Optical Theorem Research Articles

Understanding the optical theorem of scattering: Scattering surface area against scattering cross-section, an example with ellipsoidal scattering

In this paper, we propose using the scattering surface area rather than the scattering cross-section to characterize the scattering behavior of ellipsoidal rigid bodies. We examined the scattering behavior of ellipsoidal rigid bodies, focusing on the relationship between their surface area and total scattering cross-section. Building on the foundational work of Carson Flammer, we utilize the spheroidal coordinate system to derive solutions for both prolate and oblate spheroids. Our analysis reveals that under the long-wavelength approximation, the total scattering cross-section is equivalent to the surface area of the ellipsoid, a relationship that holds true for both small and moderate eccentricities. This finding extends the established optical theorem, previously validated for spherical bodies, to more complex geometries.

Celestial optical theorem

We derive the celestial optical theorem from the S-matrix unitarity, which provides nonperturbative bootstrap equations of conformal partial wave (CPW) coefficients. This theorem implies that the imaginary parts of CPW coefficients exhibit a positivity property. By making certain analyticity assumptions and using the celestial optical theorem, we derive nonperturbative constraints concerning the analytic structure of CPW coefficients. We discover that the CPW coefficients of four massless particles must and can only have simple poles located at specific positions. The CPW coefficients involving massive particles exhibit double-trace poles, indicating the existence of double-trace operators in nonperturbative celestial conformal field theory. It is worth noting that, in contrast to AdS/CFT, the conformal dimensions of double-trace operators do not have anomalous dimensions. Published by the American Physical Society 2025

QUANTUM CORRECTION TO THE SYNCHROTRON RADIATION

We calculate the quantum corrections to synchrotron radiation by method developed by Schwinger and Tsai. The traditional calculation method working with the particle wave functions is here replaced by the mass operator approach avoiding the particle final states and the integration over photon angular distribution. The algorithm of the calculation of the quantum corrections to the synchrotron radiation consists in the evaluation of the forward Compton scattering process in the external magnetic field and then in application of the optical theorem to obtain the angular and frequency distribution.

Scattering, absorption and emission of highly excited strings

We study tree-level scattering processes of arbitrary string states using the DDF formalism and suitable coherent vertex operators. We obtain new exact compact formulae for heavy-heavy-light-light scattering amplitudes in open or closed bosonic string theories, and derive explicit exact expressions for the absorption cross-sections, and corresponding emission rates, of highly excited string states using the optical theorem and time reversal symmetry. We show that these expressions are independent of the microscopic structure of the excited string states without averaging. For the absorption of massless modes in open string theory, in particular, we find a constant, frequency-independent cross-section. In contrast, the corresponding cross-section for the absorption of massless modes by excited closed strings depends linearly on the frequency, implying a non-trivial grey-body factor. In both cases, at energies below the scale set by the mass of the highly excited strings, we find emission rates with a Boltzmann factor at Hagedorn temperature.

Cosmological cutting rules for Bogoliubov initial states

The field theoretic wavefunction in cosmological spacetimes has received much attention as a fundamental object underlying the generation of primordial perturbations in our universe. Assuming an initial Bunch-Davies state, unitary time evolution implies an infinite set of cutting rules for the wavefunction to all orders in perturbation theory, collectively known as the cosmological optical theorem. In this work, we generalise these results to the case of Bogoliubov initial states, accounting for both parity-even and parity-odd interactions. We confirm our findings in a few explicit examples, assuming IR-finite interactions. In these examples, we preserve scale invariance by adiabatically turning on interactions in the infinite past rather than imposing a Bogoliubov state at some finite initial time. Finally, we give a prescription for computing Bogoliubov wavefunction coefficients from the corresponding Bunch-Davies coefficients for both nn-point contact and four-point exchange diagrams.

Barr-Zee diagrams at a high-energy muon collider

The sensitivity of electron EDM experiments has been increasing at a rapid pace, and could yield indications of new physics in the coming decade. An intriguing possibility is that an EDM signal could be generated by new, electroweak-charged particles at the TeV scale that couple to the Higgs and contribute to the electron EDM at two-loop order via Barr-Zee diagrams. A high-energy muon collider could decisively search for new physics at this scale. In this work, we explore this complementarity between colliders and EDM experiments, and note that Barr-Zee diagrams from the aforementioned particles are closely related to vector-boson scattering processes at a muon collider. These loop corrections lead to kinematic features in the differential cross sections of these processes, dictated by the optical theorem. We demonstrate this connection in the context of the singlet-doublet and doublet-triplet extensions to the SM, explore the detectability of these features at a muon collider experiment, and discuss how these measurements can be used to ascertain the underlying model parameters.

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.

There and Back Again: Mapping and Factorizing Cosmological Observables.

Cosmological correlators encode invaluable information about the wave function of the primordial Universe. In this Letter we present a duality between correlators and wave function coefficients that is valid to all orders in the loop expansion and manifests itself as a Z_{4} symmetry. To demonstrate the power of the duality, we derive a correlator-to-correlator factorization formula for the parity-odd part of cosmological correlators that relates n-point observables to lower-point ones via a series of diagrammatic cuts. These relations serve as the first example of physically testable cutting rules as they involve observables defined for arbitrary physical kinematics. We further show how the duality allows us to translate the cosmological optical theorem for wave function coefficients into statements about cosmological correlators.

Acoustic scattering and "failure" of the optical theorem.

For plane wave scattering by an obstacle, the optical theorem relates the scattering cross section to the far-field scattered field in the forward direction. This simple and useful result fails to hold when the incident field is not a plane wave. "Failures" of this kind are explored. For scattering by a sphere, an explicit formula for the scattering cross section is obtained, applicable to arbitrary incident fields.

Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions

We present the analytic total cross section of top quark pair production in electron-positron annihilation at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD). By utilizing the optical theorem, the NNLO corrections are related to the imaginary parts of three-loop self-energy Feynman diagrams, of which the master integrals are calculated with canonical differential equations. The analytic results for the NNLO corrections are expressed in terms of multiple polylogarithms as well as elliptic functions. We discuss the asymptotic expansions near the threshold and in the high energy limit in detail. Numerical results are provided for the total cross section of top quark pair production at future lepton colliders.

Spectral Domain Optical Theorem and Radiative Transfer in Random Media With Large-Scale Fluctuations

Spectral Domain Optical Theorem and Radiative Transfer in Random Media With Large-Scale Fluctuations

Signatures of top versus bottom illuminations and their predicted implications for infrared transmission microspectroscopy.

Since both top and bottom illuminations are widely used in infrared transmission measurements, in this paper, we study the effects of different illuminations on the signatures in infrared microspectroscopy. By simulating a series of dielectric samples, we show that their extinction efficiency, , remains unchanged when the direction of the incident plane wave is reversed, even though the field distributions both inside and outside of the sample may be dramatically different. We find features in that are correlated with whispering gallery modes for one beam direction and correspond to completely different field distributions for the opposite beam direction. In addition, by linking the optical theorem and the reciprocity relation of far-field scattered field, we rigorously prove the invariance of for arbitrary dielectric targets under opposite plane-wave illuminations. Furthermore, we show the difference in the apparent absorbance spectrum for opposite beam directions when considering numerical apertures.

Optical theorem in the 3-D scattering from a locally perturbed lossless or lossy thin dielectric plate: silver disk-sealed hole analysis.

This paper is aimed at devising a new optical theorem formulation for the 3-D plane-wave scattering from an infinite resistive plane and, more generally, a thin dielectric plate with a finite-size inhomogeneity shaped as a hollow or sealed hole. This formulation is further modified to cover the case of the plane guided wave scattering from the same inhomogeneity. For the lossless plane, the diffracted field combines a classical outgoing spherical wave, satisfying the Silver-Muller radiation condition, with an outgoing cylindrical guided wave supported by the plane; the power absorbed in the lossy filling is finite. When a lossy plane is involved, a complication appears: the total absorbed power is infinite. However, a change in the inhomogeneity characteristics perturbs the absorbed power density, thus suggesting the perturbative absorption analysis. After developing the analytical procedure for the resistive plane case and the corresponding generalization to the thin dielectric plate case, we illustrate the significance of the new optical theorem by the numerical analysis of the visible-light scattering from a dielectric plate with a circular nanosize hole sealed with a silver disk. Our analysis uses the in-house code having mathematically guaranteed convergence; it reveals the scattering and absorption resonances on the plasmon modes of the silver nanodisk. The derived optical theorem allows us to see that, in the resonances, the power carried by the guided waves can be comparable to the power scattered into the free space.

Entanglement in flavored scalar scattering

We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.

The in-out formalism for in-in correlators

Cosmological correlators, the natural observables of the primordial universe, have been extensively studied in the past two decades using the in-in formalism pioneered by Schwinger and Keldysh for the study of dissipative open systems. Ironically, most applications in cosmology have focused on non-dissipative closed systems. We show that, for non-dissipative systems, correlators can be equivalently computed using the in-out formalism with the familiar Feynman rules. In particular, the myriad of in-in propagators is reduced to a single (Feynman) time-ordered propagator and no sum over the labelling of vertices is required. In de Sitter spacetime, this requires extending the expanding Poincaré patch with a contracting patch, which prepares the bra from the future. Our results are valid for fields of any mass and spin but assuming the absence of infrared divergences.We present three applications of the in-out formalism: a representation of correlators in terms of a sum over residues of Feynman propagators in the energy-momentum domain; an algebraic recursion relation that computes Minkowski correlators in terms of lower order ones; and the derivation of cutting rules from Veltman’s largest time equation, which we explicitly develop and exemplify for two-vertex diagrams to all loop orders.The in-out formalism leads to a natural definition of a de Sitter scattering matrix, which we discuss in simple examples. Remarkably, we show that our scattering matrix satisfies the standard optical theorem and the positivity that follows from it in the forward limit.

Perturbative unitarity and the wavefunction of the Universe

Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: i)i) the role of the i\epsiloniϵ-prescription and its compatibility with the requirement of unitarity; ii)ii) the origin of the different ``cutting rules’’; iii)iii) the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the i\epsiloniϵ-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name . The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones.

Undecay

Unstable particles decay sooner or later, so they are not described by asymptotic one-particle states and they should not be included as independent states in unitarity relations such as the optical theorem. The same applies to any countable collection of unstable particles. We show that the behaviour of unparticle stuff, that is, a continuous collection of particles with different masses and common decay channels, is pretty different: it has a non-vanishing probability of surviving for ever and the corresponding asymptotic states must be taken into account to comply with unitarity. We also discuss compressed spectra and the transition from the discrete to the continuous case.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Scattering of ultrashort electron wave packets: optical theorem, differential phase contrast and angular asymmetries

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1 fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams.

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