Related papers: Khuri-Treiman equations for $\pi\pi$ scattering
Using the analysis of ChPT to two loops, we perform an error analysis of the threshold and low energy parameters, based on the uncertainties for the one loop low energy parameters and the resonance saturation mechanism. Different sets of…
The leading non-Coulombic electromagnetic contributions to pi pi s-wave scattering lengths are computed in Chiral Perturbation Theory. It is shown that these corrections are zeroth order in the chiral expansion and associated with…
The relationship between the pionium lifetime and the $\pi\pi$ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a…
The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The K-matrix is a powerful, yet comparatively simple, method…
We have evaluated forward dispersion relations for scattering amplitudes that follow from direct fits to several sets of pion-pion scattering experiments, together with the precise K decay results, and high to energy data. We find that some…
The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop…
Dispersive representations of the pi-pi scattering amplitudes and pion form factors, valid at two-loop accuracy in the low-energy expansion, are constructed in the presence of isospin-breaking effects induced by the difference between the…
We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural…
The S and P wave $\pi \pi$ phase shifts are recalculated in terms of two phenomenological parameters using the one loop CPTh and the elastic unitarity condition. Using these phase shifts, the vector and scalar form factors are calculated…
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the…
Mixtures of polarised fermions of two different masses can form weakly-bound clusters, such as dimers and trimers, that are universally described by the scattering length between the heavy and light fermions. We use the resonating group…
We derive a set of sum rules for threshold parameters of pion-pion scattering whose dispersion integrals are rapidly convergent and are dominated by S- and P-waves absorptive parts. Stringent constraints on some threshold parameters are…
We compare the low-energy partial wave analyses $\pi N$ scattering with a high-energy data via finite energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy,…
This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical…
Peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed analyzing the experimental data on processes $\pi\pi\to\pi\pi,K\bar{K}$ in the $I^GJ^{PC}=0^+0^{++}$ channel in a model-independent approach…
$K\pi$ $S$ wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, $I_{\pi\pi\pi} = 2$, $1$ and $0$. Using the generic-isospin extension of the RFT formalism…
Once and twice subtracted crossing symmetric dispersion relations applied to $\pi\pi \to \pi\pi$ scattering data are analyzed and compared. Both sets of dispersion relations can be used to test the $\pi\pi$ amplitudes in low partial waves…
Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit,…