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We present here the mathematical background of our approach, presented inPhys. Rev. B 86, 134526 (2012) regarding the gap function and symmetry for thenoncentrosymmetric (NCS) superconductor $Li_2Pt_3B$. As revealed by theexperiment, this NCS superconductor gives rise to line nodes in thesuperconducting order parameter, which is responsible for many of itsexperimental behaviors. Owing to the enhanced d-character of the relevant bandsthat cross the Fermi level,the system gets weakly correlated. The nature andsymmetry of this nodal behavior is explained from a microscopic viewpoint. Inthis article starting with an Hubbard model relevant for this NCS system byconsidering the effect of the onsite Coulomb repulsion on the pairing potentialperturbatively, we extract the superconducting gap equation. Further analysisof this equation predicts a $s_\pm$ wave gap function with line nodes as themost promising candidate in the superconducting state.

Derivation of the superconducting gap equation for the noncentrosymmetric superconductor Li2Pt3B