1TABLE IV. Calculation of I'(X -+ 27ry). i-1 I A11 B I BII and (54) lead to two values of Rx for each solution given in Eqs. (22) and (23). These are tabulated in Table IV.
VII. DISCUSSIONIf, on the basis of the calculation for the ratio r(q -f 2y)/r(n0 + 2y), we discard the lower value of the K inass used in solution B in Eqs. (23) and accept the solution A1 over AII, we suinrnarize the following results for the partial decay rates of the X meson:quark model. We ma> remind ourselves that the value of I'(X + qnn) is of course independent of the specific quark models. I t is not possible to compare these results with the data, since the total width of X is not yet accurately kno~n.~"f we take our results in Eqs. (57) seriousl>, then for the srmaller of the two values for r(X-+ 2ny) we have the ratio r ( X + 2ny)l r ( X -q~n).v0.2, which is not far from the experinientally quoted" value of about 0.3 However, the width for , Y + 27 seems to be too small. A word of caution is necessary. Most of our calculations are based on the soft-q appro~in~ation and we have no idea how good this approximation is. The fact that the Lfaki-Hara quarlr model seems to be preferred in our present calculations may also be spurious if, for instance, possible strong-interaction corrections to Eq. (38) do not drop out froin the ratios of rates calculated in Sec. VI A, or if the mass of the K meson turns out to be much differe~it from the value talren in obtaining the results (57). r ( X --t 2ny)e1.3 or 4.3 MeV, 22S. Barash-Schmidt et al., Rev. Mod. Phys. 41, 109 (1969). These tables quote an upper limit of 4 MeV for the decay width where we have quoted our results only for the RIH of X .
P H Y S I C A L R E V I EThe unitary Pad6 approximants, successfully introduced in strong-interaction physics for the pion and kaon systems, are now applied to the nucleon-nucleon problem. I t is assumed that the interaction between two nucleons is described by the renormalizable Lagrangian LI =igGY &TIC. @+A(@.We present the result of the complete calculation of the [1,1] unitary Pad6 approximant, which does not involve the second term in the Lagrangian: This implies that no free parameters appear in our model. X complete description of lo~ir-energy nucleon-nucleon physics is then obtained which qualitatively and often quantitatively agrees mith experiment. Bound states appear only in S waves, and a real pole is found in the deuteron amplitude a t 4.8 MeV when the pion-nucleon coupling constant is taken a t its physical value g2/4rr= 14.7. The Regge trajectories rise mith energy: The deuteron recurrence does not become physical, while the recurrences of the virtual ' S O state give rise to narrow resonances in the ID2 and lGq waves. For all waves (yith the exception of the 'So which in the [l,l] Pad6 approximation has a wrong threshold behavior), the calculated phase shifts are in good qualitative agreement with the experimental phase-shift analysis.
