Higher-order Corrections Research Articles

Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch

In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.

Renormalization group improvement for thermally resummed effective potential

We propose a novel method for renormalization group improvement of thermally resummed effective potential. In our method, β-functions are temperature dependent as a consequence of the divergence structure in resummed perturbation theory. In contrast to the ordinary MS¯ scheme, the renormalization group invariance of the resummed finite-temperature effective potential holds order by order, which significantly mitigates a notorious renormalization scale dependence of phase transition quantities such as a critical temperature even at the one-loop order. We also devise a tractable method that enables one to incorporate temperature-dependent higher-order corrections by fully exploiting the renormalization group invariance. Published by the American Physical Society 2024

Dynamical de Sitter black holes in a quasi-stationary expansion

We revisit and improve the analytic study (Gregory et al 2018 Class. Quantum. Grav. 35 155008) of spherically symmetric but dynamical black holes in Einstein’s gravity coupled to a real scalar field. We introduce a series expansion in a small parameter ε that implements slow time dependence. At the leading order (LO), the generic solution is a quasi-stationary Schwarzschild–de Sitter (SdS) metric, i.e. one where time-dependence enters only through the mass and cosmological constant parameters of SdS. The two coupled ODEs describing the LO time dependence are solved up to quadrature for an arbitrary scalar potential. Higher order corrections can be consistently computed, as we show by explicitly solving the Einstein equations at the next to LO as well. We comment on how the quasi-stationary expansion we introduce here is equivalent to the non-relativistic 1/c expansion.

Analytic third-order QCD corrections to top-quark and semileptonic b→u decays

We present the first analytic results of next-to-next-to-next-to-leading-order (N3LO) QCD corrections to the top-quark decay width. We focus on the dominant leading color contribution, which includes light-quark loops. At next-to-next-to-leading order (NNLO), this dominant contribution accounts for 95% of the total correction. By utilizing the optical theorem, the N3LO corrections are related to the imaginary parts of the four-loop self-energy Feynman diagrams, which are calculated with differential equations. The results are expressed in terms of harmonic polylogarithms, enabling fast and accurate evaluation. The third-order QCD corrections decrease the leading-order decay width by 0.667%, and the scale uncertainty is reduced by half compared to the NNLO result. The most precise prediction for the top-quark width is now 1.321 GeV for mt=172.69 GeV. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic b→u transition. The perturbative series in the on-shell mass scheme exhibits poor convergence behavior. In the MS¯ mass scheme, the scale dependence is greatly improved. A more precise determination of the CKM matrix element Vub could be obtained with such higher-order corrections. Published by the American Physical Society 2024

Higgs boson pair production and decay at NLO in QCD: the bb¯γγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b}\\gamma \\gamma $$\\end{document} final state

The Higgs boson pair production at the LHC provides a probe to the Higgs boson self-coupling. The higher-order QCD corrections in this process are sizable and must be taken into account in comparison with data. Due to the small cross section, it is necessary to consider at least one of the Higgs bosons decaying to bottom quarks. The QCD corrections to the decay processes would also be important in such cases. We present a full calculation of the total and differential cross sections for the bb¯γγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b}\\gamma \\gamma $$\\end{document} final state with next-to-leading order (NLO) QCD corrections. After applying typical kinematic cuts in the final state, we find that QCD NLO corrections in the decay decrease the LO result by 19% and reduce the scale uncertainties by a factor of two. The QCD corrections to the invariant mass mjjγγ distribution, the transverse momentum spectra of the leading bottom quark jet and photon are significant and can not be approximated by a constant factor.

Enhancing Accuracy in Numerical Simulations for High-Speed Flows: Integrating High-Order Corrections with Weighted Essentially Non-Oscillatory Flux

This study introduces a novel method to enhance numerical simulation accuracy for high-speed flows by refining the weighted essentially non-oscillatory (WENO) flux with higher-order corrections like the modified weighted compact scheme (MWCS). Numerical experiments demonstrate improved sharpness in capturing shock waves and stability in complex conditions like two interacting blast waves. Key highlights include simultaneous capture of small-scale smooth fluctuations and shock waves with precision surpassing the original WENO and MWCS methods. Despite the significantly improved accuracy, the extra computational cost brought by the new method is only marginally increased compared to the original WENO, and it outperforms MWCS in both accuracy and efficiency. Overall, this method enhances simulation fidelity and effectively balances accuracy and computational efficiency across various problems.

Four-jet event shapes in hadronic Higgs decays

We present next-to-leading order perturbative QCD predictions for four-jet-like event-shape observables in hadronic Higgs decays. To this end, we take into account two Higgs-decay categories: involving either the Yukawa-induced decay to a \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{b}}\\overline{{\ ext{b}} }$$\\end{document} pair or the loop-induced decay to two gluons via an effective Higgs-gluon-gluon coupling. We present results for distributions related to the event-shape variables thrust minor, light-hemisphere mass, narrow jet broadening, D-parameter, and Durham four-to-three-jet transition variable. For each of these observables we study the impact of higher-order corrections and compare their size and shape in the two Higgs-decay categories. We find large NLO corrections with a visible shape difference between the two decay modes, leading to a significant shift of the peak in distributions related to the H → gg decay mode.

Electric Octupole-Dependent Contributions to Optical Binding Energy

Contributions to the radiation-induced dispersion energy shift between two interacting particles dependent on the electric octupole moment are calculated using a physical picture in which moments induced by applied fluctuating electromagnetic fields are coupled via retarded interaction tensors. The specific potentials evaluated include those found between an electric dipole-polarisable molecule and either a mixed electric dipole–octupole- or purely octupole-polarisable molecule, and those between two mixed electric dipole–octupole-polarisable molecules. Interaction energies are obtained for molecular and pair orientationally averaged situations. Terms dependent on the octupole weight-1 moment may be viewed as higher-order corrections to the leading dipole–dipole interaction energy as also found in energy transfer and dispersion forces. A comprehensive polarisation analysis is carried out for linearly and circularly polarised laser light incident parallel and perpendicular to the inter-particle axis. Contributions to the optical binding energy arising when one of the pair is polar and characterised by either a permanent electric dipole or octupole moment are also evaluated. Neither of these energy shifts survive orientational averaging.

Higher-order NLO radiative corrections to polarized muon decay spectrum

Higher-order QED radiative corrections to the muon decay spectrum are evaluated within the QED structure function approach in the next-to-leading-order logarithmic approximation. New analytical results are given in the O(α3ln2(mμ2/me2)) order. Earlier results in the O(α2ln1(mμ2/me2)) and O(α3ln3(mμ2/me2)) orders are partially corrected. Numerical estimates of different contributions are presented. Published by the American Physical Society 2024

Making the leap. Part I. Modelling the reconstructed lensing convergence PDF from cosmic shear with survey masks and systematics

The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure — the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly nonlinear regime. The goal of this series of papers is to make the leap and lay out the steps to perform an actual data analysis with this theoretical tool. Building upon the LDT framework, in this work (paper I) we demonstrate how to accurately model the Probability Distribution Function (PDF) of a reconstructed Kaiser-Squires convergence field under a realistic mask, that of the third data release of the Dark Energy Survey (DES). We also present how weak lensing systematics and higher-order lensing corrections due to intrinsic alignments, shear biases, photo-z errors and baryonic feedback can be incorporated in the modelling of the reconstructed convergence PDF. In an upcoming work (paper II) we will then demonstrate the robustness of our modelling through simulated likelihood analyses, the final step required before applying our method to actual data.

Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimensional reduction

Models with radiative symmetry breaking typically feature strongly supercooled first-order phase transitions, which result in an observable stochastic gravitational wave background. In this work, we analyse the role of higher-order thermal corrections for these transitions, applying high-temperature dimensional reduction to a theory with dimensional transmutation. In particular, we study to what extent high-temperature effective field theories (3D EFT) can be used. We find that despite significant supercooling down from the critical temperature, the high-temperature expansion for the bubble nucleation rate can be applied using the 3D EFT framework, and we point out challenges in the EFT description. We compare our findings to previous studies and find that the next-to-leading order corrections obtained in this work have a significant effect on the predictions for GW observables, motivating a further exploration of higher-order thermal effects.

Heavy quarks in polarised deep-inelastic scattering at the electron-ion collider

We extend the FONLL general-mass variable-flavour-number scheme to the case of longitudinally polarised DIS structure functions, accounting for perturbative corrections up to Oαs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\alpha _s^2\\right) $$\\end{document}. We quantify the impact of charm quark mass and higher-order perturbative corrections on projected measurements of inclusive and charm-tagged longitudinal asymmetries at the Electron-Ion Collider (EIC) and at the Electron-ion collider in China (EicC). We demonstrate how the inclusion of these corrections is essential to compute predictions with an accuracy that matches the projected precision of the measurements. The computation is made publicly available through the open-source EKO and YADISM programs.

Resummation of Next-to-Leading Nonglobal Logarithms at the LHC.

In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as nonglobal logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading nonglobal logarithms remained a challenge that we solve in this Letter using renormalization group methods in effective field theory. To achieve next-to-leading logarithmic accuracy, we implement the two-loop anomalous dimension governing the resummation of nonglobal logarithms into a large-N_{c} parton shower framework, together with one-loop matching corrections. As a first application, we study the interjet energy flow in e^{+}e^{-} annihilation into two jets. We then present, for the first time, resummed predictions at next-to-leading logarithmic accuracy for a gap-between-jets observable at hadron colliders.

Kerr-Schild double copy for Kundt spacetimes of any dimension

We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) — these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.

Black hole shadows in Einstein-Bel-Robinson gravity* *Supported by the Internal Project (2023/2211) of Excellent Research of the Faculty of Science of Hradec Králové University

Gravity models given by higher-order scalar curvature corrections are believed to bear important consequences. Einstein-Bel-Robinson (EBR) gravity with quartic curvature modification motivated Sajadi et al. to explore static spherically symmetric black hole solutions using perturbative methods. In this study, inspired by their work, we investigate AdS black hole shadows in EBR gravity and demonstrate how the gravity parameter alters the energy emission rate. Finally, we address the same problem in the presence of plasma, because the black holes are thought to be surrounded by a medium that changes the geodesic of photons.

Uncertainty principle from the noise of gravitons

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023). There the authors have calculated the quantum gravity modified Newton’s law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum.

Generalized perturbative singles corrections to the random phase approximation method: Impact on noncovalent interaction energies of closed- and open-shell dimers.

The post-Kohn-Sham (KS) random phase approximation (RPA) method may provide a poor description of interaction energies of weakly bonded molecules due to inherent density errors in approximate KS functionals. To overcome these errors, we develop a generalized formalism to incorporate perturbative singles (pS) corrections to the RPA method using orbital rotations as a perturbation parameter. The pS schemes differ in the choice of orbital-rotation gradient and Hessian. We propose a pS scheme termed RPA singles (RPAS)[Hartree-Fock (HF)] that uses the RPA orbital-rotation gradient and time-dependent HF Hessian. This correction reduces the errors in noncovalent interaction energies of closed- and open-shell dimers. For the open-shell dimers, the RPAS(HF) method leads to a consistent error reduction by 50% or more compared to the RPA method for the cases of hydrogen-bonding, metal-solvent, carbene-solvent, and dispersion interactions. We also find that the pS corrections are more important in error reduction compared to higher-order exchange corrections to the RPA method. Overall, for open shells, the RPAS(HF)-corrected RPA method provides chemical accuracy for noncovalent interactions and is more reliable than other perturbative schemes and dispersion-corrected density functional approximations, highlighting its importance as a reliable beyond-RPA correction.

Extension of the Schwarzschild black hole solution in f(R) gravitational theory and its physical properties

The successes of f(R) gravitational theory as a logical extension of Einstein’s theory of general relativity (GR) encourage us to delve deep into this theory and continue our study to attempt to derive an extension of the Schwarzschild black hole (BH) solution. In this study, in order to solve the output nonlinear differential equation, we closed the form of the system by assuming the derivative of f(R) with respect to the scalar curvature R to have the form F(r)=df(R(r))dR(r)=1-αr4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(r)=\\frac{\ extrm{d}f(R(r))}{\ extrm{d}R(r)}=1- \\frac{\\alpha }{r^4}$$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is a dimensional constant. Our study shows that when α→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 0$$\\end{document}, we obtain the Schwarzschild BH solution of GR assuming some constraints on the constant of integration, and if these constraints are bounded, we obtain the anti-de Sitter (AdS)/de Sitter (dS) spacetime. For the general case, i.e., when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0$$\\end{document}, we obtain a BH solution that tends asymptotically to AdS/dS spacetime. Moreover, we derive the timelike and null particle geodesics of the BH solution studied in this article. The equation of motion and effective potential of test particles are calculated to study the stability of radial orbits (trajectories). The energy and angular momentum are calculated to study the circular motion and stability of circular orbits. We also derive the stability condition using the geodesic deviation. Moreover, we discuss the physics of the output BH solutions through calculation of the thermodynamic quantities including entropy, the Hawking temperature, and Gibbs free energy. Finally, we check the validity of the first law of thermodynamics applied to the BH of this study. Although we can derive a Schwarzschild black hole solution in the lower order of f(R), specifically when f(R)=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)=R$$\\end{document}, where the gravitational mass is generated from the source of gravity, we demonstrate that in the higher orders of f(R), when f(R)≠R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)\ e R$$\\end{document}, the source of gravity is attributed primarily to higher-order corrections, and the source of gravity that was originally derived from the Schwarzschild black hole has ceased to be dominant.

Numerical Modeling of Sediment Transport and Bed Evolution in Nonuniform Open-Channel Flows

Abstract The shallow-water and multilayer hydrostatic models have been commonly used to analyze the problems of a sediment-laden, plane open-channel flow. The models are adequate to solve a quasi-hydrostatic flow problem, but their accuracy deteriorates as the e ects of the vertical acceleration gain in significance. Herein, a higher-order numerical model for treating the problems of unsteady, plane open-channel flow over a movable bed is proposed. In this model, the flow hydrodynamics is governed by the depth-averaged Boussinesq-type equations, and the bed morphodynamics is determined by an Exner-type equation and additional equations describing the non-equilibrium transports of suspended load and bed load. A hybrid finite-volume and finite-di erence scheme was used to discretize and solve the governing equations, yielding solutions that are in satisfactory agreement with the experimental data. Overall, the results of the proposed model for the temporal free-surface profile and bed evolution were fairly adequate. For the two particular cases considered, however, the quality of its results was moderately a ected by the e ects of the three-dimensional characteristics of the dam-break flow and the sliding of the dike body due to sub-surface flow. The results of this investigation highlight the importance of including a higher-order Boussinesq-type correction for refining sediment transport computations.

Cumulant Green's function methods for molecules.

The cumulant expansion of the Green's function is a computationally efficient beyond-GW approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous GW approximation of many-body perturbation theory, ab initio cumulant expansions performed on top of GW (GW + C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of GW + C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (Ne, HF, H2O, NH3, and CH4) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available.