Anomaly in decay of 8Be and 4He -- can a chirally symmetric light boson be able to mediate the low energy nucleon-nucleon interaction ?

We present a hypothesis that the anomaly in the folding angle distribution of electron-positron pairs, emitted in the decay of the excited levels of nucleus $^{8}$Be and $^{4}$He can be related to the cluster structure of the decaying state. Furthermore, we present a hypothesis that the potentially observed boson with rest mass $m_{X}$=17 MeV can mediate the nucleon-nucleon interaction at the low-energy regime of QCD, in particular in the weakly bound cluster state p+$^{3}$H. We present a range of possible equations of state of symmetric nuclear matter corresponding to the vector meson mass $m_{v}$=17 MeV, and obtained using relativistic mean field theory of nuclear force, QHD-I in particular. The narrow range of cubic and quartic couplings $\kappa$ and $\lambda$ allows to obtain both very stiff and very soft equations of state, including the equations of state of physical interest with incompessibility K$_{0}$=240-260 MeV. The values of couplings $g_{v}$, $g_{s}$ are lower than unity. Based on predictions of instanton liquid model, we show that reduction of the rest mass of pseudoscalar particle from physical value $m_{\pi}$=135 MeV to $m_{X}$=17 MeV is equivalent to reduction of the quark mass from dynamical value around 310 MeV down to current quark mass around 5 MeV ($\frac{m_{X}^2} {m_{q,curr}} \simeq \frac{m_{\pi}^2} {m_{q,dyn}}$). Results from both relativistic mean field theory of nuclear force and from instanton liquid model thus point towards apparent restoration of chiral symmetry in nucleon-nucleon interaction at large distances. Observation of boson with rest mass $m_{X}$=17 MeV in the decay of high lying excited states of $^{8}$Be and $^{4}$He can possibly resolve one of the longest lasting open questions in nuclear physics.