2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27303We give a mean-field calculation for the odd-resonating-valence-bond ORVB pairing scheme. We obtain interesting quasi-particle excitation energy $E_{\bf k}$ as a function of momentum ${\bf k}$. It is distinctively different from those of the $d_{x^2-y^2}$-wave, the anisotropic-s-wave, and the p-wave. It is a gapless theory for superconductivity with well defined Fermi surface. The ground state of the ORVB scheme is not an eigenstate of the parity or the time-reversal transformation, thus both symmetries are violated. Some of them are already manifested in $E_{\bf k}\neq E_{-{\bf k}} $. It is interesting to find out if such pairing order-parameter scheme exits in some materials in nature.12 pages, uses phyzzxCondensed Mattertext