Related papers: Relation between scattering amplitude and Bethe-Sa…
We reexamine the relations between the Bethe-Salpeter (BS) wave function of two particles, the on-shell scattering amplitude, and the effective potential in quantum filed theory. It is emphasized that there is an exact relation between the…
We propose a method to calculate scattering amplitudes using the Bethe-Salpeter wave function inside the interaction range on the lattice. For an exploratory study of this method, we evaluate a scattering length of $I=2$ S-wave two pions by…
We evaluate scattering amplitudes at on-shell and half off-shell for $I=2$ S-wave two-pion system using the Bethe-Salpeter wave function inside the interaction range in the quenched QCD. The scattering length and effective range are…
We observe that the ratio of the on-shell scattering amplitude to the Bethe-Salpeter (BS) wave function outside the interaction range is almost independent of time in our quenched calculation of the $I=2$ two-pion scattering with almost…
The Bethe-Salpeter (BS) amplitude for $\pi N$ scattering is evaluated at the off mass shell points corresponding to the Low Energy Theorems (LET) based on PCAC and current algebra. The results suggest a way of maintaining consistency…
We evaluate $I=2$ two-pion scattering length through the scattering amplitude obtained by the Bethe-Salpeter wave function inside the interaction range. The scattering length is computed with $m_\pi = 0.52-0.86$ GeV in the quenched lattice…
We reemphasize the momentum dependence of the coefficients of the derivative expansion as already explained in our paper [1]. We also discuss how the momentum dependence plagues the time-dependent HALQCD method and what is a necessary…
There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated…
We investigate the on-shell approximation in the context of s-wave scattering for ultracold two-body collisions. Our analysis systematically covers spatial dimensions D=1,2,3 , with the aim of identifying the regimes in which the…
We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles in quantum field theories. To deal with $n$-particles in the center of mass flame coherently,…
We investigate the scattering theory of two particles in a generic $D$-dimensional space. For the s-wave problem, by adopting an on-shell approximation for the $T$-matrix equation, we derive analytical formulas which connect the Fourier…
Bethe-Salpeter equation for the massive particles with spin 1 is considered. The scattering amplitude decomposition of the particles with spin 1 by relativistic tensors is derived. The transformation coefficients from helicity amplitudes to…
For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For…
We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method…
The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter…
When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and…