Experimental constraint on widths of postulated low-mass dibaryons

The consistency of a postulated ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance near $E_L=390\mathrm{}$ MeV with the experimentally determined nucleon-nucleon phase shifts at $E_L=325, 380, \mathrm{and} 425$ MeV is examined. It is found that the data require that the width of such a resonance $\Gamma \lesssim 0.3$ MeV. A similar restriction on the width of a postulated ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ resonance near $E_L=300\mathrm{}$ MeV is implied by the accuracy of the data at $E_L=210, 325, \mathrm{and} 380$ MeV.