Analysis of mass shift due to weak interactions

Abstract

Within the framework of light-cone algebra it is shown thatthere is no logarithmic divergence of order g W 2 in the mass shift for a hadron due to weak interactions for currents having V-A structure, provided the weak interactions are mediated by vector bosons. As previously shown for electromagnetic mass shift, the source of this divergence is the mass term in the quark propagator. The contribution of this term to light-cone algebra vanishes due to the V ∓ A character of weak currents and this is the reason for absence of divergence of order g W 2 in the weak mass shift. This result has important implications for unified gauge models for weak interactions based on semi-simple Lie groups of type SU L( n) ⊗ U(1) or SU L( n) ⊗ SU R( n) ⊗ U(1). for these models g W 2 ≈ α, and the logarithmic divergence in the mass shift of a hadron can only arise from the current associated with U(1). For mass difference of order α between an isospin multiplet to be finite and computable, U(1) must be associated with an isoscalar quantity.