Born Amplitude Research Articles

Fermion scattering on topological solitons in theCPN−1model

The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic wave functions can be expressed in terms of the confluent Heun functions. The question of the existence of bound states for the fermion-soliton system is then investigated. General formulae describing fermion scattering are obtained, and a symmetry property for the partial phase shifts is derived. The amplitudes and cross-sections of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and the symmetry properties and asymptotic forms of the Born amplitudes are investigated. The dependences of the first few partial phase shifts on the fermion momentum are obtained by numerical methods, and some of their properties are investigated and discussed.

Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD

We present the first full analytic evaluation of the scattering amplitude for the process qq → Qoverline{Q} up-to two loops in Quantum Chromodynamics, for a massless (q) and a massive (Q) quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant.

On the inverse problem of reflection Green’s function seismograms over stratified acoustic media: Estimation of background models

A theory is presented for estimating the background velocity and density of an acoustic stratified medium by iterative least-squares waveform inversion in the frequency-horizontal slowness domain of low-frequency precritical reflection incidence seismograms of time length [Formula: see text]. The initial model is constant. The prerequisites for the method are that the reflection seismograms should be Green’s function seismograms and that the fundamental frequency component [Formula: see text] is present. Then, the gradients of the objective function provide the low-wavenumber trend of the medium. A matrix formulation for the model update is expressed mathematically by the classic seismogram residual, Jacobian, gradient, and Hessian in the Levenberg-Marquardt approximation. The first iteration, which is equal to a constant-parameter migration inversion (CPMI), is thoroughly analyzed, and expressions for band-limited gradients and block Hessians are found. For primary precritical reflection incidence seismograms of infinite bandwidth, it is shown theoretically that the partial gradients in the CPMI model become a reflection strength-weighted sum of shifted discrete sign functions, typical of step or staircase functions, which provide interface locations in Born depth and amplitudes that can be mapped to velocity and density information. For frequency-band-limited primary reflection seismograms, the partial gradients become a reflection strength-weighted sum of wavenumber-band-limited discrete sign functions. When the fundamental frequency component in the seismograms is present, the band-limited discrete sign functions are oscillatory but keep the information of the step function characteristic of the partial gradient. When the fundamental frequency component in the seismograms is absent, the band-limited discrete sign functions keep information of where the steps are located but lose the information of the amplitudes of the steps. The Hessian elements are nonstandard with the Hessian modeled over a broader frequency range than the frequencies of the observed low-frequency seismogram to avoid it becoming close to singular. The main mathematical findings are illustrated by a simple model and seismograms, for which the background models are found after two iterations. For the sake of completeness, the background models are classically used as initial models in a Levenberg-Marquardt least-squares inversion scheme to estimate the layer velocities and densities from broadband seismograms.

Cross section of the process e+e−→pp¯ in the vicinity of charmonium ψ(3770) including three-gluon and D -meson loop contributions

The total cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}p\overline{p}$ is calculated within the energy range close to the mass of $\ensuremath{\psi}(3770)$ charmonium state. It was shown that the main contribution to this cross section comes from three gluon mechanism which is also responsible of the large phase with respect to the Born amplitude. This phase provides the characteristic dip behavior of the cross section in contrast to the usual Breit-Wigner peak shape. Okubo--Zweig--Iizuka-allowed mechanism with $D$-mesons in the intermediate state was also estimated and gives relatively small contribution to the cross section and to the phase.

Standard model O(α) renormalization of gA and its impact on new physics searches

We present an $\mathcal{O}(\alpha)$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\beta$ decays. We find that \textit{a priori} contributions arise from the photonic vertex correction and $\gamma W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\gamma W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find $\Delta_R^A = 0.02532(22)$ and $\Delta_R^V = 0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in $\Delta_R^A-\Delta_R^V=0.60(5) \times 10^{-3}$, which allows us to extract $g_A^0$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\beta$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\alpha)$result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|V_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix, resolving a long-standing tension and leading to increased precision.

Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation

We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point by point in the loop integrand. The remainders of the subtraction are integrable in four dimensions and can be computed in the future with numerical integration. The counterterms capture the divergences of the amplitudes and factorize in terms of the Born amplitude and the finite remainder of the one-loop amplitude. They consist of simple one- and two-loop integrals with at most three external momenta and can be integrated analytically in a simple manner with established methods. We uncover novel aspects of fully local IR factorization, where vertex and self energy subdiagrams must be modified by new symmetrizations over loop momenta, in order to expose their tree-like tensor structures and hence factorization of IR singularities prior to loop integration. This work is a first step towards isolating locally the hard contributions of generic gauge theory amplitudes and rendering them integrable in exactly four dimensions with numerical methods.

ZH production in gluon fusion: two-loop amplitudes with full top quark mass dependence

We present results for the two-loop helicity amplitudes entering the NLO QCD corrections to the production of a Higgs boson in association with a Z -boson in gluon fusion. The two-loop integrals, involving massive top quarks, are calculated numerically. Results for the interference of the finite part of the two-loop amplitudes with the Born amplitude are shown as a function of the two kinematic invariants on which the amplitudes depend.

There are two solutions to the equations of Feynman’s Quantum Electrodynamics (QED): the newly discovered solution is free of quantum weirdness

No one previously noticed there is a second solution to the equations of Richard Feynman’s Quantum Electrodynamics (QED). It makes identical predictions in the lab. The new solution (Reverse-QED) is closer to nature: it is free of quantum weirdness. For example, it eliminates Schrödinger’s cat. This article is the first time the equations of R-QED have been published. The R-QED amplitude is the negative of Feynman’s amplitude. Because of the Born rule, both amplitude and negative amplitude, when squared, produce the same probability to be tested against empirical data. If you were to measure the distance from Los Angeles to New York City with R-QED’s accuracy, it would be exact to the breadth of a human hair. If reality corresponds to the newly discovered R-QED equations, but scientists use the old QED equations, the result would be predictions for the lab that are precisely accurate, but scientists would be unable to construct a coherent picture of the quantum world. R-QED is based on a different picture of how the quantum world is organized. Experiments, including a neutron interferometer experiment we review, show that particles follow waves backward. R-QED integrates in the same direction that the waves travel.

On-shell constructibility of Born amplitudes in spontaneously broken gauge theories

We perform a comprehensive study of on-shell recursion relations for Born amplitudes in spontaneously broken gauge theories and identify the minimal shifts required to construct amplitudes with a given particle content and spin quantum numbers. We show that two-line or three-line shifts are sufficient to construct all amplitudes with five or more particles, apart from amplitudes involving longitudinal vector bosons or scalars, which may require at most five-line shifts. As an application, we revisit selection rules for multi-boson amplitudes using on-shell recursion and little-group transformations.

Elastic Scattering of Electrons by Helium Atoms in Born Approximation

Elastic scattering phenomena arising in electron-helium scattering are dominant processes. The determination of accurate elastic differential cross sections for electron-helium scattering has a considerable importance. An accurate calculation of the plane-wave first Born exchange amplitude of electrons elastic scattering by helium atoms is reported. The direct and exchange amplitudes are calculated analytically from the Hartree-Fock orbital wave functions by using a variational method. The forms of these wave functions are very suitable for analytical calculations and powerful to generalize to more complex atomic systems. The interaction potential is modelled by the static Coulomb interaction between the incident electron and the atomic system. The differential cross sections are calculated at intermediate energies taking into account the exchange effects. We have established in the high energies region, by neglecting the exchange effects, the analytical expressions of the total and momentum transport cross sections suitable for the calculation of the plasma transport properties. A very compact form of the Born amplitude has been proposed as a finite series of Gaussian functions, which represents a major tool in the calculations of differential cross sections of two-electron atomic systems. Numerical results are used to analyze the contribution of the exchange amplitude to the differential cross sections at intermediate and high energies. The differential cross sections are calculated for the energy range 30-400 eV. We find good agreement in high energy domain scattering with experimental results and other sophisticated calculations without using any adjustable parameter.

Radiative corrections to neutron and nuclear beta decays revisited

The universal radiative corrections common to neutron and super-allowed nuclear beta decays (also known as ``inner'' corrections) are revisited in light of a recent dispersion relation study that found $+2.467(22)\%$, i.e.~about $2.4\sigma$ larger than the previous evaluation. For comparison, we consider several alternative computational methods. All employ an updated perturbative QCD four-loop Bjorken sum rule (BjSR) defined QCD coupling supplemented with a nucleon form factor based Born amplitude to estimate axial-vector induced hadronic contributions. In addition, we now include hadronic contributions from low $Q^2$ loop effects based on duality considerations and vector meson resonance interpolators. Our primary result, $2.426(32)\%$ corresponds to an average of a Light Front Holomorphic QCD approach and a three resonance interpolator fit. It reduces the dispersion relation discrepancy to approximately $1.1\sigma$ and thereby provides a consistency check. Consequences of our new radiative correction estimate, along with that of the dispersion relation result, for CKM unitarity are discussed. The neutron lifetime-$g_A$ connection is updated and shown to suggest a shorter neutron lifetime $< 879$ s. We also find an improved bound on exotic, non-Standard Model, neutron decays or oscillations of the type conjectured as solutions to the neutron lifetime problem, $\text{BR}(n\to \text{exotics}) < 0.16 \%$.

Approximate Formula for the Total Cross Section for a Moderately Small Eikonal Function

We study the eikonal approximation of the total cross section for the scattering of two unpolarized particles and obtain an approximate formula in the case where the eikonal function χ(b) is moderately small, |χ(b)| ≲ 0.1. We show that the total cross section is given by a series of improper integrals of the Born amplitude AB. The advantage of this representation compared with standard eikonal formulas is that these integrals contain no rapidly oscillating Bessel functions. We prove two theorems that allow relating the large-b asymptotic behavior of χ(b) to analytic properties of the Born amplitude and give several examples of applying these theorems. To check the effectiveness of the main formula, we use it to calculate the total cross section numerically for a selection of specific expressions for AB, choosing only Born amplitudes that result in moderately small eikonal functions and lead to the correct asymptotic behavior of χ(b). The numerical calculations show that if only the first three nonzero terms in it are taken into account, this formula approximates the total cross section with a relative error of O(10−5).

Double-logarithms in mathcal{N} = 8 supergravity: impact parameter description & mapping to 1-rooted ribbon graphs

The set of double-logarithmic (DL) contributions (α t ln2s)n to the 4-graviton amplitude in mathcal{N} = 8 supergravity (SUGRA), with α being the gravitational coupling and (s, t) the Mandelstam invariants, is studied in impact parameter (ρ) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as s increases, which is not present in mathcal{N} < 4 SUGRA theories, there exists a critical line ρc(s) above which the Born amplitude prevails. The short distance region ρ < ρc(s) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small ρ characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in mathcal{N} = 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.

Features of forward πN scattering from a Reggeized model

Charge exchange process ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ and elastic scatterings ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ are investigated within the Regge framework where the relativistic Born amplitude is Reggeized for the $t$-channel meson exchange. The charge exchange cross section is featured by single $\ensuremath{\rho}$ exchange. Additional corrections by Regge cuts, $\ensuremath{\rho}\text{\ensuremath{-}}{f}_{2}$ and $\ensuremath{\rho}$-Pomeron, agree with differential cross sections, and a new trajectory for the ${\ensuremath{\rho}}^{\ensuremath{'}}(1450)$ exchange is attempted to reproduce polarization data. For the description of elastic scattering data up to pion momentum ${P}_{\mathrm{Lab}}\ensuremath{\approx}250$ GeV/c, Pomeron exchange of the Donnachie-Landshoff type is newly constructed and applied in this work. Elastic cross section data are well reproduced with the dominance of ${f}_{2}$ and Pomeron exchanges in intermediate and high energies. Analysis of nucleon resonances is presented to test the validity of the present Regge framework below $W\ensuremath{\le}2$ GeV.

Photoproduction of γp→K+Λ*(1520) and decay of Λ*(1520)→K−p in the Reggeized framework

Photoproduction of the $\Lambda^*(1520)$ resonance of spin-parity ${3\over2}^-$ off the proton target is investigated within the Regge framework where the $t$-channel reggeization is applied for the $K(494)+K^*(892)+K_2^*(1430)$ exchanges in the Born amplitude. The present model is based on the two basic ingredients; the one is the minimal gauge prescription for the convergence of the reaction and the other is the role of the $K_2^*$ crucial to be consistent with high energy data. The cross sections for the total, differential and photon polarization asymmetry are reproduced without fit parameters and compared with existing data. The LAMP2 and LEPS measurements of the angular distribution of the $K^-$ in the $\Lambda^*(1520)\to K^-p$ decay are investigated and found to be dominated by the decay of $\Lambda^*$ with helicity $\pm3/2$ based on the analysis of the density matrix elements related. Detailed discussion on the density matrix elements is given to clarify the analysis of the observable. The reaction mechanism is featured by the dominance of the contact term with the $K$ and $K_2^*$ exchanges following in the low energy region. The $K^*$ exchange appears in minor role. At high energies beyond $E_\gamma\approx 5$ GeV the role of $K_2^*$ exchange leads over other exchanges in the reaction process.

Investigating convergence of the reaction γp → π±Δ and tensor meson a2 exchange at high energy

A Regge approach to the reaction processes γp→π−Δ++ and γp→π+Δ0 is presented for the description of existing data up to Eγ=16 GeV. The model consists of the t-channel π(139)+ρ(775)+a2(1320) exchanges which are reggeized from the relevant Born amplitude. Discussion is given on the minimal gauge prescription for the π exchange to render convergent the divergence of the u-channel Δ-pole in the former process. A new Lagrangian is constructed for the a2NΔ coupling in this work and applied to the process for the first time with the coupling constant deduced from the duality plus vector dominance. It is shown that, while the π exchange dominates over the process, the role of the a2 exchange is crucial rather than the ρ in reproducing the cross sections for total, differential, and photon polarization asymmetry to agree with data at high energy.

Planar radiation zeros in five-parton QCD amplitudes

We demonstrate the existence of `planar', or `type-II', radiation zeros in 5-parton QCD scattering processes. That is, the Born amplitudes are shown to completely vanish for particular kinematic configurations, when all the particle 3-momenta lie in a plane. This result is shown to follow particularly simply from the known BCJ relations between the colour-ordered tree amplitudes, and the MHV formalism is used to express the additional kinematic constraint as a relatively simple expression in terms of only rapidity differences between the final-state partons. In addition, we find that zeros exist for non-planar configurations of the final-state partons, but for which the normal `type-I' conditions on the particle four-momenta do not generally apply. We present numerical results and comment on the possibility of observing planar radiation zeros in hadronic collisions, via central exclusive three-jet production.

Soft evolution of multi-jet final states

We present a new framework for computing resummed and matched distributions in processes with many hard QCD jets. The intricate color structure of soft gluon emission at large angles renders resummed calculations highly non-trivial in this case. We automate all ingredients necessary for the color evolution of the soft function at next-to-leading-logarithmic accuracy, namely the selection of the color bases and the projections of color operators and Born amplitudes onto those bases. Explicit results for all QCD processes with up to $2\to 5$ partons are given. We also devise a new tree-level matching scheme for resummed calculations which exploits a quasi-local subtraction based on the Catani-Seymour dipole formalism. We implement both resummation and matching in the Sherpa event generator. As a proof of concept, we compute the resummed and matched transverse-thrust distribution for hadronic collisions.

The second Born approximation in laser-assisted (e, 2e) collisions in hydrogen

The second Born approximation has been used to calculate the triple differential cross sections for electron-impact ionization of atomic hydrogen in the presence of a linearly polarized laser field. The interaction of the laser field with the unbound electrons is treated in a nonperturbative way by the use of Volkov waves. We have used the wave function proposed by Joachain et al (1988 Phys. Rev. Lett. 61 165) for the ejected electron moving in the combined field of the residual photon and of the laser. We present a more precise treatment of the small-energy region of the incident electron by performing the calculation of the second Born term in this energy region. Detailed calculations of the scattering amplitudes are evaluated by using the Sturmian basis expansion. The second-order Born amplitude is capable of giving a reasonable correction to the first Born approximation model in studying laser-assisted (e, 2e) problems in the low energy range.

Second-order Born effects in the coplanar to perpendicular plane single ionization of Xe (5p)

Differential cross section results for the coplanar to perpendicular plane ionization of xenon atoms at incident electron energies of 40 and 20 eV above ionization potential are reported. The cross sections have been calculated in the modified distorted wave Born approximation (DWBA) formalism including the second-order Born amplitude. Our present attempt verifies the role of second-order processes in the ionization of xenon atoms at low and intermediate energy ranges. We compare the (e, 2e) triple differential cross section results of our calculation with the very recent measurements of Nixon and Murray (2012 Phys. Rev. A 85 022716) and relativistic DWBA-G results of Illarionov and Stauffer (2012 J. Phys. B: At. Mol. Opt. Phys. 45 225202). Overall agreement with measurements has been improved by inclusion of a second-order term in the description of the collision process.