Scattering amplitude

In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. The plane wave is described by the wavefunction : \psi(\mathbf{r}) = e^{ikz} + f(\theta)\frac{e^{ikr}}{r} ;, where \mathbf{r}\equiv(x,y,z) is the position vector; r\equiv|\mathbf{r}|; e^{ikz} is the incoming plane wave with the wavenumber k along the z axis; e^{ikr}/r is the outgoing spherical wave; θ is the scattering angle; and f(\theta) is the scattering amplitude. The dimension of the scattering amplitude is length. The scattering amplitude is a probability amplitude; the differential cross-section as a function of scattering angle is given as its modulus squared, : \frac{d\sigma}{d\Omega} = |f(\theta)|^2 ;. X-rays The scattering length for X-rays is th

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Positive moments for scattering amplitudes

Riccardo Rattazzi, Marc Riembau Saperas, Francesco Riva

We find the complete set of conditions satisfied by the forward 2 -> 2 scattering amplitude in unitary and causal theories. These are based on an infinite set of energy dependent quantities (the arcs) which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound effective field theories (EFTs), at any finite order in the energy expansion. At tree level arcs are in a one to one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both energy and couplings, where the latter has to satisfy two-sided bounds. We also extend our results to the case of small but finite t. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than E-6 cannot be UV completed.

AMER PHYSICAL SOC2021

Scattering amplitude of a single fracture under uniaxial stress

Thomas Emmanuel Blum

Remotely sensing the properties of fractures has applications ranging from exploration geophysics to hazard monitoring. Newly developed capabilities to measure the in-plane component of dense laser-based ultrasound wave fields allow us to test the applicability of a linear slip model to describe fracture properties. In particular, we estimate the diameter, and the normal and tangential compliance of a fracture from the measured scattering amplitudes of P and S waves in the laboratory. Finally, we show that the normal compliance decreases linearly with increasing uniaxial static stress in the plane of the fracture, but that our measurements of the SV scattered field do not show significant changes in the tangential compliance. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Wiley-Blackwell2014

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

Mario Herrero Valea, Inar Timiryasov, Anna Tokareva

We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV completion, we derive constraints on the Wilson coefficients of the first higher order derivative operators. We show that the values allowed by the constraints are consistent with the phenomenological applications of the Higgs-Dilaton model.

IOP PUBLISHING LTD2019

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