Renormalization of heavy-light currents in moving NRQCD

Heavy-light decays such as $B \to \pi \ell \nu$, $B \to K^{*} \gamma$ and $B \to K^{(*)} \ell \ell$ can be used to constrain the parameters of the Standard Model and in indirect searches for new physics. While the precision of experimental results has improved over the last years this has still to be matched by equally precise theoretical predictions. The calculation of heavy-light form factors is currently carried out in lattice QCD. Due to its small Compton wavelength we discretize the heavy quark in an effective non-relativistic theory. By formulating the theory in a moving frame of reference discretization errors in the final state are reduced at large recoil. Over the last years the formalism has been improved and tested extensively. Systematic uncertainties are reduced by renormalizing the m(oving)NRQCD action and heavy-light decay operators. The theory differs from QCD only for large loop momenta at the order of the lattice cutoff and the calculation can be carried out in perturbation theory as an expansion in the strong coupling constant. In this paper we calculate the one loop corrections to the heavy-light vector and tensor operator. Due to the complexity of the action the generation of lattice Feynman rules is automated and loop integrals are solved by the adaptive Monte Carlo integrator VEGAS. We discuss the infrared and ultraviolet divergences in the loop integrals both in the continuum and on the lattice. The light quarks are discretized in the ASQTad and highly improved staggered quark (HISQ) action; the formalism is easily extended to other quark actions.Comment: 24 pages, 11 figures. Published in Phys. Rev. D. Corrected a typo in eqn. (51

Palladium nanoparticles by electrospinning from poly(acrylonitrile-co-acrylic acid)-PdCl2 solutions. Relations between preparation conditions, particle size, and catalytic activity

Catalytic palladium (Pd) nanoparticles on electrospun copolymers of acrylonitrile and acrylic acid (PAN-AA) mats were produced via reduction of PdCl2 with hydrazine. Fiber mats were electrospun from homogeneous solutions of PAN-AA and PdCl2 in dimethylformamide (DMF). Pd cations were reduced to Pd metals when fiber mats were treated in an aqueous hydrazine solution at room temperature. Pd atoms nucleate and form small crystallites whose sizes were estimated from the peak broadening of X-ray diffraction peaks. Two to four crystallites adhere together and form agglomerates. Agglomerate sizes and fiber diameters were determined by scanning and transmission electron microscopy. Spherical Pd nanoparticles were dispersed homogeneously on the electrospun nanofibers. The effects of copolymer composition and amount of PdCl2 on particle size were investigated. Pd particle size mainly depends on the amount of acrylic acid functional groups and PdCl2 concentration in the spinning solution. Increasing acrylic acid concentration on polymer chains leads to larger Pd nanoparticles. In addition, Pd particle size becomes larger with increasing PdCl2 concentration in the spinning solution. Hence, it is possible to tune the number density and the size of metal nanoparticles. The catalytic activity of the Pd nanoparticles in electrospun mats was determined by selective hydrogenation of dehydrolinalool (3,7-dimethyloct-6- ene-1-yne-3-ol, DHL) in toluene at 90 °C. Electrospun fibers with Pd particles have 4.5 times higher catalytic activity than the current Pd/Al2O3 catalyst

Understanding and extending subgraph GNNs by rethinking their symmetries

Subgraph GNNs are a recent class of expressive Graph Neural Networks (GNNs) which model graphs as collections of subgraphs. So far, the design space of possible Subgraph GNN architectures as well as their basic theoretical properties are still largely unexplored. In this paper, we study the most prominent form of subgraph methods, which employs node-based subgraph selection policies such as ego-networks or node marking and deletion. We address two central questions: (1) What is the upper-bound of the expressive power of these methods? and (2) What is the family of equivariant message passing layers on these sets of subgraphs?. Our first step in answering these questions is a novel symmetry analysis which shows that modelling the symmetries of node-based subgraph collections requires a significantly smaller symmetry group than the one adopted in previous works. This analysis is then used to establish a link between Subgraph GNNs and Invariant Graph Networks (IGNs). We answer the questions above by first bounding the expressive power of subgraph methods by 3-WL, and then proposing a general family of message-passing layers for subgraph methods that generalises all previous node-based Subgraph GNNs. Finally, we design a novel Subgraph GNN dubbed SUN, which theoretically unifies previous architectures while providing better empirical performance on multiple benchmarks

Towards Loop Quantization of Plane Gravitational Waves

The polarized Gowdy model in terms of Ashtekar-Barbero variables is further reduced by including the Killing equations for plane-fronted parallel gravitational waves with parallel rays. The resulting constraint algebra, including one constraint derived from the Killing equations in addition to the standard ones of General Relativity, are shown to form a set of first-class constraints. Using earlier work by Banerjee and Date the constraints are expressed in terms of classical quantities that have an operator equivalent in Loop Quantum Gravity, making space-times with pp-waves accessible to loop quantization techniques.Comment: 14 page

Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction

A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($\chi^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are discussed. We provide examples of quantum interference, sub-Planck phase space structures, and Gaussian versus non-Gaussian dynamical evolution of the state. The results also apply to the description of a nanomechanical resonator with an intrinsic Duffing nonlinearity.Comment: 10 pages, 11 figure

Inflation with blowing-up solution of cosmological constant problem

The cosmological constant problem is how one chooses, without fine-tuning, one singular point $\Lambda_{eff}=0$ for the 4D cosmological constant. We argue that some recently discovered {\it weak self-tuning} solutions can be viewed as blowing-up this one point into a band of some parameter. These weak self-tuning solutions may have a virtue that only de Sitter space solutions are allowed outside this band, allowing an inflationary period. We adopt the hybrid inflation at the brane to exit from this inflationary phase and to enter into the standard Big Bang cosmology.Comment: LaTeX file of 20 pages including 2 eps figure

Deep-red electrophosphorescence from a platinum(II)–porphyrin complex copolymerised with polyfluorene for efficient energy transfer and triplet harvesting

A series of polyfluorene-based polymers with a range of weight percentages (w/w) of a platinum(II)-containing porphyrin, 5,15-dimesityl-10,20-diphenylporphyrinato platinum(II) (MPP(Pt)), were synthesised and incorporated into organic light-emitting diodes. All polymers showed emission predominantly in the red/NIR region with only those polymers with porphyrin w/w of less than 2% showing residual tails at wavelengths lower than 600 nm, indicating increased emission from the porphyrin as w/w increases. The 2% loading of MPP(Pt) gave the highest efficiency LED (0.48%) and light output (2630 mW/m2)

Polar magneto-optical Kerr effect for low-symmetric ferromagnets

The polar magneto-optical Kerr effect (MOKE) for low-symmetric ferromagnetic crystals is investigated theoretically based on first-principle calculations of optical conductivities and a transfer matrix approach for the electrodynamics part of the problem. Exact average magneto-optical properties of polycrystals are described, taking into account realistic models for the distribution of domain orientations. It is shown that for low-symmetric ferromagnetic single crystals the MOKE is determined by an interplay of crystallographic birefringence and magnetic effects. Calculations for single and bi-crystal of hcp 11-20 Co and for a polycrystal of CrO_2 are performed, with results being in good agreement with experimental data.Comment: 14 pages, 7 figures, accepted for publication in Phys. Rev.

Superposition in nonlinear wave and evolution equations

Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages, 2 figures, style change