Polarized electroweak bosons in W+W− production at the LHC including NLO QCD effects

The measurement of polarization fractions of massive gauge bosons at the LHC provides an important check of the Standard Model and in particular of the Electroweak Symmetry Breaking mechanism. Owing to the unstable character of W and Z bosons, devising a theoretical definition for polarized signals is not straightforward and always subject to some ambiguity. Focusing on W-boson pair production at the LHC in the fully leptonic channel, we propose to compute polarized cross-sections and distributions based on the gauge-invariant doubly-resonant part of the amplitude. We include NLO QCD corrections to the leading quark-induced partonic process and also consider the loop- induced gluon-initiated process contributing to the same final state. We present results for both an inclusive setup and a realistic fiducial region, with special focus on variables that are suited for the discrimination of polarized cross-sections and on quantities that can be measured experimentally.

On Numerical Simulation Approach for Multiple Resonance Modes in Servo Systems

Mechanical resonance is one of the most pervasive problems in servo control. Closed-loop simulations are requisite when the servo control system with high accuracy is designed. The mathematical model of resonance mode must be considered when the closed-loop simulations of servo systems are done. There will be a big difference between the simulation results and the real actualities of servo systems when the resonance mode is not considered in simulations. Firstly, the mathematical model of resonance mode is introduced in this paper. This model can be perceived as a product of a differentiation element and an oscillating element. Secondly, the second-order differentiation element is proposed to simulate the resonant part and the oscillating element is proposed to simulate the antiresonant part. Thirdly, the simulation approach for two resonance modes in servo systems is proposed. Similarly, this approach can be extended to the simulation of three or even more resonances in servo systems. Finally, two numerical simulation examples are given.

An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

Global averaging and parametric resonances in damped semilinear wave equations

The long-time behaviour of solutions to a semilinear damped wave equation in a three-dimensional bounded domain with the nonlinearity rapidly oscillating in time (f = f(ε, u, t/ε)) is studied. It is proved that (under natural assumptions) the behaviour of solutions whose initial energy is not very large can be described in terms of global (uniform) attractors Aε of the corresponding dynamical processes and that, as ε → 0, these attractors tend to the global attractor A0 of the corresponding averaged system. We also give the detailed description of these attractors in the case where the limit attractor A0 is regular.Moreover, we give explicit examples of semilinear hyperbolic equations where the uniform attractor Âε (for the initial data belonging to the whole energy phase space) contains the irregular resonant part, which tends to infinity as ε → 0, and formulate the additional restrictions on the nonlinearity f which guarantee that this part is absent.

Resonant Continuum Modes in the Eady Model with Rigid Lid

The Eady model with rigid upper lid is considered. The resonant, linearly amplifying solution that exists in the situation of neutral normal modes when an infinitely thin potential vorticity (PV) perturbation is located precisely at the steering level of a zero-PV neutral mode is explicitly derived. This resonant solution is discussed by partitioning the solution into nonzero-PV and zero-PV contributions. It possesses key observed properties of a growing baroclinic structure. The partitioning of the resonant solution clearly demonstrates the existence of modal growth in a short-wave Eady setting. In contrast to the semi-infinite model, a nonamplifying zero-PV contribution is necessary, in addition to the resonant part, to ensure vanishing vertical velocity at both the upper and the lower lid.

Oscillations of a gas in a closed tube near half the fundamental frequency

The oscillations are driven by the sinusoidal motion of a piston at one end of the tube. Near half the fundamental frequency the first overtone, driven by nonlinear effects, becomes resonant. For small boundary-layer friction the amplitude of this resonant part is comparable with the non-resonant acoustic solution and shocks are formed. Theoretical results are compared with pressure signals measured at the closed end of the tube. The viscous effects are large for air at atmospheric pressure and the nonlinear effects remain small. Experiments with xenon, sulphurhexafluoride (SF6) and Freon RC-318 (C4F8) were therefore conducted and shocks formed as predicted. The comparison of the nonlinear theory by Keller (1975) with the experiments shows very good agreement.

Resonant Approximation for Single-Particle Resonances in the Renormalized RPA-Problem

An approximate version of the renormalized RPA-treatment for scattering of nucleons on a hole nucleus is given, in which the shape resonances are treated according to a method of BALASHOV et al. In order to make the results more transparent we take into account the additional influence of the non resonant part of the single-particle continuum with the help of a separable particle-hole force.