2,409 research outputs found
The Differential equation method: calculation of vertex-type diagrams with one non-zero mass
The differential equation method is applied to evaluate analytically two-loop
vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop
diagrams with zero thresholds contributing to the processes Z --> bb bar (for
zero b mass) and/or H --> gg are calculated in order to demonstrate a new
application of this method.Comment: 12 pages, LATEX, uses axodray.st
MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections
The relationship between MS and pole masses of the vector bosons Z and W is
calculated at the two-loop level in the Standard Model. We only consider the
purely bosonic contributions which represents a gauge invariant subclass of
diagrams. All calculations were performed in the linear gauge with
three arbitrary gauge parameters utilizing the method of asymptotic expansions.
The results are presented in analytic form as series in the small parameters
and mass ratio . As a byproduct we obtain the
bosonic two-loop contributions to the renormalization of the weak mixing
parameter and of the Fermi constant. The running of Fermi
constant will become important at high energy colliders.Comment: LaTeX, 36 p., 10 fig.; in v3 more technical details about
renormalization procedure are adde
Selection rules for breaking selection rules
Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics and result in selection rules. When a DS is broken, selection rule deviations are expected. Typically, information about the symmetry-breaking perturbation/phase and the time-dependent dynamics can be extracted from these deviations, hence they are regarded as a background free gauge of symmetry breaking. However, to date, DS breaking & selection rule deviations are not described by a general approach, thus there is no universal insight about the interplay between selection rule deviations, the symmetry breaking perturbation, and the broken DS. Here we consider DS breaking in Floquet systems from a general standpoint, formulating a general theory that analytically connects the symmetry-broken and fully symmetric systems. Using an external laser (of arbitrary frequency and polarization), as a model DS breaking perturbation, we discover that the broken symmetry systematically imposes selection rules on the symmetry-broken system, which physically manifest as scaling laws of selection rule deviations. We term these rules 'selection rules for breaking selection rules'—a new concept in physics. We numerically validate the analytical theory in the context of high harmonic generation. Our discovery is a general feature of nonlinear wave-mixing phenomena, and we expect it to apply to any Floquet system (classical & quantum) and to any DS breaking mechanism (either by intrinsic or extrinsic elements of the system)
The portable sawmill in forest management
Master of ScienceForestryUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/114344/1/39015003261669.pd
Jet-like tunneling from a trapped vortex
We analyze the tunneling of vortex states from elliptically shaped traps.
Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear
Schr\"odinger) equation, we derive analytically and demonstrate numerically a
novel type of quantum fluid flow: a jet-like singularity formed by the
interaction between the vortex and the nonhomogenous field. For strongly
elongated traps, the ellipticity overwhelms the circular rotation, resulting in
the ejection of field in narrow, well-defined directions. These jets can also
be understood as a formation of caustics since they correspond to a convergence
of trajectories starting from the top of the potential barrier and meeting at a
certain point on the exit line. They will appear in any coherent wave system
with angular momentum and non-circular symmetry, such as superfluids,
Bose-Einstein condensates, and light.Comment: 4 pages, 4 figure
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