Neutron-Proton Scattering Phase Shifts in S-Channel using Phase Function Method for Various Two Term Potentials

The scattering phase shifts for n-p scattering have been modeled using various two term exponential type potentials such as Malfliet-Tjon, Manning-Rosen and Morse to study the phase shifts in the S-channels. As a first step, the model arameters for each of the potentials are determined by obtaining binding energy of the deuteron using matrix methods vis-a-vis Variational Monte-Carlo (VMC) technique to minimize the percentage error w.r.t. the experimental value. Then, the first order ODE as given by phase function method (PFM), is numerically solved using 5th order Runge-Kutta (RK-5) technique, by substituting the obtained potentials for calculating phase shifts for the bound 3S1 channel. Finally, the potential parameters are varied in least squares sense using VMC technique to obtain the scattering phase-shifts for each of the potentials in the 1S0 channel. The numerically obtained values are seen to be matching with those obtained using other analytical techniques and a comparative analysis with the experimental values up to 300 MeV is presented.

Elastic scattering phase shift generalizations to two spin-3 2 particles: On the determination of Ω–Ω scattering phase amplitudes in elongated boxes

The relationship between the elastic scattering phase shifts of the [Formula: see text] system and the two-particle energy spectrum in elongated boxes is established in center-of-mass frame under periodic boundary conditions. The formulas are also extended to cubic boxes to confirm the results in elongated boxes. Our analytical results will be helpful to the study of [Formula: see text] interaction on lattice by using Lüscher’s finite volume method.

${\bf I=2} \boldsymbol{\pi\pi}$ potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$$\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on a $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contamination to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$$\pi\pi$ system by the hybrid method within a reasonable numerical cost; these phase shifts are consistent with the result obtained with the conventional method. The knowledge that we obtain in this study will become useful for the investigation of hadron resonances that require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.

Fully solvable mathematical scheme in finding out the right mass and width values of f0(500) and ρ0(770) mesons

Starting from the phase representations with one subtraction of the pion scalar-isoscalar and vector-isovector charged pion electromagnetic form factor and exploiting the most accurate information on the S-wave isoscalar and the P-wave isovector ππ scattering phase shifts, respectively, to be obtained from the existing inaccurate experimental data by means of the Garcia- Kamiński-Peláez-Yndurain Roy-like equations with an imposed crossing symmetry condition, in the framework of the so-called “fully solvable mathematical scheme” the most reliable values of the f0(500) and ρ0(770) meson mass and width are found.