Scattering Amplitudes Research Articles

Noninvertible Symmetries, Anomalies, and Scattering Amplitudes.

We show that crossing symmetry of S matrices is modified in certain theories with noninvertible symmetries or anomalies. Focusing on integrable flows to gapped phases in two dimensions, we find that S matrices derived previously from the bootstrap approach are incompatible with noninvertible symmetries along the flow. We present consistent alternatives, which, however, violate standard crossing symmetry and obey modified rules dictated by fusion categories. We extend these rules to theories with discrete anomalies.

Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr(Φ3) theory

Scattering amplitudes for the simplest theory of colored scalar particles—the Tr(Φ3) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr(Φ3) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr(Φ3) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U(N)→U(N−k)×U(k). The Goldstone amplitudes for this theory coincide with those of pions in the U(N)×U(N)→U(N) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr(Φ3) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024

One-loop QCD amplitudes in the Feynman-diagram gauge

Scattering amplitudes for the massless QCD process, qq¯→q′q¯′, are calculated in the one-loop order in the Feynman-Diagram (FD) gauge, where gluons are quantized on the light cone with opposite direction of the three-momenta. We find non-decoupling of the Faddeev-Popov ghosts and nonconventional UV singularities in dimensional regularization. The known QCD amplitudes with asymptotic freedom are reproduced only after summing propagator and vertex corrections. By quantizing gluons in the Feynman gauge on the FD gauge background, we obtain the one-loop improved FD gauge amplitudes. Published by the American Physical Society 2024

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Ultrasonic Imaging of Deeper Bone Defect Using Virtual Source Synthetic Aperture with Phased Shift Migration: A Phantom Study.

Ultrasound imaging for bone is a difficult task in the field of medical ultrasound. Compared with other phase array techniques, the synthetic aperture (SA) has a better lateral resolution but a limited imaging depth due to the limited ultrasonic energy emitted by the single emitter in each transmission. In contrast, the virtual source (VS) synthetic aperture allows a simultaneous multi-element emission and could provide a higher ultrasonic incident energy in each transmission. Therefore, the VS might achieve a high imaging quality at a deeper depth for bone imaging than the traditional SA. In this study, we proposed the virtual source phase shift migration (VS-PSM) method to achieve ultrasonic imaging of the deeper bone defect featured in the multilayer structure. The proposed VS-PSM method was validated using standard soft tissue phantom and printed bone phantom with artificial defects. The image quality was evaluated in terms of contrast-to-noise ratios (CNR) and amplitudes of scatters and defects at different imaging depths. The results showed that the VS-PSM method could achieve a high imaging quality of the soft tissues with a significant improvement in the scattering amplitude and without a significant sacrifice of the lateral and axial resolution. The PSM was superior to the DAS in suppressing the background noise in the images. Compared with the traditional SA-PSM, the VS-PSM method could image deeper bone defects at different ultrasonic frequencies, with an average improvement of 50% in CNR. In conclusion, this study demonstrated that the proposed VS-PSM method could image deeper bone defects and might help the diagnosis of bone disease using ultrasonic imaging.

Distributional celestial amplitudes

Scattering amplitudes are tempered distributions, which are defined through their action on functions in the Schwartz space Sℝ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S}\\left(\\mathbb{R}\\right) $$\\end{document} by duality. For massless particles, their conformal properties become manifest when considering their Mellin transform. Therefore we need to mathematically well-define the Mellin transform of distributions in the dual space S′ℝ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{S}}^{\\prime}\\left({\\mathbb{R}}^{+}\\right) $$\\end{document}. In this paper, we investigate this problem by characterizing the Mellin transform of the Schwartz space Sℝ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S}\\left({\\mathbb{R}}^{+}\\right) $$\\end{document}. This allows us to rigorously define the Mellin transform of tempered distributions through a Parseval-type relation. Massless celestial amplitudes are then properly defined by taking the Mellin transform of elements in the topological dual of the Schwartz space Sℝ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S}\\left({\\mathbb{R}}^{+}\\right) $$\\end{document}. We conclude the paper with applications to tree-level graviton celestial amplitudes.

Multiparton Cwebs at five loops

Scattering amplitudes involving multiple partons are plagued with infrared singularities. The soft singularities of the amplitude are captured by the soft function which is defined as the vacuum expectation value of Wilson line correlators. Renormalization properties of soft function allows us to write it as an exponential of the finite soft anomalous dimension. An efficient way to study the soft function is through a set of Feynman diagrams known as Cwebs (webs). We present the mixing matrices and exponentiated colour factors (ECFs) for the Cwebs at five loops that connect six Wilson lines, except those that are related by relabeling of Wilson lines. Further, we express these ECFs in terms of 29 basis colour factors. We also find that this basis can be categorized into two colour structures. Our results are the first key ingredients for the calculation of the soft anomalous dimension at five loops.

Relative Contributions of Cross-Even and Cross-Odd Parts to the Spin-Dependent Elastic Hadron Scattering Amplitudes at High Energies

Relative Contributions of Cross-Even and Cross-Odd Parts to the Spin-Dependent Elastic Hadron Scattering Amplitudes at High Energies

High-Energy Behavior of Scattering Amplitudes in Theories with Purely Virtual Particles

We study a class of renormalizable quantum field theories with purely virtual particles that exhibits nonrenormalizable behavior in the high-energy limit of scattering cross sections, which grow as powers of the center-of-mass energy squared and seems to violate unitarity bounds. We point out that the problem should be viewed as a violation of perturbativity, instead of unitarity, and show that the resummation of self energies fixes the issue. As an explicit example, we consider a class of O(N) theories at the leading order in the large-N expansion and show that the different quantization prescription of purely virtual particles takes care of the nonrenormalizable behavior, making the resummed cross sections to decrease at high energies and the amplitudes to satisfy the unitarity bounds. We compare the results to the case of theories with ghosts, where the resummation cannot change the behavior of cross sections due to certain cancellations in the high-energy expansion of the self energies. These results are particularly relevant for quantum gravity.

Relativistic three-body scattering and the D0D*+−D+D*0 system

Scattering amplitudes involving three-particle scattering processes are investigated within the isobar approximation which respects constraints from two- and three-body unitarity. The particular system considered is the D0D*+−D+D*0, where the D*+ (D*0) enters as a p-wave D+π0 or D0π+ (D0π0 or D+π−) resonance. The interaction potentials in the coupled-channel D0D*+−D+D*0 system contain the σ, ρ, ω, and π-exchange. The analytic continuation of the amplitudes across the three-body unitary cuts is investigated to search for poles on the unphysical Riemann sheets. Associated with an unstable particle D*+ (D*0) is a complex two-body unitarity cut, through which one can further analytically continue into another unphysical Riemann sheet. Dynamical singularities emerged from the π-exchange potential are stressed. The pole generated from the D0D*+−D+D*0 interaction and its line shape in D0D0π+ break-up production are in agreement with double-charmed tetraquark Tcc+ observed by the LHCb Collaboration. Published by the American Physical Society 2024

The High Energy Scattering Amplitude One-loop Gravitation in the Effective Field Theory

In this work, the Newton potential, together with the low-key corrective energy, an attractive loop of two large non-relativistic masses has been found. The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers was studied in the one-loop gravitation effective field theory.

Inverse Scattering Problem for the High Order Schrödinger Operator at Fixed Angles Scattering Amplitude

We consider the inverse scattering problem for the higher order Schrödinger operator H=(-Delta )^m+q(x), m=1,2, 3,ldots. We show that the scattering amplitude of H at fixed angles can uniquely determines the potential q(x) under certain assumptions, which extends the early results on this problem. The uniqueness of q(x) mainly depends on the construction of the Born approximation sequence and its estimation.

Adjacency for scattering amplitudes from the Gröbner fan

Scattering amplitudes in planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.Starting from the Plücker ideal, we describe how the polynomial cluster variables are encoded in non-prime initial ideals associated to certain maximal cones of the positive tropical fan. Following [1] we show that extending the Plücker ideal by such variables leads to a Gröbner fan with a single maximal Gröbner cone spanned by the positive tropical rays. The associated initial ideal encodes the compatibility relations among the full set of cluster variables. Thus we find that the Gröbner structure naturally encodes both the symbol alphabet and the cluster adjacency relations exhibited by scattering amplitudes without invoking the cluster algebra at all.As a potential application of these ideas we then examine the kinematic ideal associated to non-dual conformal massless scattering written in terms of spinor helicity variables. For five-particle scattering we find that the ideal can be identified with the Plücker ideal for Gr(3, 6) and the corresponding tropical fan contains a number of non-prime ideals which encode all additional letters of the two-loop pentagon function alphabet present in various calculations of massless five-point finite remainders.

MASAP: A package for atomic scattering amplitude in solids

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic tl-matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure. Program summaryProgram Title: MASAPCPC Library link to program files:https://doi.org/10.17632/gtxp3mn5hs.1Licensing provisions: Apache 2.0Programming language: FORTRAN 77, Python3External routines:•SciPy (https://www.scipy.org)•Atomic Simulation Environment (https://wiki.fysik.dtu.dk/ase/)•h5py (https://www.h5py.org)•wxPython (https://www.wxpython.org)Nature of problem: Calculation of atomic scattering amplitudes of scattered electrons by an embedded atom in a solid including damping and relativistic effects. Comparison between ASA's in an isolated atomic system and a solid. Introduction of an effective ASA for electrons propagating in a solid derived from Multiple Scattering Theory.Solution method: Potential scattering theory. Muffin-tin approximation. Superposition of atomic electron densities obtained by self-consistent Dirac-Fock atomic calculations. Hedin-Lundqvist potential as an optical potential. Fully relativistic theory, with scalar-relativistic and non-relativistic approximations for comparison.Additional comments including restrictions and unusual features: Even though the program can perform calculations at impinging electron energies up to ≈15 Kev, DCS calculations are recommended in the range 50 : ≈1500 eV both in the case of isolated atoms and atoms embedded in solids, since this interval is more suitable for studying the details of the atomic potentials in their environment.In the case of solids, at energies lower than ≈50 eV, the details of the electronic structure might be important, whereas in the case of isolated atoms this range might suffer from the neglect of the polarization potential and coupling to available inelastic channels. In this respect an option to add an empirical form of a polarization potential to investigate its effects is available to the interested user.

Numerical scattering amplitudes with pySecDec

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples. Program summaryProgram Title: pySecDecCPC Library link to program files:https://doi.org/10.17632/dnrkf5jxzh.4Developer's repository link:https://github.com/gudrunhe/secdec, https://secdec.readthedocs.io (Online documentation)Licensing provisions: GNU Public License v3Programming language: Python, Form, C++, CudaExternal routines/libraries:GSL [1], NumPy [2], SymPy [3], Nauty [4], Cuba [5], Form [6], GiNaC and CLN [7], Normaliz [8], GMP [9].Journal reference of previous version: Comput. Phys. Commun. 273 (2022) 108267 [1].Does the new version supersede the previous version?: Yes.Nature of problem: Scattering amplitudes at higher orders in perturbation theory are typically represented as a linear combination of coefficients — containing the kinematic invariants and the space-time dimension — multiplied with loop integrals which contain singularities and whose analytic representation might be unknown.Solution method: Extraction of singularities in the dimensional regularization parameter as well as in analytic regulators for potential spurious singularities is done using sector decomposition. The combined evaluation of the integrals with their coefficients is performed in an efficient way.Restrictions: Depending on the complexity of the problem, limited by memory and CPU/GPU time.

Lagrangians manifesting color-kinematics duality in the NMHV sector of Yang-Mills

Scattering amplitudes in Yang-Mills theory are known to exhibit kinematic structures which hint to an underlying kinematic algebra that is dual to the gauge group color algebra. This color-kinematics duality is still poorly understood in terms of conventional Feynman rules, or from a Lagrangian formalism. In this work, we present explicit Lagrangians whose Feynman rules generate duality-satisfying tree-level BCJ numerators, to any multiplicity in the next-to-MHV sector of pure Yang-Mills theory. Our Lagrangians make use of at most three pairs of auxiliary fields (2, 1, 0-forms) — surprisingly few compared to previous attempts of Lagrangians at low multiplicities. To restrict the Lagrangian freedom it is necessary to make several non-trivial assumptions regarding field content, kinetic terms, and interactions, which we discuss in some detail. Future progress likely hinges on relaxing these assumptions.

All Order Gravitational Waveforms from Scattering Amplitudes.

Waveforms are classical observables associated with any radiative physical process. Using scattering amplitudes, these are usually computed in a weak-field regime to some finite order in the post-Newtonian or post-Minkowskian approximation. Here, we use strong-field amplitudes to compute the waveform produced in scattering of massive particles on gravitational plane waves, treated as exact nonlinear solutions of the vacuum Einstein equations. Notably, the waveform contains an infinite number of post-Minkowskian contributions, as well as tail effects. We also provide, and contrast with, analogous results in electromagnetism.

The Quantized Constants with Remmen’s Scattering Amplitude to Explain Riemann Zeta Zeros

Riemann Hypothesis has been proposed by Bernhard Riemann since year 1859. Nowadays, there are lots of proof or disproof all over the internet society or the academic professional authority etc. However, none of them is accepted by the Clay’s Mathematics Institute for her Millennium Prize. In the past few months, this author discovered that there may be a correlation exists between the real and imaginary parts of Riemann Zeta function for the first 10 non-trivial zeros of the Riemann function etc. Indeed, when one tries to view the correlation relationship as a constant like the Planck’s one. Then we may show that Riemann Zeta zeros are indeed discrete quantum energy levels or the discrete spectrum as electrons falling from some bound quantum state to a lower energy state (or Quantum Field Theory). That may be further explained by Remmen’s scattering amplitude or the S-matrix. We may approximate the S-matrix by applying the HKLam theory to it and predict the scattering amplitude or even the Riemann Zeta non-trival zeros etc. By the way, the key researching equations or formula in the following content will be around the Taylor expansion of the Riemann Zeta function, their convergence etc. In additional, I will also investigate the (*’’) as shown below: ∏_(i=1)^∞▒(z-z_i ) = ξ(0.5 + i*t) = (∑_(n=1)^∞▒1)⁄n^((0.5+i*t) ) = ∏_(j=1)^∞▒(1-1⁄(p_j^((0.5+i*t) ) ))^(-1) ------------ (*’’) as we may find the existence of some constants like the Planck’s one. For the application of the aforementioned scholarly outcome, it is well-known that if one can find the pattern of the appearance to the prime number and hence break the public key cryptography in the everyday usage of information technology security etc.

Scatter correction for cone-beam CT via scatter kernel superposition-inspired convolutional neural network

Objective. X-ray scatter leads to signal bias and degrades the image quality in Computed Tomography imaging. Conventional real-time scatter estimation and correction methods include the scatter kernel superposition (SKS) methods, which approximate x-ray scatter field as a convolution of the scatter sources and scatter propagation kernels to reflect the spatial spreading of scatter x-ray photons. SKS methods are fast to implement but generally suffer from low accuracy due to the difficulties in determining the scatter kernels. Approach. To address such a problem, this work describes a new scatter estimation and correction method by combining the concept of SKS methods and convolutional neural network. Unlike conventional SKS methods which estimate the scatter amplitude and the scatter kernel based on the value of an individual pixel, the proposed method generates the scatter amplitude maps and the scatter width maps from projection images through a neural network, from which the final estimated scatter field is calculated based on a convolution process. Main Results. By incorporating physics in the network design, the proposed method requires fewer trainable parameters compared with another deep learning-based method (Deep Scatter Estimation). Both numerical simulations and physical experiments demonstrate that the proposed SKS-inspired convolutional neural network outperforms the conventional SKS method and other deep learning-based methods in both qualitative and quantitative aspects. Significance. The proposed method can effectively correct the scatter-related artifacts with a SKS-inspired convolutional neural network design.

Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes.

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory and in general relativity. We point out that the general relativity amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational nonlinearities in the wave region, whose proper treatment requires higher order effective field theory loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher-dimensional BHs. Our results are manifestly gauge invariant and coordinate independent, thereby providing a valuable consistency check for the commonly used off-shell methods.