Scattering Amplitudes Research Articles

Analytic Form of Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD.

We present the analytic form of the planar two-loop five-gluon scattering amplitudes in QCD for a complete set of independent helicity configurations of external gluons. These include the first analytic results for five-point two-loop amplitudes relevant for the computation of next-to-next-to-leading-order QCD corrections at hadron colliders. The results were obtained by reconstructing analytic expressions from numerical evaluations. The complexity of the computation is reduced by exploiting physical and analytical properties of the amplitudes, employing a minimal basis of so-called pentagon functions that have recently been classified.

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion.

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

General Relativity from Scattering Amplitudes.

Weoutline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multigraviton, two-body, on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to nonanalytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.

All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories.

In massless quantum field theories the Landau equations are invariant under graph operations familiar from the theory of electrical circuits. Using a theorem on the Y-Δ reducibility of planar circuits we prove that the set of first-type Landau singularities of an n-particle scattering amplitude in any massless planar theory, at any finite loop order, is a subset of those of a certain n-particle ⌊(n-2)^{2}/4⌋-loop "ziggurat" graph. We determine this singularity locus explicitly for n=6 and find that it corresponds precisely to the vanishing of the symbol letters familiar from the hexagon bootstrap in supersymmetric Yang-Mills (SYM) theory. Further implications for SYM theory are discussed.

Traintracks through Calabi-Yau Manifolds: Scattering Amplitudes beyond Elliptic Polylogarithms.

We describe a family of finite, four-dimensional, L-loop Feynman integrals that involve weight-(L+1) hyperlogarithms integrated over (L-1)-dimensional elliptically fibered varieties we conjecture to be Calabi-Yau manifolds. At three loops, we identify the relevant K3 explicitly and we provide strong evidence that the four-loop integral involves a Calabi-Yau threefold. These integrals are necessary for the representation of amplitudes in many theories-from massless φ^{4} theory to integrable theories including maximally supersymmetric Yang-Mills theory in the planar limit-a fact we demonstrate.

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance.

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n-1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.

Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems

We discuss some examples of equations of the three-body problem with the oscillating asymptotics at large momentum: (i) the fixed-center approximation, (ii) the unitarized equation in the fixed-center approximation, (iii) Skornyakov--Ter-Martirosyan equation, and (iv) equations with operators used in the effective field theory, i.e., which can be expanded in power-series with positive powers of momentum. We show that in the aforementioned three-body problems the situation analogous to the falling down to the center in the two-body problem takes place -- there appears an infinite number of bound states. The energy of these states is not bounded from below. In that sense the situation is close to the falling down to the center in the two-body problem.

Cluster Adjacency Properties of Scattering Amplitudes in N=4 Supersymmetric Yang-Mills Theory.

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.

Multispectral, non-contact diffuse optical tomography of healthy human finger joints.

Rheumatoid arthritis (RA) is an inflammatory joint disease often affecting the hands, which if untreated causes disability. Diffuse optical tomography (DOT) provides information about the underlying functional properties of biological tissue. To detect pathophysiological changes in inflamed RA joints, a good understanding of the baseline values for healthy subjects is first required. Finger joints from healthy subjects were imaged using a non-contact, multispectral, continuous wave DOT system, recovering physiological parameters of oxygen saturation, total haemoglobin, water concentration and scatter amplitude. Reconstructed values across the cohort demonstrated good consistency between finger joints from the same participant, with greater variation seen between subjects.

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders

Scattering amplitudes of partons in QCD contain infrared divergences which can be resummed to all orders in terms of an anomalous dimension. Independently, in the limit of high-energy forward scattering, large logarithms of the energy can be resummed using Balitsky-Fadin-Kuraev-Lipatov theory. We use the latter to analyse the infraredsingular part of amplitudes to all orders in perturbation theory and to next-to-leading-logarithm accuracy in the high-energy limit, resumming the two-Reggeon contribution. Remarkably, we find a closed form for the infrared-singular part, predicting the Regge limit of the soft anomalous dimension to any loop order.

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models.

We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

Clinical Feasibility of Suppression Head Impulse Test in Vestibulopathy Patients

Background and Objectives The suppression head impulse (SHIMP) test has emerged as one of the new vestibular function tests. The SHIMP test is an analysis of anti-compensatory saccadic movements in gazing moving targets as the head moves. In this study, we investigated the accuracy and sensitivity of the test. Subjects and Method We analyzed the results of SHIMP test (gain, amplitude, and latency) in 24 cases, which included normal, vestibular neuritis, benign paroxysmal positional vertigo (BPPV), Meniere’s disease, bilateral vestibular function loss, temporal bone fracture, tuberculosis meningitis and acoustic schwannoma patients. We also carried out a physical exam, audiologic study, video electronystagmography (vENG) and a conventional video head impulse test to evaluate the feasibility of SHIMP test in cases of vesitibulopathy. Results In patients with vestibulopathy, the analysis of SHIMP test indicated high sensitivity and accuracy, which were supported by accompanying audio-vestibular studies. Patients suspected with BPPV, vestibular neuronitis and Meniere’s disease showed low vestibulo ocular reflex (VOR) gain and delayed anticompensatory saccade with smaller and more scattered amplitudes than the control. Patients with bilateral vestibular function loss, temporal bone fracture, tuberculosis meningitis, and acoustic schwannoma showed delayed latency, and small amplitude or few anticompensatory saccades. Finally, changes in the SHIMP test values might be a hint that patients had recovered from vestibular neuronitis and tuberculosis meningitis. Conclusion We found the feasibility of SHIMP test in detecting the pathologic condition of VOR in vestibulopathy patients. We argue that the usefulness of SHIMP test might be extended to evaluating the effectiveness of rehabilitation. Key words: Head impulse test ㆍ Saccades ㆍ Vestibular function tests ㆍ Vestibulo-ocular reflex ㆍ Vestibulopathy

Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers-Heisenberg-Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.

String-theoretic deformation of the Parke-Taylor factor

Scattering amplitudes in a range of quantum field theories can be computed using the Cachazo-He-Yuan (CHY) formalism. In theories with colour ordering, the key ingredient is the so-called Parke-Taylor factor. In this note we give a fully $\text{SL}(2,\mathbb{C})$-covariant definition and study the properties of a new integrand called the string Parke-Taylor factor. It has an $\alpha'$ expansion whose leading coefficient is the field-theoretic Parke-Taylor factor. Its main application is that it leads to a CHY formulation of open string tree-level amplitudes. In fact, the definition of the string Parke-Taylor factor was motivated by trying to extend the compact formula for the first $\alpha'$ correction found by He and Zhang, while the main ingredient in its definition is a determinant of a matrix introduced in the context of string theory by Stieberger and Taylor.

Cluster functions and scattering amplitudes for six and seven points

Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. We explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.

Relativistic Model of Hamiltonian Renormalization for Bound States and Scattering Amplitudes

We test the renormalization group procedure for effective particles on a model of fermion–scalar interaction based on the Yukawa theory. The model is obtained by truncating the Yukawa theory to just two Fock sectors in the Dirac front form of Hamiltonian dynamics, a fermion, and a fermion and a boson, for the purpose of simple analytic calculation that exhibits steps of the procedure.

A point-based scattering model for the incoherent component of the scattered field.

A numerical model for calculation of the incoherent component of the field scattered from random rough surfaces is described. This model is based on the point scattering approach, where the mean scatterer amplitudes are calculated from deterministic models. These amplitudes are then scaled by a complex circular Gaussian random variable to simulate scattering from a surface with minimal coherence length. The resulting simulated fields are shown to agree with theory for the mean field, mean square field, statistical distribution, and the spatial coherence length.

Effects of tissue mechanical and acoustic anisotropies on the performance of a cross-correlation-based ultrasound strain imaging method

The anisotropic mechanical properties (mechanical anisotropy) and view-dependent ultrasonic backscattering (acoustic anisotropy) of striated muscle due to the underlying myofiber arrangement have been well documented, but whether they impact on ultrasound strain imaging (USI) techniques remains unclear. The aim of this study was therefore to investigate the performance of a cross-correlation-based two-dimensional (2D) USI method in anisotropic media under controlled quasi-static compression in silico and in vitro. First, synthetic pre- and post-deformed 2D radiofrequency images of anisotropic phantoms were simulated in two scenarios to examine the individual effect of the mechanical and acoustic anisotropies on strain estimation. In the first scenario, the phantom was defined to be transversely isotropic with the scatterer amplitudes following a zero-mean Gaussian distribution, while in the second scenario, the phantom was defined to be mechanically isotropic with Gaussian distributed scatterer amplitudes correlated along the principal directions of pre-defined fibers. These two anisotropies were then jointly incorporated into the ultrasound image simulation model with additional depth-dependent attenuation. Three imaging planes—the fiber plane with the fiber direction perpendicular to the ultrasound beam (TISperp_fb), the fiber plane with the fiber direction parallel to the beam (TISpara), and the transverse fiber plane (TISperp_cfb)—were studied. The absolute relative error (ARE) of the lateral strain estimates in TISperp_fb (20.99 ± 15.65%) was much higher than that in TISperp_cfb (4.14 ± 3.17%). The ARE in TISpara was unavailable owing to the large spatial extent of false peaks. The effect of tissue anisotropy on the performance of the 2D USI was further confirmed in an in vitro porcine skeletal muscle phantom. The best in-plane strain quality was again shown in TISperp_cfb (elastographic signal-to-noise ratio, or SNRe: >25 dB), whereas the most unreliable strain estimates were found as expected in TISpara (SNRe: <10 dB). The strain filter explained the effect of the mechanical anisotropy and required the underlying strain to be within an optimal range for estimation. Sonographic SNR (SNRs) was found to be altered by the acoustic anisotropy and was much lower in TISpara (~10 dB) than in TISperp_fb (~50 dB) in vitro, which affected the accuracy of the strain estimation. Speckle size showed no evident impact on strain estimation but requires further examination.

General Unquenching Properties of Two-meson Scattering and Production Amplitudes

General Unquenching Properties of Two-meson Scattering and Production Amplitudes