to the twist-2 and twist-3 terms in the correlation functions are calculated. The $\bar{MS}$ $b$-quark mass is employed, instead of the one-loop pole mass used in the previous analyses. The light-cone sum rule for $f^+_{B\pi}(q^2)$ is fitted to the measured $q^2$-distribution in $B\to \pi l \nu_l$, fixing the input parameters with the largest uncertainty: the Gegenbauer moments of the pion distribution amplitude. For the $B\to \pi$ vector form factor at zero momentum transfer we predict $f^+_{B\pi}(0)= 0.26^{+0.04}_{-0.03}$. Combining it with the value of the product $|V_{ub}f^+_{B\pi}(0)|$ extracted from experiment, we obtain $|V_{ub}|=(3.5\pm 0.4\pm 0.2\pm 0.1) \times 10^{-3}$. In addition, the scalar and penguin $B\to \pi$ form factors $f^0_{B\pi}(q^2)$ and $f^T_{B\pi}(q^2)$ are calculated.Comment: 33 pages, 7 figures, one figure and a few comments added, version to appear in JHE

The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.Comment: 8 pages, no figures, a few references adde

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases

B_s^0 - bar{B}_s^0 Mixing and the B_s -> J/psi phi Asymmetry in Supersymmetric Models

We analyse supersymmetric contributions to B_s mixing and their impact on mixing-induced CP asymmetries, using the mass insertion approximation. We discuss in particular the correlation of SUSY effects in the CP asymmetries of B_s -> J/psi phi and B_d -> phi K_S and find that the mass insertions dominant in B_s mixing and B_d -> phi K_S are (delta_{23}^d)_{LL, RR} and (delta_{23}^d)_{LR, RL}, respectively. We show that models with dominant (delta_{23}^d)_{LR, RL} can accomodate a negative value of S_{phi K_S}, in agreement with the BELLE measurement of that observable, but yield a B_s mixing phase too small to be observed. On the other hand, models with dominant (delta_{23}^d)_{LL, RR} predict sizeable SUSY contributions to both Delta M_s and the mixing phase, but do not allow the asymmetry in B_d -> phi K_S to become negative, except for small values of the average down squark mass, which, in turn, entail a value of Delta M_s too large to be observed at the Tevatron and the LHC. We conclude that the observation of B_s mixing at hadron machines, together with the confirmation of a negative value of S_{phi K_S}, disfavours models with a single dominant mass insertion.Comment: 17 pages, 5 figure

Operator Relations for SU(3) Breaking Contributions to K and K* Distribution Amplitudes

We derive constraints on the asymmetry a1 of the momentum fractions carried by quark and antiquark in K and K* mesons in leading twist. These constraints follow from exact operator identities and relate a1 to SU(3) breaking quark-antiquark-gluon matrix elements which we determine from QCD sum rules. Comparing our results to determinations of a1 from QCD sum rules based on correlation functions of quark currents, we find that, for a1^\parallel(K*) the central values agree well and come with moderate errors, whereas for a1(K) and a1^\perp(K*) the results from operator relations are consistent with those from quark current sum rules, but come with larger uncertainties. The consistency of results confirms that the QCD sum rule method is indeed suitable for the calculation of a1. We conclude that the presently most accurate predictions for a1 come from the direct determination from QCD sum rules based on correlation functions of quark currents and are given by: a1(K) = 0.06\pm 0.03, a1^\parallel(K*) = 0.03\pm 0.02, a1^\perp(K*) = 0.04\pm 0.03.Comment: 21 page

Non-parametric models in the monitoring of engine performance and condition: Part 2: non-intrusive estimation of diesel engine cylinder pressure and its use in fault detection

An application of the radial basis function model, described in Part 1, is demonstrated on a four-cylinder DI diesel engine with data from a wide range of speed and load settings. The prediction capabilities of the trained model are validated against measured data and an example is given of the application of this model to the detection of a slight fault in one of the cylinders

Models for Light-Cone Meson Distribution Amplitudes

Leading-twist distribution amplitudes (DAs) of light mesons like pi,rho etc. describe the leading nonperturbative hadronic contributions to exclusive QCD reactions at large energy transfer, for instance electromagnetic form factors. They also enter B decay amplitudes described in QCD factorisation, in particular nonleptonic two-body decays. Being nonperturbative quantities, DAs cannot be calculated from first principles, but have to be described by models. Most models for DAs rely on a fixed order conformal expansion, which is strictly valid for large factorisation scales, but not always sufficient in phenomenological applications. We derive models for DAs that are valid to all orders in the conformal expansion and characterised by a small number of parameters which are related to experimental observables.Comment: 19 pages, 10 figure