Operator Coefficients Research Articles

Effective field theory descriptions of Higgs boson pair production

Higgs boson pair production is traditionally considered to be of particular interest for a measurement of the trilinear Higgs self-coupling. Yet it can offer insights into other couplings as well, since – in an effective field theory (EFT) parameterisation of potential new physics – both the production cross section and kinematical properties of the Higgs boson pair depend on various other Wilson coefficients of EFT operators. This note summarises the ongoing efforts related to the development of EFT tools for Higgs boson pair production in gluon fusion, and provides recommendations for the use of distinct EFT parameterisations in the Higgs boson pair production process. This document also outlines where further efforts are needed and provides a detailed analysis of theoretical uncertainties. Additionally, benchmark scenarios are updated. We also re-derive a parameterisation of the next-to-leading order (NLO) QCD corrections in terms of the EFT Wilson coefficients both for the total cross section and the distribution in the invariant mass of the Higgs boson pair, providing for the first time also the covariance matrix. A reweighting procedure making use of the newly derived coefficients is validated, which can be used to significantly speed up experimental analyses.

An novel finite difference dispersion error elimination mechanism in the Lax–Wendroff high‐order time discretization

AbstractTime domain finite difference methods have been widely used for wave‐equation modelling in exploration geophysics over many decades. When using time domain finite difference methods, it is desirable to use a larger time step so as to save numerical simulation time. The Lax–Wendroff method is one of the well‐known methods to allow larger time step without increasing the time grid dispersion. However, the Lax–Wendroff method suffers from more time consumption because there are more spatial derivatives required to be approximated by the finite difference operators. We propose a new finite difference scheme for the Lax–Wendroff method so as to reduce the numerical simulation time. Then we determine the finite difference operator coefficients and analyse the dispersion error of the proposed finite difference scheme for the Lax–Wendroff method. At last, we apply the proposed finite difference scheme for the Lax–Wendroff method to different velocity models. The numerical simulation results indicate that the proposed finite difference scheme for the Lax–Wendroff method can effectively suppress time grid dispersion and is more efficient compared to the traditional finite difference scheme for the Lax–Wendroff method.

Identification of fractional order time delay system with measurement noise using variable period integration operational matrix

This paper proposes a parameter identification method for fractional-order time-delay systems with measurement noise, based on the Legendre wavelet variable-period integration operational matrix. A variable-period integration operational matrix and a variable-period time-delay integration operational matrix are constructed by variable-period sampling principle. For the impulse noise, global Gaussian noise and local Gaussian noise present in the identification data, the variable-period sampling, operational matrix global coefficient decomposition and matrix local coefficient decomposition methods are used to reconstruct the variable-period integration operational matrix to separate the noise from the data; the fractional-order time-delay system is expressed as an integral equation by using the reconstructed variable-period operational matrix, this reduces the influence of measurement noise on system identification accuracy. To further improve the parameter identification accuracy, the integral equation is solved by the multi-innovation least squares algorithm. The proposed method’s effectiveness is verified through several simulations and an experimental study of a constant-temperature system.

Particle swarm optimization for hybrid mutant slime mold: An efficient algorithm for solving the hyperparameters of adaptive Grey-Markov modified model

Thegrey prediction model is a scientific and effective prediction method for small amounts of incomplete data. In this paper, we proposed a particle swarm optimization for mixed mutant slime mold (namely SCPSO) combined with an extended adaptive Grey-Markov modified model called AOPGM(1,1,λ,µ), which constructs an AOPGM(1,1,λ,µ) based hyperparameters optimization for SCPSO. Firstly, the values of the exponential cumulative generation operator coefficient λ and the background value µ of the adaptive Grey-Markov modified model are refined, and λ and µ are also calculated using SCPSO. Secondly, a competitive SCPSO is formed by introducing a good point set, identifying attack strategy, mutation slime mold algorithm, and Sigmoid function into particle swarm optimization. It was also compared with the improved optimization algorithms on the CEC2020 test set and with classical and newer intelligent algorithms on the CEC2022 test set. The results of numerical experiments show that SCPSO can be considered a competitive and promising global optimization algorithm. Finally, SCPSO is used to optimize the hyperparameters of the AOPGM(1,1,λ,µ) and applied to the prediction of oil production and proven reserves in China. In terms of optimizing the hyperparameters of the AOPGM(1,1,λ,µ), the numerical experimental results of this method were better than the prediction results of 7 intelligent algorithms and the results of 4 prediction models. The validity of the proposed methodology was verified through five evaluation indicators.

Valvular and perivalvular thrombosis following self-expandable aortic valve replacement: analysis of 100 multi-detector computed tomography scans

Abstract Aims Subclinical thrombosis may represent an early stage of prosthesis structural disease. Most of the available evidence on the incidence, location, predictors, and consequences of thrombosis comes from studies that have employed balloon-expandable valves. We aimed to describe the different localisations of valvular and perivalvular thrombosis and analyse prosthesis-host multi-detector computed tomography predictors in the context of self-expandable prosthesis. Additionally, we aimed to assess the impact of valvular and perivalvular thrombosis on prosthesis performance and subsequent clinical outcomes. Methods and results This analysis includes 100 consecutive patients with normal renal function who underwent transcatheter aortic valve replacement using Evolut R and received multi-detector computed tomography and transthoracic bi-dimensional echocardiography at the 6 month follow-up. Leaflet thrombosis was detected in 18 (18%) patients; 6 (6%) had at least one leaflet with severe thrombosis. Thrombosis of the anatomic sinus was detected in 24 patients (24%) and was more prevalent in the non-coronary sinus. Subvalvular thrombosis with partial or complete circumferential involvement of the prosthesis inner skirt was diagnosed in 23 patients (23%). Bicuspid valve was the predictor with highest association with hypoattenuated lesions [least absolute shrinkage and selection operator coefficient 0.35, 95%, confidence interval (CI) 0.21–0.68]. There was no difference in terms of haemodynamic structural valve dysfunction, neurological events, and re-hospitalisation between the groups with and without thrombosis (hazard ratio: 0.86, 95% CI: 0.24–3.06, P = 0.82). Conclusion This study showed that in a relatively low-risk population, valvular and perivalvular thrombosis were not rare phenomena following transcatheter aortic valve replacement at early follow-up. Bicuspid valve showed the strongest association with post-implant thrombosis.

Top-down and bottom-up: Studying the SMEFT beyond leading order in $1/\Lambda^2$

In order to assess the relevance of higher order terms in the Standard Model effective field theory (SMEFT) expansion we consider four new physics models and their impact on the Drell Yan cross section. Of these four, one scalar model has no effect on Drell Yan, a model of fermions while appearing to generate a momentum expansion actually belongs to the vacuum expectation value expansion and so has a nominal effect on the process. The remaining two, a leptoquark and a Z'Z′ model exhibit a momentum expansion. After matching these models to dimension-ten we study the how the inclusion of dimension-eight and dimension-ten operators in hypothetical effective field theory fits to the full ultraviolet models impacts fits. We do this both in the top-down approach, and in a very limited approximation to the bottom up approach of the SMEFT to infer the impact of a fully general fit to the SMEFT. We find that for the more weakly coupled models a strictly dimension-six fit is sufficient. In contrast when stronger interactions or lighter masses are considered the inclusion of dimension-eight operators becomes necessary. However, their Wilson coefficients perform the role of nuisance parameters with best fit values which can differ statistically from the theory prediction. In the most strongly coupled theories considered (which are already ruled out by data) the inclusion of dimension-ten operators allows for the measurement of dimension-eight operator coefficients consistent with theory predictions and the dimension-ten operator coefficients then behave as nuisance parameters. We also study the impact of the inclusion of partial next order results, such as dimension-six squared contributions, and find that in some cases they improve the convergence of the series while in others they hinder it.

Experimental demonstration of quantum encryption in phase space with displacement operator in coherent optical communications

We provide experimental validation of quantum encryption in phase space using displacement operators in coherent states (DOCS) in a conventional coherent optical communication system. The proposed encryption technique is based on displacing the information symbols in the phase space using random phases and amplitudes to achieve encryption randomly and provide security at the physical layer. We also introduce a dual polarization encryption approach where we use two different and random DOCS to encrypt the X and Y polarizations separately. The experimental results show that only authorized users can decrypt the signal correctly, and any mismatch in the displacement operator coefficients, amplitudes, or phases will lead to a bit error ratio (BER) of approximately 50%. We also compare the performance of the system with and without encryption over 80 km of standard-single mode fiber (SSMF) transmission to assess the added penalty of such encryption. The achieved net bit rates are 224, 448, and 560 Gb/s for QPSK, 16QAM, and 32QAM modulation formats, respectively. The experimental results showcase the efficacy of the DOCS encryption technique in resisting various decryption attempts, demonstrating its effectiveness in ensuring the security and confidentiality of transmitted data in a real-world transmission scenario.

Nuclear matrix elements of neutrinoless double-beta decay in covariant density functional theory with different mechanisms

Nuclear matrix elements (NMEs) for neutrinoless double-beta (0νββ) decay in candidate nuclei play a crucial role in interpreting results from current experiments and in designing future ones. Accurate NME values serve as important nuclear inputs for constraining parameters in new physics, such as neutrino mass and the Wilson coefficients of lepton-number-violating (LNV) operators. In this study, we present a comprehensive calculation of NMEs for 0νββ decay in 76Ge, 82Se, 100Mo, 130Te, and 136Xe, using nuclear wave functions obtained from multi-reference covariant density functional theory (MR-CDFT). We employ three types of transition potentials at the leading order in chiral effective field theory. Our results, along with recent data, are utilized to constrain the coefficients of LNV operators. The results demonstrate that the combined NMEs based on the Feynman diagrams at the hadronic scale for the nonstandard mechanisms leads to the uncertainty by different nuclear models comparable to that for the standard mechanism. The use of NMEs from various nuclear models does not dramatically change the parameter space intervals for the coefficients, although MR-CDFT yields the most stringent constraint. Furthermore, our NMEs can also be used to perform a more comprehensive analysis with multiple isotopes.

Extremal Higgs couplings

We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, cH, is well defined and satisfies a two-sided bound. cH is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable s, expressed as M(HiHi→HjHj)=cHs+O(gSM,s−2) where gSM represents all Standard Model couplings. This observable is and, as a result, not sign-definite. We also determine the conditions under which the bound on cH is equivalent to a bound on the dimension-six operator OH=∂|H|2∂|H|2. Published by the American Physical Society 2024

Effects of squared four-fermion operators of the standard model effective field theory on meson mixing

The standard model effective field theory (SMEFT) is a universal way of parametrizing new physics (NP) manifesting as new, heavy particle interactions with the Standard Model (SM) degrees of freedom, that respect the SM gauged symmetries. Higher order terms in the NP interactions possibly lead to sizable effects, mandatory for meaningful phenomenological studies, such as contributions to neutral meson mixing, which typically pushes the scale of NP to energy scales much beyond the reach of direct searches in colliders. I discuss the leading-order renormalization of double-insertions of dimension-6 four-fermion operators that change quark flavor by one unit (i.e., |ΔF|=1, F=strange-, charm-, or bottom-flavor), by dimension-8 operators relevant to meson mixing (i.e., |ΔF|=2) in SMEFT. Then, I consider the phenomenological implications of contributions proportional to large Yukawas, setting bounds on the Wilson coefficients of operators of dimension-6 via the leading logarithmic contributions. Given the underlying interest of SMEFT to encode full-fledged models at low energies, this work stresses the need to consider dimension-8 operators in phenomenological applications of dimension-6 operators of SMEFT. Published by the American Physical Society 2024

First transition dynamics of reaction–diffusion equations with higher order nonlinearity

AbstractIn this study, the dynamics of a reaction–diffusion equation on a bounded interval at the first dynamic transition point is investigated. The main difference of this study from the existing ones in the dynamic transition literature is that in this work, no specific form of the nonlinear operator is assumed except that it is an analytic function of and . The linear operator is also assumed to be a general operator with sinusoidal eigenvectors. Moreover, we assume that there is a first transition as a real simple eigenvalue changes sign. With this general framework, we make a rigorous analysis of the dependence of the first transition dynamics on the coefficients of the Taylor expansion of the nonlinear operator. The main tool we use in this study is the center manifold reduction combined with the classification of the dynamic transition theory. This study is a generalization of a recent work where the nonlinear operator contains only low‐order (quadratic and cubic) nonlinearities. The current generalization requires certain technical difficulties such as the validity of the genericity conditions on the Taylor coefficients of the nonlinear operator and a bootstrapping argument using these genericity conditions. The results of this work can be generalized in various directions, which are discussed in the conclusions section.

Bounded Solutions of a Second-Order Differential Equation with Piecewise-Constant Operator Coefficients

Bounded Solutions of a Second-Order Differential Equation with Piecewise-Constant Operator Coefficients

Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications

For a certain class of radial weights, we prove weighted norm estimates for commutators with BMO coefficients of singular operators in local generalized Morrey spaces. As a consequence of these estimates, we obtain norm inequalities for such commutators in the generalized Stummel-Morrey spaces. We also discuss a.e. well-posedness of singular operators and their commutators on weighted generalized Morrey spaces. The obtained estimates are applied to prove interior regularity for solutions of elliptic PDEs in the frameworks of the corresponding weighted Sobolev spaces based on the local generalized Morrey spaces or Stummel-Morrey spaces. To this end also conditions for the applicability of the representation formula, for the second-order derivatives of solutions to elliptic PDEs, are found for the case of such weighted spaces. In both results, for commutators and applications, we admit weights beyond the Muckenhoupt range.

Probing positivity at the LHC with exclusive photon-fusion processes

By tagging one or two intact protons in the forward direction, it is possible to select and measure exclusive photon-fusion processes at the LHC. The same processes can also be measured in heavy ion collisions, and are often denoted as ultraperipheral collisions (UPC) processes. Such measurements open up the possibility of probing certain dimension-8 operators and their positivity bounds at the LHC. As a demonstration, we perform a phenomenological study on the γγ → ℓ+ℓ− processes, and find out that the measurements of this process at the HL-LHC provide reaches on a set of dimension-8 operator coefficients that are comparable to the ones at future lepton colliders. We also point out that the γq → γq process could potentially have better reaches on similar types of operators due to its larger cross section, but a more detailed experimental study is need to estimate the signal and background rates of this process. The validity of effective field theory (EFT) and the robustness of the positivity interpretation are also discussed.

Bounded in the mean and stationary solutions of second-order difference equations with operator coefficients

We study the question of the existence of a unique bounded in the mean solution for the second-order difference equation with piecewise constant operator coefficients and of the stationary solution of the corresponding difference equation with constant operator coefficients. The case is considered when the corresponding “algebraic” operator equations have separated roots.

Characters of [formula omitted] and vertex operators

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group GLn(Fq). Green's theory of GLn(Fq) is recovered and enhanced under the realization of the Grothendieck ring of representations RG=⨁n≥0R(GLn(Fq)) as two isomorphic Fock spaces associated to two infinite-dimensional F-equivariant Heisenberg Lie algebras hˆF‾ˆq and hˆF‾q, where F is the Frobenius automorphism of the algebraically closed field F‾q. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. One of the features of the current approach is a simpler identification of the Fock space RG as the Hall algebra of symmetric functions via vertex operator calculus, and another is that we are able to compute in general the character table, where Green's degree formula is demonstrated as an example.

On spectral enclosures for Maxwell’s equations with the Drude–Lorentz model

In this paper, we compare two approaches to derive spectral enclosures for Maxwell’s equations with the Drude–Lorentz model in possibly unbounded domains. The enclosures can be computed in the infinite-dimensional case as well as for the matrix-valued function obtained after a discretization. The enclosures are minimal given only the numerical ranges of the operator coefficients and we compare in the case of purely imaginary poles the derived enclosures with enclosures from the literature.

Numerical investigation on vortex characteristics in a low-head Francis turbine operating of adjustable-speed at part load conditions

In this paper, the vortex characteristics in a low-head Francis turbine operating of adjustable-speed at part load conditions are numerically investigated. First, the rules of fixed-speed and adjustable-speed operations are introduced in detail, aiming at operating limits extension. Second, comparative analysis on vortex rope is conducted, with emphasis on vortex rope volume, tail water excitation and spontaneous power swing. Finally, inter-blade vortex has been analyzed and successfully demonstrated, and its induced high amplitude pressure fluctuation characteristic is explored. It is found that at deep part load, vortex rope volume and power swing coefficient of adjustable-speed operation decreased by 69 % and 61 % respectively. The amplitude of Rheingans frequency decreased by 17 %, while the amplitude of blade passing frequency increased by 83 %. After decreasing runner speed, inter-blade vortex is stranded at blade suction surface leading-edge. In addition to low-frequency disturbance, pressure fluctuation shows high-frequency wide-band characteristics. It is concluded that adjustable-speed operation has beneficial effects on improvement of cavity cavitation and energy stability. As for hydraulic stability, the Rotor-Stator Interaction effect cannot be ignored. After changing runner speed, the inter-blade vortex becomes more serious, which could provoke low-cycle and high-cycle fatigue of the blades.

QCD corrections to the Darwin coefficient in inclusive semileptonic B→Xuℓν¯ℓ decays

In this paper, we compute αs corrections to the matching coefficients of the dimension-six operators in the heavy quark expansion of the inclusive semileptonic heavy hadron decay rate and leptonic invariant mass spectrum with a massless quark and both a massive or massless lepton in the final state, analytically. The obtained results can be applied to the inclusive semileptonic B→Xuℓν¯ℓ (ℓ=e, μ, τ) and D→Xℓν¯ℓ (ℓ=e, μ) decays. The main application of our results is the background subtraction of the B→Xuℓν¯ℓ decay in the measurement of the B→Xcℓν¯ℓ decay, which is important for the precise extraction of Vcb and R(D(*)). They also play a role in the computation of lifetimes of heavy hadrons. Published by the American Physical Society 2024

Floating-Point Quantization Analysis of Multi-Layer Perceptron Artificial Neural Networks

The impact of quantization in Multi-Layer Perceptron (MLP) Artificial Neural Networks (ANNs) is presented in this paper. In this architecture, the constant increase in size and the demand to decrease bit precision are two factors that contribute to the significant enlargement of quantization errors. We introduce an analytical tool that models the propagation of Quantization Noise Power (QNP) in floating-point MLP ANNs. Contrary to the state-of-the-art approach, which compares the exact and quantized data experimentally, the proposed algorithm can predict the QNP theoretically when the effect of operation quantization and Coefficient Quantization Error (CQE) are considered. This supports decisions in determining the required precision during the hardware design. The algorithm is flexible in handling MLP ANNs of user-defined parameters, such as size and type of activation function. Additionally, a simulation environment is built that can perform each operation on an adjustable bit precision. The accuracy of the QNP calculation is verified with two publicly available benchmarked datasets, using the default precision simulation environment as a reference.