Operator Coefficients Research Articles

Determination of first order perturbation for bi-harmonic operator by asymptotic boundary spectral data

Abstract This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of Rn, with n ≥ 2, we prove the stability of the first and zero order coefficients of the bi-harmonic operator from some asymptotic behavior of the boundary spectral data of the corresponding bi-harmonic operator i.e., the Dirichlet eigenvalues and the Neumann trace on the boundary of the associated eigenfunctions.

Three-loop OPE Wilson coefficients of dimension-four operators for (axial-)vector and (pseudo-)scalar current correlators

We calculate the three-loop Wilson coefficients of all physically relevant dimension-four operators, i.e. GμνaGa,μν, miq¯jqj and mimjmk2, in the short-distance expansion of the time-ordered product of a pair of gauge-singlet vector, axial-vector, scalar and pseudo-scalar currents. The results are given for a general non-Abelian gauge theory with arbitrary (compact semi-simple) gauge group and nf light fermion flavors (quarks) in a common arbitrary representation of the gauge group, which includes QCD as a special case. In particular, we allow for arbitrary flavor contents of each of the currents. For the axial-vector current the included contributions from so-called singlet diagrams are consistent with the one-loop axial anomaly.

Prospects for establishing limits on the SMEFT operators from the production processes of three and four top quarks in hadron collisions

Numerical simulations of three and four top quark hadroproduction processes are carried out in the SMEFT model framework. The simulated data are used to derive expected theoretical constraints on Wilson coefficients of relevant SMEFT operators of dimension six. Obtained limits for both cases are discussed and compared in terms of processes’ sensitivity to possible BSM contribution. Results show that operator [Formula: see text] is better constrained by the process of four top quark production, whereas other four operators [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], are similarly constrained in three and four top quark production processes. In all cases, the expected limits taken from the simultaneous analysis of the production of three and four top quarks are strengthened. Analytical expressions for the partial amplitudes of the processes [Formula: see text] and [Formula: see text] caused by the operators [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] were obtained for the first time. Based on the expressions of the obtained partial amplitudes, graphs of the perturbative unitarity boundary for the listed operators were drawn. The question of how kinematic cuts motivated by partial unitarity affect the resulting constraints on the Willson coefficients is addressed. It is shown that in all cases the limits are getting somewhat worse if such cuts are applied.

Positivity bounds in scalar Effective Field Theories at one-loop level

Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients (that would be positive if generated at the tree level), as well as their β-functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. Our results may have important implications on the robustness of experimental tests of positivity bounds.

Eigenvalues of Toeplitz matrices emerging from finite differences for certain ordinary differential operators

We consider Hermitian Toeplitz matrices emerging from finite linear combinations with non-negative coefficients of the differential operators (−1)kd2k/dx2k over the interval (0,1) after discretizing them on a uniform grid of step size 1/(n+1). The collective distribution in the Szegő–Weyl sense of the eigenvalues of these matrices as n goes to infinity can be described by GLT theory. However, we focus on the asymptotic behavior of the individual eigenvalues, on both the inner eigenvalues in the bulk and on the extreme eigenvalues. The difficulty of the problem is that not only the order of the matrices depends on n but also their so-called symbols. Our main results are third order asymptotic formulas for the eigenvalues in the case k⩽2. These results reveal some basic phenomena one should expect when considering the problem in full generality.

Commutator technique for the heat kernel of minimal higher derivative operators

We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic 2Mth order, F(∇)=(−□)M+⋯, in the background field formalism of gauge theories and quantum gravity. This technique represents the conversion of the recently suggested Fourier integral method of generalized exponential functions [A. O. Barvinsky and W. Wachowski, Heat kernel expansion for higher order minimal and nonminimal operators, ] into the commutator algebra of special differential operators, which allows one to express expansion coefficients for F(∇) in terms of the Schwinger-DeWitt coefficients of a minimal second-order operator H(∇). This procedure is based on special functorial properties of the formalism including the Mellin-Barnes representation of the complex operator power HM(∇) and naturally leads to the origin of generalized exponential functions without directly appealing to the Fourier integral method. The algorithm is essentially more straightforward than the Fourier method and consists of three steps ready for a computer codification by symbolic manipulation programs. They begin with the decomposition of the operator into a power of some minimal second-order operator H(∇) and its lower derivative perturbation part W(∇), F(∇)=HM(∇)+W(∇), followed by considering their multiple nested commutators. The second step is the construction of special local differential operators—the perturbation theory in powers of the lower derivative part W(∇). The final step is the so-called procedure of their “Syngification,” consisting of a special modification of the covariant derivative monomials in these operators by the Synge world function σ(x,x′) with their subsequent action on the Hadamard-Minakshisundaram-DeWitt coefficients of H(∇). Published by the American Physical Society 2024

Conformal anomalies for (maximal) 6d conformal supergravity

We compute the conformal anomalies for 6d (2,0) conformal supergravity by direct calculation in component fields. The main novel results consist of the type-B anomaly coefficients for the gravitino and the 3-form, as well as their explicit quadratic action on some specific backgrounds. We also comment on the graviton contribution, whose Lagrangian is essentially given by the \U0001d4ac-curvature. We confirm the expectation that, when coupling (2,0) conformal supergravity to 26 copies of the (2,0) tensor multiplet, the resulting theory is free of conformal anomalies. We also consider the conformal anomalies for its (1,0) truncation and confirm their relation with the chiral anomaly polynomial recently derived. For calculating the anomalies, we work with an Einstein on-shell background and make a factorised Ansatz for the operators governing the quadratic fluctuations. This reduces the calculation to evaluating heat-kernel coefficients of standard 2-derivative operators. We fix and check our Ansatz against the explicit evaluation of the component-field supergravity action in some cases.

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.

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. 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). 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.

APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR SEMILINEAR ELLIPTIC CONVECTION-DIFFUSION EQUATIONS WITH BOUNDARY OBSERVATION OF THE CONORMAL DERIVATIVE, WITH CONTROLS IN THE COEFFICIENTS OF THE CONVECTIVE TRANSPORT OPERATOR AND THE NONLINEAR TERM OF THE EQUATION

The paper studies difference approximations of the optimal control problem with boundary observation of the conormal derivative of the state described by the Dirichlet problem for semi-linear elliptic equations with controls in the coefficients of the convective transport operator and the nonlinear term of the equation. The issues of the correctness of the formulation of the optimal control problem were considered. Differential approximations of the optimal control problem are constructed. The issues of convergence of approximations in terms of functionality and control are studied. The regularization of approximations is carried out.

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