p−presonances: A link between nuclear and hadronic excitations

Evidence of resonant behavior has recently been discovered in $p-p$ scattering, and possibly also in $n-p$ scattering. In particular, the $p-p$ data indicate the existence of ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}F_3^{}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ resonances at energies of approximately 2140, 2260, and 2430 MeV. The correlation between increasing $l$ values and increasing energies that is observed in these resonances suggests a form of rotational motion. Since a virtually bound nucleon-nucleon state represents the low-mass limit of a multinucleon (nuclear) system, we logically expect the rotational behavior of this dinucleon state to follow the known systematics of nuclear physics. The rotational motion is highly nonadiabatic for this very light dinucleon system, so that an $l(l+1\mathrm{})\mathrm{}$ energy interval rule is expected to apply, where $l$ is the orbital angular momentum quantum number. In support of this idea, we show experimental data plots which reveal that (1) rotational bands in very light nuclei and in the dinucleon follow the expected $l(l+1\mathrm{})\mathrm{}$ interval rule, and (2) the experimental moments of inertia of the rotating bandheads exhibit the expected $A^{\frac{5}{3}}$ behavior, where $A$ is the atomic weight. We can extend these concepts even farther by formally sorting the observed baryon and meson resonances into nonadiabatic rotational bands. When we do this, we discover that the experimental moments of inertia of these hadron rotational bands, plotted as a function of the bandhead masses, extrapolate smoothly into the moments of inertia of the very light atomic nuclei. Applying the $l(l+1\mathrm{})\mathrm{}$ energy interval rule to the observed ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}F_3^{}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ $p-p$ resonances, and then extrapolating to $l=0\mathrm{}$ to obtain the mass of the unobserved $p-p$ bandhead, we discover that it corresponds to a virtual $\mathrm{pp}\pi$ bound state, which is a characteristic hadronic excitation. Hence the $p-p$ resonances form a direct and unique experimental link between nuclear and hadronic excitations: The $p-p$ rotational levels, which are nuclear in origin, can be used to pinpoint the mass of the $p-p$ bandhead excitation, which is hadronic in origin. The $C_{\mathrm{LL}}$, $\Delta {\sigma }_L$, and