Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

Satellite-Detected Fluorescence Reveals Global Physiology of Ocean Phytoplankton

Phytoplankton photosynthesis links global ocean biology and climate-driven fluctuations in the physical environment. These interactions are largely expressed through changes in phytoplankton physiology, but physiological status has proven extremely challenging to characterize globally. Phytoplankton fluorescence does provide a rich source of physiological information long exploited in laboratory and field studies, and is now observed from space. Here we evaluate the physiological underpinnings of global variations in satellite-based phytoplankton chlorophyll fluorescence. The three dominant factors influencing fluorescence distributions are chlorophyll concentration, pigment packaging effects on light absorption, and light-dependent energy-quenching processes. After accounting for these three factors, resultant global distributions of quenching-corrected fluorescence quantum yields reveal a striking consistency with anticipated patterns of iron availability. High fluorescence quantum yields are typically found in low iron waters, while low quantum yields dominate regions where other environmental factors are most limiting to phytoplankton growth. Specific properties of photosynthetic membranes are discussed that provide a mechanistic view linking iron stress to satellite-detected fluorescence. Our results present satellite-based fluorescence as a valuable tool for evaluating nutrient stress predictions in ocean ecosystem models and give the first synoptic observational evidence that iron plays an important role in seasonal phytoplankton dynamics of the Indian Ocean. Satellite fluorescence may also provide a path for monitoring climate-phytoplankton physiology interactions and improving descriptions of phytoplankton light use efficiencies in ocean productivity models

Precise Prediction for M_W in the MSSM

We present the currently most accurate evaluation of the W boson mass, M_W, in the Minimal Supersymmetric Standard Model (MSSM). The full complex phase dependence at the one-loop level, all available MSSM two-loop corrections as well as the full Standard Model result have been included. We analyse the impact of the different sectors of the MSSM at the one-loop level with a particular emphasis on the effect of the complex phases. We discuss the prediction for M_W based on all known higher-order contributions in representative MSSM scenarios. Furthermore we obtain an estimate of the remaining theoretical uncertainty from unknown higher-order corrections.Comment: 38 pages, 25 figures. Minor corrections, additional reference

The acceleration of the universe and the physics behind it

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.Comment: 18 pages, 18 figure

Cosmological Non-Linearities as an Effective Fluid

The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a large backreaction? Related to this, what is the effective theory that describes the universe on large scales? In this paper we make progress in addressing these questions. We show that the effective theory for the long-wavelength universe behaves as a viscous fluid coupled to gravity: integrating out short-wavelength perturbations renormalizes the homogeneous background and introduces dissipative dynamics into the evolution of long-wavelength perturbations. The effective fluid has small perturbations and is characterized by a few parameters like an equation of state, a sound speed and a viscosity parameter. These parameters can be matched to numerical simulations or fitted from observations. We find that the backreaction of small-scale non-linearities is very small, being suppressed by the large hierarchy between the scale of non-linearities and the horizon scale. The effective pressure of the fluid is always positive and much too small to significantly affect the background evolution. Moreover, we prove that virialized scales decouple completely from the large-scale dynamics, at all orders in the post-Newtonian expansion. We propose that our effective theory be used to formulate a well-defined and controlled alternative to conventional perturbation theory, and we discuss possible observational applications. Finally, our way of reformulating results in second-order perturbation theory in terms of a long-wavelength effective fluid provides the opportunity to understand non-linear effects in a simple and physically intuitive way.Comment: 84 pages, 3 figure

Electroweak Corrections to the Charged Higgs Boson Decay into Chargino and Neutralino

The electroweak corrections to the partial widths of the $H^+ \to \tilde{\chi}^+_i \tilde{\chi}_j^0 (i=1,j=1,2)$ decays including one-loop diagrams of the third generation quarks and squarks, are investigated within the Supersymmetric Standard Model. The relative corrections can reach the values about 10%, therefore they should be taken into account for the precise experimental measurement at future colliders.Comment: 21 pages, 6 eps figures, 1 Latex fil

Gauge and Scheme Dependence of Mixing Matrix Renormalization

We revisit the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized ${\bar {\rm MS}}$ scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultra-violet safe and has a pure dispersive form. Employing the unitarity properties of the theory, we can successfully utilize the afore-mentioned scheme-dependent relation to preserve basic global or local symmetries of the bare Lagrangian through the entire process of renormalization. As an immediate application of our study, we derive the gauge-independent renormalization-group equations of mixing matrices in a minimal extension of the Standard Model with isosinglet neutrinos.Comment: 31 pages, LaTeX, uses axodraw.st

Two-loop scalar self-energies in a general renormalizable theory at leading order in gauge couplings

I present results for the two-loop self-energy functions for scalars in a general renormalizable field theory, using mass-independent renormalization schemes based on dimensional regularization and dimensional reduction. The results are given in terms of a minimal set of loop-integral basis functions, which are readily evaluated numerically by computers. This paper contains the contributions corresponding to the Feynman diagrams with zero or one vector propagator lines. These are the ones needed to obtain the pole masses of the neutral and charged Higgs scalar bosons in supersymmetry, neglecting only the purely electroweak parts at two-loop order. A subsequent paper will present the results for the remaining diagrams, which involve two or more vector lines.Comment: 26 pages, 4 figures, revtex4, axodraw.sty. Version 2: sentence after eq. (A.13) corrected, references added. Version 3: typos in eqs. (5.17), (5.20), (5.21), (5.32) are corrected. Also, the MSbar versions of eqs. (5.32) and (5.33) are now include

Large-scale magnetic fields from inflation due to a CPTCPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb-Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be induced.Comment: 18 pages, 6 figures, version accepted for publication in Eur. Phys. J.

Threats to the validity of the Collegiate Learning Assessment (CLA+) as a measure of critical thinking skills and implications for Learning Gain

The University of Reading Learning Gain project is a three-year longitudinal project to test and evaluate a range of available methodologies and to draw conclusions on what might be the right combination of instruments for the measurement of Learning Gain in higher education. This paper analyses the validity of a measure of critical thinking skills, the Collegiate Learning Assessment (CLA+) and the implications of using this standardised test as a proxy for Learning Gain. The paper reviews five inferences regarding the interpretations and use of test scores: construct representation, scoring, generalisation, extrapolation and decision-making. Each section reviews some of the available evidence in support of the claims the CLA+ makes and the threats to their validity. The possible impact of these issues on Learning Gain in the UK is considered