Lepton Polarization and Forward-Backward Asymmetries in b -> s tau+ tau-

We study the spin polarizations of both tau leptons in the decay b -> s tau+ tau-. In addition to the polarization asymmetries involving a single tau, we construct asymmetries for the case where both polarizations are simultaneously measured. We also study forward-backward asymmetries with polarized tau's. We find that a large number of asymmetries are predicted to be large, >~ 10%. This permits the measurement of all Wilson coefficients and the b-quark mass, thus allowing the standard model (SM) to be exhaustively tested. Furthermore, there are many unique signals for the presence of new physics. For example, asymmetries involving triple-product correlations are predicted to be tiny within the SM, O(10^{-2}). Their observation would be a clear signal of new physics.Comment: 21 pages, LaTeX, 4 figures (included). Paper somewhat reorganized, references greatly expanded, conclusions unchange

Clustering transitions in vibro-fluidized magnetized granular materials

We study the effects of long range interactions on the phases observed in cohesive granular materials. At high vibration amplitudes, a gas of magnetized particles is observed with velocity distributions similar to non-magnetized particles. Below a transition temperature compact clusters are observed to form and coexist with single particles. The cluster growth rate is consistent with a classical nucleation process. However, the temperature of the particles in the clusters is significantly lower than the surrounding gas, indicating a breakdown of equipartition. If the system is quenched to low temperatures, a meta-stable network of connected chains self-assemble due to the anisotropic nature of magnetic interactions between particles.Comment: 4 pages, 5 figure

Possible Supersymmetric Effects on Angular Distributions in B→K∗(→Kπ)ℓ+ℓ−B \to K^* (\to K \pi) \ell^+ \ell^- Decays

We investigate the angular distributions of the rare B decay, $B \to K^* (\to K \pi) \ell^+ \ell^-$, in general supersymmetric extensions of the standard model. We consider the new physics contributions from the operators $O_{7,8,9,10}$ in small invariant mass region of lepton pair. We show that the azimuthal angle distribution of the decay can tell us the new physics effects clearly from the behavior of the distribution, even if new physics does not change the decay rate substantially from the standard model prediction

A Systematic Analysis of the Lepton Polarization Asymmetries in the Rare B Decay, B -> X_s\tau^+\tau^-

The most general model-independent analysis of the lepton polarization asymmetries in the rare B decay, \Bstt, is presented. We present the longitudinal, normal and transverse polarization asymmetries for the $\tau^+$ and $\tau^-$, and combinations of them, as functions of the Wilson coefficients of twelve independent four-Fermi interactions, ten of them local and two nonlocal. These procedures will tell us which type of operators contributes to the process. And it will be very useful to pin down new physics systematically, once we have the experimental data with high statistics and a deviation from the Standard Model is found.Comment: 24 pages, 8 figures, LaTe

Correlated sampling in quantum Monte Carlo: a route to forces

In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate numerical forces and potential energy surfaces in diffusion Monte Carlo. It employs a novel coordinate transformation, earlier used in variational Monte Carlo, to greatly reduce the statistical error. Results are presented for first-row diatomic molecules.Comment: 5 pages, 2 postscript figure

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Explicit differential characterization of the Newtonian free particle system in m > 1 dependent variables

In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), to the Newtonian free particle equation Y_XX = 0. This result, preliminary to the deep group-theoretic classification of second order analytic ordinary differential equations, was parachieved later in 1896 by Arthur Tresse, a French student of S. Lie. In the present paper, following closely the original strategy of proof of S. Lie, which we firstly expose and restitute in length, we generalize this explicit characterization to the case of several second order ordinary differential equations. Let K=R or C, or more generally any field of characteristic zero equipped with a valuation, so that K-analytic functions make sense. Let x in K, let m > 1, let y := (y^1, ..., y^m) in K^m and let y_xx^j = F^j(x,y,y_x^l), j = 1,...,m be a collection of m analytic second order ordinary differential equations, in general nonlinear. We provide an explicit necessary and sufficient condition in order that this system is equivalent, under a point transformation (x, y^1, ..., y^m) --> (X(x,y), Y^1(x,y),..., Y^m(x, y)), to the Newtonian free particle system Y_XX^1 = ... = Y_XX^m = 0. Strikingly, the (complicated) differential system that we obtain is of first order in the case m > 1, whereas it is of second order in S. Lie's original case m = 1.Comment: 76 pages, no figur

Lepton polarization correlations in B→K∗τ−τ+B \to K^* \tau^- \tau^+

In this work we will study the polarizations of both leptons ($\tau$) in the decay channel $B\to K^* \tau^- \tau^+$. In the case of the dileptonic inclusive decay $B\to K^* \ell^- \ell^+$, where apart from the polarization asymmetries of single lepton $\ell$, one can also observe the polarization asymmetries of both leptons simultaneously. If this sort of measurement is possible then we can have, apart from decay rate, FB asymmetry and the six single lepton polarization asymmetries (three each for $\ell^-$ and $\ell^+$), nine more double polarization asymmetries. This will give us a very useful tool in more strict testing of SM and the physics beyond. We discuss the double polarization asymmetries of $\tau$ leptons in the decay mode $B\to K^* \tau^- \tau^+$ within the SM and the Minimal Supersymmetric extensions of it.Comment: 21 pages, 21 figures; version to match paper to appear in PR

Experimental Probes of Localized Gravity: On and Off the Wall

The phenomenology of the Randall-Sundrum model of localized gravity is analyzed in detail for the two scenarios where the Standard Model (SM) gauge and matter fields are either confined to a TeV scale 3-brane or may propagate in a slice of five dimensional anti-deSitter space. In the latter instance, we derive the interactions of the graviton, gauge, and fermion Kaluza-Klein (KK) states. The resulting phenomenological signatures are shown to be highly dependent on the value of the 5-dimensional fermion mass and differ substantially from the case where the SM fields lie on the TeV-brane. In both scenarios, we examine the collider signatures for direct production of the graviton and gauge KK towers as well as their induced contributions to precision electroweak observables. These direct and indirect signatures are found to play a complementary role in the exploration of the model parameter space. In the case where the SM field content resides on the TeV-brane, we show that the LHC can probe the full parameter space and hence will either discover or exclude this model if the scale of electroweak physics on the 3-brane is less than 10 TeV. We also show that spontaneous electroweak symmetry breaking of the SM must take place on the TeV-brane.Comment: 62 pages, Latex, 22 figure

Effectiveness of Metyrapone in Treating Cushing's Syndrome: A Retrospective Multicenter Study in 195 Patients

Background: Cushing's syndrome (CS) is a severe condition with excess mortality and significant morbidity necessitating control of hypercortisolemia. There are few data documenting use of the steroidogenesis inhibitor metyrapone for this purpose. Objective: The objective was to assess the effectiveness of metyrapone in controlling cortisol excess in a contemporary series of patients with CS. Design: This was designed as a retrospective, multicenter study. Setting: Thirteen University hospitals were studied. Patients: We studied a total of 195 patients with proven CS: 115 Cushing's disease, 37 ectopic ACTH syndrome, 43 ACTH-independent disease (adrenocortical carcinoma 10, adrenal adenoma 30, and ACTH-independent adrenal hyperplasia 3). Measurements: Measurements included biochemical parameters of activity of CS: mean serum cortisol “day-curve” (CDC) (target 150–300 nmol/L); 9 am serum cortisol; 24-hour urinary free cortisol (UFC). Results: A total of 164/195 received metyrapone monotherapy. Mean age was 49.6 ± 15.7 years; mean duration of therapy 8 months (median 3 mo, range 3 d to 11.6 y). There were significant improvements on metyrapone, first evaluation to last review: CDC (91 patients, 722.9 nmol/L [26.2 μg/dL] vs 348.6 nmol/L [12.6 μg/dL]; P < .0001); 9 am cortisol (123 patients, 882.9 nmol/L [32.0 μg/dL] vs 491.1 nmol/L [17.8 μg/dL]; P < .0001); and UFC (37 patients, 1483 nmol/24 h [537 μg/24 h] vs 452.6 nmol/24 h [164 μg/24 h]; P = .003). Overall, control at last review: 55%, 43%, 46%, and 76% of patients who had CDCs, UFCs, 9 am cortisol less than 331 nmol/L (12.0 μg/dL), and 9 am cortisol less than upper limit of normal/600 nmol/L (21.7 μg/dL). Median final dose: Cushing's disease 1375 mg; ectopic ACTH syndrome 1500 mg; benign adrenal disease 750 mg; and adrenocortical carcinoma 1250 mg. Adverse events occurred in 25% of patients, mostly mild gastrointestinal upset and dizziness, usually within 2 weeks of initiation or dose increase, all reversible. Conclusions: Metyrapone is effective therapy for short- and long-term control of hypercortisolemia in CS