Scaling regimes in spherical shell rotating convection

Rayleigh-B\'enard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7} \leq E \leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\times 10^{10}$ and a Prandtl number unity. We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly-rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a subset of our numerical data approaches the asymptotic diffusivity-free scaling of rotating convection $Nu\sim Ra^{3/2}E^{2}$ in a narrow fraction of the parameter space delimited by $6\,Ra_c \leq Ra \leq 0.4\,E^{-8/5}$. Using a decomposition of the viscous dissipation rate into bulk and boundary layer contributions, we establish a theoretical scaling of the flow velocity that accurately describes the numerical data. In rapidly-rotating turbulent convection, the fluid bulk is controlled by a triple force balance between Coriolis, inertia and buoyancy, while the remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman layers. Beyond $Ra \simeq E^{-8/5}$, the rotational constraint on the convective flow is gradually lost and the flow properties vary to match the regime changes between rotation-dominated and non-rotating convection. The quantity $Ra E^{12/7}$ provides an accurate transition parameter to separate rotating and non-rotating convection.Comment: 42 pages, 20 figures, 3 tables, accepted for publication in JF

Measurements of the CKM angle β/ϕ1\beta/\phi_1 at the B Factories

We report measurements of time-dependent CP asymmetries related to the CKM angle $\beta/\phi_1$, using decays of neutral B mesons to charmonium, open charm and in $b\to s$ loop processes. A preliminary measurement of time-dependent CP asymmetries in $B^0\to \rho^0(770) K^0_S$ decays from the BaBar experiment is given here.Comment: Contributed to the Proceedings of the XLI Rencontres de Moriond - Electroweak Interactions and Unified Theory, La Thuile Italy, March 11-18, 2006. 6 page

Time Reversal Violation from the entangled B0-antiB0 system

We discuss the concepts and methodology to implement an experiment probing directly Time Reversal (T) non-invariance, without any experimental connection to CP violation, by the exchange of "in" and "out" states. The idea relies on the B0-antiB0 entanglement and decay time information available at B factories. The flavor or CP tag of the state of the still living neutral meson by the first decay of its orthogonal partner overcomes the problem of irreversibility for unstable systems, which prevents direct tests of T with incoherent particle states. T violation in the time evolution between the two decays means experimentally a difference between the intensities for the time-ordered (l^+ X, J/psi K_S) and (J/psi K_L, l^- X) decays, and three other independent asymmetries. The proposed strategy has been applied to simulated data samples of similar size and features to those currently available, from which we estimate the significance of the expected discovery to reach many standard deviations.Comment: 17 pages, 2 figures, 6 table

Sea-quark flavor asymmetry in the nucleon from a relativistic analysis of the Drell-Yan scattering off nuclei

It is shown that accounting for the relativistic structure of the deuteron allows to explain the ratio of the Drell-Yan pair production cross-section at the low Bjorken $x$ off the deuteron and the proton. Thus, the sea quark distributions in the nucleon should be studied with accounting for the effects of the relativistic structure of the deuteron. The suggested approach reduces theoretical uncertainty in extracting the ratio $\bar u/\bar d$ from the data and it is important for the clarification of the nature of the sea quark asymmetry in the nucleon.Comment: 4 pages, 1 figures, Chiral Symmetry in Hadron and Nuclear Physics November 13-16, 2007, Osak

Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model

Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system &lt;i&gt;e&lt;/i&gt;-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo

Large Direct CP Violation in B^0 -> pi^+ pi^- and an Enhanced Branching Ratio for B^0 -> pi^0 pi^0

Recent measurements of B^0 -> pi pi decays reveal two features that are in conflict with conventional calculations: the channel B^0 (Bbar^0) -> pi^+ pi^- shows a large direct CP-violating asymmetry, and the channel B^0 (B^0) -> pi^0 pi^0 has an unexpectedly high branching ratio. We show that both features can be understood in terms of strong-interaction mixing of pi pi and D Dbar channels in the isospin-zero state, an effect that is important because of the large experimentally observed ratio Gamma(B^0 / Bbar^0 -> D^+ D^-) / Gamma (B^0 / Bbar^0 -> pi^+ pi^-) approx. 50. Our dynamical model correlates the branching ratios and the CP-violating parameters C and S, for the decays B^0 (Bbar^0) -> pi^+ pi^-, B^0 (Bbar^0) -> pi^0 pi^0, B^0 (Bbar^0) -> D^+ D^- and B^0 (Bbar^0) -> D^0 Dbar^0.Comment: 10 pages, 2 figures, 1 table; v2: Misprint corrected in Eq. (12), second line: -a_m replaced by +a_m. To appear in Phys. Lett.

CP violation and limits on New Physics including recent BsB_s measurements

We analyse present constraints on the SM parameter space and derive, in a model independent way, various bounds on New Physics contributions to $B_d^0$--$\bar B_d^0$ and $B_s^0$--$\bar B_s^0$ mixings. Our analyses include information on a large set of asymmetries, leading to the measurement of the CKM phases $\gamma$ and $\bar\beta$, as well as recent data from D0 and CDF related to the $B_s^0$--$\bar B_s^0$ system such as the measurement of $\Delta M_{B_s}$, $A_{SL}$ and $\Delta\Gamma_{s}^{CP}$. We examine in detail several observables such as the asymmetries $A_{sl}^d$, $A_{SL}$, the width differences $\Delta\Gamma_{d}$ and $\Delta\Gamma_{s}^{CP}$ and discuss the r\^ole they play in establishing the limits on New Physics. The present data clearly favour the SM, with the New Physics favoured region placed around the SM solution. A New Physics solution significantly different from the SM is still allowed, albeit quite disfavoured (2.6% probability). We analyse the presently available indirect knowledge on the phase $\bar\chi$ entering in $B_s^0$--$\bar B_s^0$ mixing and study the impact of a future measurement of $\bar\chi$ to be achieved at LHC, through the measurement of the time-dependent CP asymmetry in $B_s\to J/\Psi \Phi$ decays.Comment: 29 pages, 31 figures; updated analyses and reference

Comment on form factor shape and extraction of |V_ub| from B --> pi l nu

We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays.Comment: 14 pages, 3 figures; journal version, results and conclusions unchange