Search results for "scattering amplitude"
showing 10 items of 170 documents
Form factors of the isovector scalar current and the ηπ scattering phase shifts
2015
33 pages.- 14 figures.- v2: Some clarifications and corrections of typos
Compton scattering by a pion and off-shell effects
1994
We consider Compton scattering by a pion in the framework of chiral perturbation theory. We investigate off--shell effects in the s-- and u--channel pole diagrams. For that purpose we perform a field transformation which, in comparison with the standard Gasser and Leutwyler Lagrangian, generates additional terms at order $p^4$ proportional to the lowest--order equation of motion. As a result of the equivalence theorem the two Lagrangians predict the same Compton scattering S--matrix even though they generate different off--shell form factors. We conclude that off--shell effects are not only model--dependent but also representation--dependent.
Two-photon exchange in muon-nuclear scattering
1980
We obtain a low-momentum-transfer theorem for positive- and negative-muon--nuclear scattering, in terms of the charge and the electric and magnetic polarizabilities. The result opens the way to use muons as a tool to probe the electromagnetic structure of composite objects. Predictions of this two-photon effect for the asymmetry in the angular distribution of negative and positive muons scattered by /sup 4/He are given.
Scattering Matrix and Observables in Scattering and Decays
2013
As an interlude in the analysis of canonical field quantization, this section describes important concepts of scattering theory for Lorentz covariant quantum field theories that will be needed for the calculation of observables such as scattering cross sections and decay probabilities.
Gravitational scattering on a global monopole
1991
The scattering amplitude and the total scattering cross section of massless particles propagating in the gravitational field of a global monopole are derived. We find that the physical signature of such defects is a ringlike angular region where the scattering amplitude is very large. The size of this ringlike region is determined by the ratio of the global monopole mass to the Planck mass and its appearance stems from the fact that the metric of the global monopole is not asymptotically flat but rather displays the characteristic spherical angle defect. The situation is therefore very much reminiscent of scattering in the gravitational field of the cosmic string.
To d , or not to d : recent developments and comparisons of regularization schemes
2017
We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.
Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD
2015
Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.
Matter Dependence of the Four-Loop Cusp Anomalous Dimension
2019
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals w…
Massless positivity in graviton exchange
2021
We formulate Positivity Bounds for scattering amplitudes including exchange of massless particles. We generalize the standard construction through dispersion relations to include the presence of a branch cut along the real axis in the complex plane for the Maldestam variable $s$. In general, validity of these bounds require the cancellation of divergences in the forward limit of the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is possible in the case of gravitons if one assumes a Regge behavior of the amplitude at high energies below the Planck scale, as previously suggested in the literature, and that the concrete UV behaviour of the amplitude is uniquely determined…
Space-like (vs. time-like) collinear limits in QCD: Is factorization violated?
2012
We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum a…