Note, if kinetic mixing is neglected, this reduces to the more familiar form of $\\sqrt{g^2_{BL} g_R/(g_R^2 + g_{BL}^2)}$. When setting the boundary conditions to relate the gauge couplings, one has to make sure that always the relations for the not GUT-normalized values are used. For instance,
Note, if kinetic mixing is neglected, this reduces to the more familiar form of $`\sqrt{g^2_{BL} g_R/(g_R^2 + g_{BL}^2)}`$. When setting the boundary conditions to relate the gauge couplings, one has to make sure that always the relations for the not GUT-normalized values are used. For instance,