Balancing asymmetric dark matter with baryon asymmetry and dilution of frozen dark matter by sphaleron transition

In this paper we study the effect of electroweak sphaleron transition or electroweak phase transition (EWPT) in balancing baryon excess to the excess stable quarks of $4^{th}$ generation. Considering the conservation of all quantum number and charges, sphaleron transition between between baryons, leptons and $4^{th}$ family of leptons and quarks is possible. We have tried to established a possible definite relationship between the value and sign of the $4^{th}$ family excess relative to baryon asymmetry under the framework of second order EWPT. In passing by we show the small, yet negligible dilution in the pre-existing dark matter density due the sphaleron transition.