Finite Width Effects Research Articles

On zero frequency zonal flow and second harmonic generation by finite amplitude energetic particle induced geodesic acoustic mode

The nonlinear self-interaction of finite amplitude energetic particle induced geodesic acoustic modes (EGAMs) is investigated using the nonlinear gyrokinetic theory. It is found that both zero frequency zonal flow (ZFZF) and second harmonic can be driven by finite amplitude EGAMs, with energetic particles (EPs) playing a dominant role in the nonlinear couplings through finite orbit width effects. For ZFZF, the effects of EPs on EGAM nonlinear self-coupling dominate those of the thermal plasmas which are also present, while the second harmonic generation is only possible via finite amplitude coupling through EPs. Our findings may improve the understanding of stabilizing zonal modes and consequently drift wave turbulence.

Accurate model of the stripe domain phase of perpendicularly magnetized multilayers

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value ${D}_{\text{thr}}$ beyond which the system is in a N\'eel state. We find that thicker films require larger values of DMI to stabilize the N\'eel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.

B \u2192\u03c0\u03c0 form factors from light-cone sum rules with B-meson distribution amplitudes

We study B → ππ form factors using QCD light-cone sum rules with B-meson distribution amplitudes. These form factors describe the semileptonic decay Bto pi pi ell {overline{nu}}_{ell } , and constitute an essential input in B → ππℓ+ℓ− and B → πππ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the P -wave {overline{B}}^0to {pi}^{+}{pi}^0 form factors with the timelike pion vector form factor are related to universal B-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for B → ρ form factors in the limit of ρ-dominance and zero width, thus providing a systematics for so far unaccounted corrections to B → ρ transitions. Using data for the pion vector form factor, we estimate finite-width effects and the contribution of excited ρ-resonances to the B → ππ form factors. We find that these contributions amount up to ∼ 20% in the small dipion mass region where they can be effectively regarded as a nonresonant (P -wave) background to the B → ρ transition.

NLO QCD and electroweak corrections to WWW production at the LHC

In this paper we calculate the next-to-leading order (NLO) QCD $[\mathcal{O}({\ensuremath{\alpha}}_{s}{\ensuremath{\alpha}}^{3})]$ and electroweak (EW) $[\mathcal{O}({\ensuremath{\alpha}}^{4})]$ corrections to the $WWW$ production at the LHC and deal with the subsequent leptonic decays from $W$ bosons by adopting an improved narrow-width approximation which takes into account the spin correlation and finite-width effects. The NLO QCD correction from the real jet radiation is discussed, which significantly enhances the production rate, particularly in the high-energy region. We also provide the integrated cross section for the $WWW$ production and various kinematic distributions of final products at the $\mathrm{QCD}+\mathrm{EW}$ NLO. We find that the convergence of the perturbative QCD description can be improved by applying a hard jet veto in the event selection, but this jet veto would introduce a new source of theoretical uncertainty. The pure NLO QCD relative correction to the integrated cross section for the ${W}^{+}{W}^{\ensuremath{-}}{W}^{+}$ production at the 14 TeV LHC is on the order of 30% in the jet-veto event selection scheme with ${p}_{T,\text{jet}}^{\mathrm{cut}}=50\text{ }\text{ }\mathrm{GeV}$, while the genuine NLO EW relative correction can reach about 15% in the inclusive event selection scheme. Our numerical results show that both the NLO QCD and NLO EW corrections should be taken into consideration in precision predictions.

High frequency fishbone driven by passing energetic ions in tokamak plasmas

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835–8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energy is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work (Wang 2001 Phys. Rev. Lett. 86 5286–8). For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold for instability and decrease mode frequency.

Electron transport in ultra-thin films and ballistic electron emission microscopy

We have developed a calculation scheme for the elastic electron current in ultra-thin epitaxial heterostructures. Our model uses a Keldysh’s non-equilibrium Green’s function formalism and a layer-by-layer construction of the epitaxial film. Such an approach is appropriate to describe the current in a ballistic electron emission microscope (BEEM) where the metal base layer is ultra-thin and generalizes a previous one based on a decimation technique appropriated for thick slabs. This formalism allows a full quantum mechanical description of the transmission across the epitaxial heterostructure interface, including multiple scattering via the Dyson equation, which is deemed a crucial ingredient to describe interfaces of ultra-thin layers properly in the future.We introduce a theoretical formulation needed for ultra-thin layers and we compare with results obtained for thick Au(1 1 1) metal layers. An interesting effect takes place for a width of about ten layers: a BEEM current can propagate via the center of the reciprocal space () along the Au(1 1 1) direction. We associate this current to a coherent interference finite-width effect that cannot be found using a decimation technique. Finally, we have tested the validity of the handy semiclassical formalism to describe the BEEM current.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression Eα(-Dfbα,β*) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an nβ dependence upon the order of coherence which is different from the familiar n2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Effects of finite laser pulse width on two-dimensional electronic spectroscopy

We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.

Analyzing signal attenuation in PFG anomalous diffusion via a modified Gaussian phase distribution approximation based on fractal derivative model

Pulsed field gradient (PFG) has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is complicated. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenuation expression can analyze the finite gradient pulse width (FGPW) effect. Additionally, it can generally be applied to all three types of PFG fractional diffusions classified based on time derivative order alpha and space derivative order beta. These three types of fractional diffusions include time-fractional diffusion, space-fractional diffusion, and general fractional diffusion. The results in this paper are consistent with reported results based on effective phase shift diffusion equation method and instantaneous signal attenuation method. This method provides a new, convenient approximation formalism for analyzing PFG anomalous diffusion experiments.

Full-scale resistance prediction in finite waters: A study using computational fluid dynamics simulations, model test experiments and sea trial measurements

The development of large medium-speed catamarans aims increasing economic viability and reducing the possible negative influence on the environment of fast sea transportation. These vessels are likely to operate at hump speed where wave-making can be the dominating component of the total resistance. Shallow water may considerably amplify the wave-making and hence the overall drag force. Computational fluid dynamics is used to predict the drag force of medium-speed catamarans at model and full scale in infinite and restricted water to study the impact on the resistance. Steady and unsteady shallow-water effects that occur in model testing or full-scale operation are taken into account using computational fluid dynamics as they are inherently included in the mathematical formulations. Unsteady effects in the ship-model response were recorded in model test experiments, computational fluid dynamics simulations and full-scale measurements and found to agree with each other. For a medium-speed catamaran in water that is restricted in width and depth, it was found that computational fluid dynamics is capable of accurately predicting the drag with a maximum deviation of no more than 6% when compared to experimental results in model scale. The influences of restricted depth and width were studied using computational fluid dynamics where steady finite width effects in shallow water and finite depth effects at finite width were quantified. Full-scale drag from computational fluid dynamics predictions in shallow water ( h/L = 0.12 – 0.17) was found to be between full-scale measurements and extrapolated model test results. Finally, it is shown that current extrapolation procedures for shallow-water model tests over-estimate residuary resistance by up to 12% and underestimate frictional forces by up to 35% when compared to validated computational fluid dynamics results. This study concludes that computational fluid dynamics is a versatile tool to predict the full-scale ship resistance to a more accurate extent than extrapolation model test data and can also be utilised to estimate model sizes that keep finite-water effects to an agreed minimum.

Saturation of single toroidal number Alfvén modes

The results of numerical simulations are presented to illustrate the saturation mechanism of a single toroidal number Alfvén mode, driven unstable, in a tokamak plasma, by the resonant interaction with energetic ions. The effects of equilibrium geometry non-uniformities and finite mode radial width on the wave-particle nonlinear dynamics are discussed. Saturation occurs as the fast-ion density flattening produced by the radial flux associated to the resonant particles captured in the potential well of the Alfvén wave extends over the whole region where mode-particle power exchange can take place. The occurrence of two different saturation regimes is shown. In the first regime, dubbed resonance detuning, that region is limited by the resonance radial width (that is, the width of the region where the fast-ion resonance frequency matches the mode frequency). In the second regime, called radial decoupling, the power exchange region is limited by the mode radial width. In the former regime, the mode saturation amplitude scales quadratically with the growth rate; in the latter, it scales linearly. The occurrence of one or the other regime can be predicted on the basis of linear dynamics: in particular, the radial profile of the fast-ion resonance frequency and the mode structure. Here, we discuss how such properties can depend on the considered toroidal number and compare simulation results with the predictions obtained from a simplified nonlinear pendulum model.

QCD and electroweak corrections toZZ+jetproduction withZ-boson leptonic decays at the LHC

In this paper we present the full NLO QCD + NLO EW corrections to the $Z$-boson pair production in association with a hard jet at the LHC. The subsequent $Z$-boson leptonic decays are included by adopting both the naive NWA and MadSpin methods for comparison. Since the $ZZ+{\rm jet}$ production is an important background for single Higgs boson production and new physics search at hadron colliders, the theoretical predictions with high accuracy for the hadronic production of $ZZ+{\rm jet}$ are necessary. We present the numerical results of the integrated cross section and various kinematic distributions of final particles, and conclude that it is necessary to take into account the spin correlation and finite width effects from the $Z$-boson leptonic decays. We also find that the NLO EW correction is quantitatively nonnegligible in matching the experimental accuracy at the LHC, particularly is significant in high transverse momentum region.

Improved kinetic neoclassical transport calculation for a low-collisionality QH-mode pedestal

The role of neoclassical, anomalous and neutral transport to the overall H-mode pedestal and scrape-off layer (SOL) structure in an ELM-free QH-mode discharge on DIII-D is explored using XGC0, a 5D full-f multi-species particle-in-cell drift-kinetic solver with self-consistent neutral recycling and sheath potentials. The work in this paper builds on previous work aimed at achieving quantitative agreement between the flux-driven simulation and the experimental electron density, impurity density and orthogonal measurements of impurity temperature and flow profiles. Improved quantitative agreement is achieved by performing the calculations with a more realistic electron mass, larger neutral density and including finite-Larmor-radius corrections self-consistently in the drift-kinetic motion of the particles. Consequently, the simulations provide stronger evidence that the radial electric field () in the pedestal is primarily established by the required balance between the loss of high-energy tail main ions against a pinch of colder main ions and impurities. The kinetic loss of a small population of ions carrying a large proportion of energy and momentum leads to a separation of the particle and energy transport rates and introduces a source of intrinsic edge torque. Ion orbit loss and finite orbit width effects drive the energy distributions away from Maxwellian, and describe the anisotropy, poloidal asymmetry and local minimum near the separatrix observed in the profile.

Neoclassical toroidal plasma viscosity with effects of finite banana width for finite aspect ratio tokamaks

Theory for neoclassical toroidal plasma viscosity has been developed to model transport phenomena, especially, toroidal plasma rotation for tokamaks with broken symmetry. Theoretical predictions are in agreement with the results of the numerical codes in the large aspect ratio limit. The theory has since been extended to include effects of finite aspect ratio and finite plasma β. Here, β is the ratio of the plasma thermal pressure to the magnetic field pressure. However, there are cases where the radial wavelength of the self-consistent perturbed magnetic field strength B on the perturbed magnetic surface is comparable to the width of the trapped particles, i.e., bananas. To accommodate those cases, the theory for neoclassical toroidal plasma viscosity is further extended here to include the effects of the finite banana width. The extended theory is developed using the orbit averaged drift kinetic equation in the low collisionality regimes. The results of the theory can now be used to model plasma transport, including toroidal plasma rotation, in real finite aspect ratio, and finite plasma β tokamaks with the radial wavelength of the perturbed symmetry breaking magnetic field strength comparable to or longer than the banana width.

Drell-Yan production of multi Z ′-bosons at the LHC within Non-Universal ED and 4D Composite Higgs Models

The Drell-Yan di-lepton production at hadron colliders is by far the preferred channel to search for new heavy spin-1 particles. Traditionally, such searches have exploited the Narrow Width Approximation (NWA) for the signal, thereby neglecting the effect of the interference between the additional Z'-bosons and the Standard Model Z and {\gamma}. Recently, it has been established that both finite width and interference effects can be dealt with in experimental searches while still retaining the model independent approach ensured by the NWA. This assessment has been made for the case of popular single Z'-boson models currently probed at the CERN Large Hadron Collider (LHC). In this paper, we test the scope of the CERN machine in relation to the above issues for some benchmark multi Z'-boson models. In particular, we consider Non-Universal Extra Dimensional (NUED) scenarios and the 4-Dimensional Composite Higgs Model (4DCHM), both predicting a multi-Z' peaking structure. We conclude that in a variety of cases, specifically those in which the leptonic decays modes of one or more of the heavy neutral gauge bosons are suppressed and/or significant interference effects exist between these or with the background, especially present when their decay widths are significant, traditional search approaches based on the assumption of rather narrow and isolated objects might require suitable modifications to extract the underlying dynamics.

Finite-width effects for the localized edge modes in zigzag graphene nanoribbons

A matrix formalism is used to derive the analytical Green's functions describing correlations between any two atomic sites on a zigzag (ZZ) graphene nanoribbon, incorporating modified electronic hopping values between edge sites that may be distinct from the hopping between interior sites. An analysis of the poles of our Green's functions shows two distinct types of localized edge modes in the electronic spectrum. The first of these, the ``zero'' mode, is a topologically induced mode arising from the bipartite honeycomb lattice structure of graphene and is always present along ZZ edges. The second type of localized edge mode is present at edges when the edge-to-bulk hopping ratio deviates significantly from unity. The correlations between edge sites are found to exhibit strikingly different features when mediated by the zero edge mode compared with mediation by the ``modified'' edge mode. In particular, the zero-mode spectral intensity for correlations between two atomic sites along opposite edges can be comparable in strength with that between two sites on the same edge of a finite-width ribbon, before it eventually tends to zero as the ribbon width tends to infinity. This remarkable behavior shows a strong dependence on the sublattice labels of the sites and is in contrast with properties of the modified hopping edge modes. The explicit form of our analytical expressions for the electronic spectrum enables us to predict the zero-mode properties (including frequency, spatial attenuation, and intensity) when the hopping values along ZZ edges are modified.

Analysis of Finite Width Effects of Single-sided Linear Induction Motor Using Hankel Functions

Construction of a prototype Single Sided Linear Induction Motor (SLIM) is not possible taking stator and rotor width to be infinite because the formation of stator winding is not possible without the overhang. Also the current path in the rotor sheet cannot be made of closed type until and unless rotor width is finite. This study takes into account, the finite width effects of both stator and rotor but ignores the discontinuity of the rotor in the longitudinal direction. The finite width effects in a SLIM are analyzed using special mathematical tools such as Hankel Function for faster numerical convergence. The basic difficulty in formulating such problem, based on electromagnetic field theory applications, is to calculate the induced current in the rotor sheet, which is electrically decoupled from the stator winding system. It is also known that currents in the rotor sheet are generally computed, based on the fact that current cannot escape the sheet. Therefore, the divergence of rotor current density being zero calls for introduction of a field quantity “Stream Function”. The present paper uses stream function effectively for tackling the above said difficulty. The results presented in the study are compared with the values of a model with stator and rotor of finite width. Such comparison results can help a designer to decide a finalized value of stator and rotor width.

Resonance on top of thresholds: TheΛc(2595)+as an extremely fine-tuned state

A dedicated study of the $\pi\Sigma_c$ scattering around its threshold is carried out in this work to probe the nature of $\Lambda_c(2595)^+$. We first demonstrate that the effective range expansion approach fails to work near the $\Lambda_c(2595)^+$ pole position, due to the presence of a nearby CDD pole around the $\pi\Sigma_c$ thresholds. We then develop a general framework to properly handle the situation with a CDD pole accompanied by nearby thresholds, which is first elaborated for the single-channel case and then generalized to the coupled-channel study. The isospin breaking effects of the three $\pi\Sigma_c$ channels with different thresholds are specially taken into account in our study. The finite-width effects from the $\Sigma_c$ baryons are considered and found to be relevant to give the $\Lambda_c(2595)^+$ width fully compatible to its experimental value. Through the compositeness analysis, our robust conclusion is that the $\pi^0\Sigma_c^+$ component is subdominant inside the $\Lambda_c(2595)^+$.

Vector boson production at hadron colliders: transverse-momentum resummation and leptonic decay

We consider the transverse-momentum ($q_T$) distribution of Drell-Yan lepton pairs produced, via $W$ and $Z/\gamma^*$ decay, in hadronic collisions. At small values of $q_T$, we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. Resummed results are consistently combined with the known ${\mathcal O}(\alpha_S^2)$ fixed-order results at intermediate and large values of $q_T$. Our calculation includes the leptonic decay of the vector boson with the corresponding spin correlations, the finite-width effects and the full dependence on the final-state lepton(s) kinematics. The computation is encoded in the numerical program DYRes, which allows the user to apply arbitrary kinematical cuts on the final-state leptons and to compute the corresponding distributions in the form of bin histograms. We present a comparison of our results with some of the available LHC data. The inclusion of the leptonic decay in the resummed calculation requires a theoretical discussion on the $q_T$ recoil due to the transverse momentum of the produced vector boson. We present a $q_T$ recoil procedure that is directly applicable to $q_T$ resummed calculations for generic production processes of high-mass systems in hadron collisions.

On the treatment of resonances in next-to-leading order calculations matched to a parton shower

In this work we present a new subtraction method for next-to-leading order calculations that is particularly convenient even when narrow resonances are present. The method is particularly suitable for the implementation of next-to-leading order calculations matched to parton shower generators. It allows at the same time for the inclusion of all finite width effects, including interferences, and for a consistent treatment of resonances in the shower approach, preserving the mass of resonances near their peak. We implement our method, in a fully general and automatic way, within the POWHEG BOX framework, and illustrate it using as a test case the process of $p p \to \mu^+ \nu_\mu j_b j$, that is dominated by $t$-channel single top production.