Standard Model Effective Field Theory: Integrating out a Generic Scalar

We consider renormalisable models extended in the scalar sector by a generic scalar field in addition to the standard model Higgs boson field, and work out the effective theory for the latter in the decoupling limit. We match the full theory onto the effective theory at tree and one-loop levels, and concentrate on dimension-6 operators of the Higgs and electroweak gauge fields induced from such matching. The Wilson coefficients of these dimension-6 operators from tree-level matching are further improved by renormalisation group running. For specific $SU(2)_L$ representations of the scalar field, some "accidental" couplings with the Higgs field are allowed and can lead to dimension-6 operators at tree and/or one-loop level. Otherwise, two types of interaction terms are identified to have only one-loop contributions, for the Wilson coefficients of which we have obtained a general formula. Using the obtained results, we analyse constraints from electroweak oblique parameters and the Higgs data on several phenomenological models.Comment: corrections on RGE improvemen

Terahertz Antiferromagnetic Spin Hall Nano-Oscillator

We consider the current-induced dynamics of insulating antiferromagnets in a spin Hall geometry. Sufficiently large in-plane currents perpendicular to the N\'{e}el order trigger spontaneous oscillations at frequencies between the acoustic and the optical eigenmodes. The direction of the driving current determines the chirality of the excitation. When the current exceeds a threshold, the combined effect of spin pumping and current-induced torques introduces a dynamic feedback that sustains steady-state oscillations with amplitudes controllable via the applied current. The ac voltage output is calculated numerically as a function of the dc current input for different feedback strengths. Our findings open a route towards terahertz antiferromagnetic spin-torque oscillators.Comment: 5+ pages, 4 figure

Electron Dynamics in Slowly Varying Antiferromagnetic Texture

Effective dynamics of conduction electrons in antiferromagnetic (AFM) materials with slowly varying spin texture is developed via non-Abelian gauge theory. Quite different from the ferromagnetic (FM) case, the spin of a conduction electron does not follow the background texture even in the adiabatic limit due to the accumulation of a SU(2) non-Abelian Berry phase. Correspondingly, it is found that the orbital dynamics becomes spin-dependent and is affected by two emergent gauge fields. While one of them is the non-Abelian generalization of what has been discovered in FM systems, the other leads to an anomalous velocity that has no FM counterpart. Two examples are provided to illustrate the distinctive spin dynamics of a conduction electron.Comment: 4 pages, 3 figure

Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page