Standard Model Effective Field Theory: Integrating out Neutralinos and Charginos in the MSSM

We apply the covariant derivative expansion method to integrate out the neutralinos and charginos in the minimal supersymmetric Standard Model. The results are presented as set of pure bosonic dimension-6 operators in the Standard Model effective field theory. Nontrivial chirality dependence in fermionic covariant derivative expansion are discussed carefully. The results are checked by computing the $h\gamma\gamma$ effective coupling and the electroweak oblique parameters using the Standard Model effective field theory with our effective operators and direct loop calculation. In global fitting the proposed lepton collider constraint projections, special phenomenological emphasis is paid to the gaugino mass unification scenario ($M_2\simeq2M_1$) and anomaly mediation scenario ($M_1\simeq3.3M_2$). These results show that the precision measurement experiments in future lepton colliders will provide a very useful complementary job in probing the electroweakino sector, in particular, filling the gap of the soft lepton plus missing $E_T$ channel search left by the traditional collider, where the neutralino as the lightest supersymmetric particle is very degenerated with the next-to-lightest chargino/neutralino.