Unitary Padé Approximants in Strong-Interaction Physics: The Nucleon-Nucleon System

The unitary Padé approximants, successfully introduced in strong-interaction physics for the pion and kaon systems, are now applied to the nucleon-nucleon problem. It is assumed that the interaction between two nucleons is described by the renormalizable Lagrangian $L_I=ig\overline{\psi }{\gamma }_5\tau \psi \Phi +\lambda {\left(\Phi ·\Phi \right)}^2$. We present the result of the complete calculation of the [1,1] unitary Padé approximant, which does not involve the second term in the Lagrangian: This implies that no free parameters appear in our model. A complete description of low-energy nucleon-nucleon physics is then obtained which qualitatively and often quantitatively agrees with experiment. Bound states appear only in $S$ waves, and a real pole is found in the deuteron amplitude at 4.8 MeV when the pion-nucleon coupling constant is taken at its physical value $\frac{g^2}{4\pi }=14.7\mathrm{}$. The Regge trajectories rise with energy: The deuteron recurrence does not become physical, while the recurrences of the virtual ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state give rise to narrow resonances in the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ waves. For all waves (with the exception of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ which in the [1,1] Padé approximation has a wrong threshold behavior), the calculated phase shifts are in good qualitative agreement with the experimental phase-shift analysis.