Constraints on the Universal Contact Interaction

Forces beyond those of the standard model may manifest themselves at low energies as four-fermion contact interactions. If these new forces are independent of colour and flavour quantum numbers including baryon and lepton number, then all low energy constraints, arising from quark-lepton universality, flavour-changing neutral currents and atomic parity violation are evaded. This is due to the global U(45) symmetry which the standard model exhibits in the limit of vanishing gauge and Yukawa couplings. The corresponding contact interaction is a unique current-current interaction. Constraints from LEP2 imply that this universal contact interaction cannot be the origin of the recently observed high-$Q^2$ events at HERA.Comment: 6 pages Latex, no figure

Local realizations of contact interactions in two- and three-body problems

Mathematically rigorous theory of the two-body contact interaction in three dimension is reviewed. Local potential realizations of this proper contact interaction are given in terms of Poschl-Teller, exponential and square-well potentials. Three body calculation is carried out for the halo nucleus 11Li using adequately represented contact interaction.Comment: submitted to Phys. Rev.

BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter

We propose new types of density dependent contact pairing interaction which reproduce the pairing gaps in symmetric and neutron matter obtained by a microscopic treatment based on the nucleon-nucleon interaction. These interactions are able to simulate the pairing gaps of either the bare interaction or the interaction screened by the medium polarization effects. It is shown that the medium polarization effects cannot be cast into the density power law function usually introduced together with the contact interaction and require the introduction of another isoscalar term. The BCS-BEC crossover of neutrons pairs in symmetric and symmetric nuclear matter is studied by using these contact interactions. It is shown that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter. For the screened pairing interaction, a two-neutron BEC state is formed in symmetric matter at $k_{Fn}\sim 0.2$ fm$^{-1}$ (neutron density $\rho_n/\rho_0\sim 10^{-3}$). Contrary the bare interaction does not form the BEC state at any neutron density