Is there a strong van der Waals force between hadrons?

Abstract

We study the question of the existence of long-range forces that are stronger than electromagnetic forces between ordinary hadrons. A phenomenological analysis is carried out which puts limits on the magnitude of the coupling constant ${\lambda }_N$ entering a hypothetical interhadronic potential $V_N\mathrm{}\left(r\right)\mathrm{}\sim \left(\frac{{\lambda }_N}{r}\right){\left(\frac{r_0}{r}\right)}^{N-1\mathrm{}}$, with a length scale $r_0\sim 1$ F and $1\le N\le 7$. Bounds on the value of ${\lambda }_N$ are obtained from a variety of sources, including Eötvös- and Cavendish-type experiments, hyperfine structure of the hydrogen molecule, and the level structure of exotic atoms. The dispersion-theoretic approach to the asymptotic behavior of interparticle potentials is reviewed and used to analyze some of the theoretical implications of long-range forces. We stress the fact that long-range potentials require that the scattering amplitude $F(s,t)\mathrm{}$ is not analytic at $t=0\mathrm{}$. Such a lack of analyticity is often connected with physical states whose mass spectrum extends down to zero. The implications of this for quantum chromodynamics (QCD) and the recent suggestions that QCD may imply the existence of a long-range force between hadrons are studied. A speculative scheme is considered which might yield such forces without requiring the existence of massless color gluons as observable particles.