Abstract:A series of analytical nonautonomous soliton solutions for the (3+1)dimensional nonlinear Schrödinger equation with variable coefficients in the presence of gain (loss) and a harmonic potential are obtained. The explicit functions which describe the evolution of the amplitude, phase and velocity are also given. Soliton's phase and velocity are independent of the gain parameter, and only the amplitude is affected by the gain parameter. The dynamical behaviors for nonautonomous chirp-free and chirped solitons in… Show more
“…Some of these terms also involve U ΦΦ and/or U HH , corresponding to possible additional insertions of background currents attached to heavy and/or light propagators in the heavy-light loop in the diagrammatic language. For illustration purpose, we shall focus on extracting the following dimension-6 operators involving Higgs fields 5 ,…”
Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.
“…Some of these terms also involve U ΦΦ and/or U HH , corresponding to possible additional insertions of background currents attached to heavy and/or light propagators in the heavy-light loop in the diagrammatic language. For illustration purpose, we shall focus on extracting the following dimension-6 operators involving Higgs fields 5 ,…”
Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.
“…To perform the path integral, we shift the Dirac and Majorana fermions to eliminate terms with mixed fermionic and bosonic fluctuations as described in Ref. [30]. We first shift the Majorana fermions by…”
Section: Regularization Scheme Translating Operators In the Uoleamentioning
confidence: 99%
“…30) and (t a G ) bc = −if abc being the generators in the adjoint representation of the gauge group. In addition to the term on the r.h.s.…”
We extend the universal one-loop effective action (UOLEA) by operators which translate between dimensional reduction (DRED) and dimensional regularization (DREG). These regularization scheme translating operators allow for an application of the UOLEA to supersymmetric high-scale models matched to non-supersymmetric effective theories. The operators are presented in a generic, model independent form, suitable for implementation into generic spectrum generators.
We enumerate the set of simplified models which match onto the complete set of gauge invariant effective operators up to dimension six describing interactions of a singlet-like Majorana fermion dark matter with the standard model. Tree level matching conditions for each case are worked out in the large mediator mass limit, defining a one to one correspondence between the effective operator coefficients and the simplified model parameters for weakly interacting models. Utilizing such a mapping, we compute the dark matter annihilation rate in the early universe, as well as other low-energy observables like nuclear recoil rates using the effective operators, while the simplified models are used to compute the dark matter production rates at high energy colliders like LEP, LHC and future lepton colliders. Combining all relevant constraints with a profile likelihood analysis, we then discuss the currently allowed parameter regions and prospects for future searches in terms of the effective operator parameters, reducing the model dependence to a minimal level. In the parameter region where such a model-independent analysis is applicable, and leaving aside the special dark matter mass regions where the annihilation proceeds through an s-channel Z or Higgs boson pole, the current constraints allow effective operator suppression scales (Λ) of the order of a few hundred GeV for dark matter masses m χ > 20 GeV at 95% C.L., while the maximum allowed scale is around 3 TeV for m χ ∼ (1 TeV). An estimate of the future reach of ton-scale direct detection experiments and planned electron-positron colliders show that most of the remaining regions can be probed, apart from dark matter masses near half of the Z-boson mass (with 500 GeV < Λ < 2 TeV) and those beyond the kinematic reach of the future lepton colliders.
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