We construct an analytic formalism for the mass function of cold dark matter halos , assuming that there is a break in the hierarchical merging process .
According to this broken-hierarchy scenario , due to the inherent nature of the gravitational tidal field the formation of massive pancakes precedes that of dark halos of low-mass .
In the framework of the Zel ’ dovich approximation which generically predicts the presence of pancakes , we first derive analytically the conditional probability that a low-mass halo observed at present epoch was embedded in an isolated pancake at some earlier epoch .
Then , we follow the standard Press-Schechter approach to count analytically the number density of low-mass halos that formed through anti-hierarchical fragmentation of the massive pancakes .
Our mass function is well approximated by a power-law dN / dM = M ^ { - l } in the mass range 10 ^ { 6 } h ^ { -1 } M _ { \odot } \leq M \leq 10 ^ { 10 } h ^ { -1 } M _ { \odot } with the slope l = 1.86 shallower than that of the currently popular Sheth-Tormen mass function l = 2.1 .
It is expected that our mass function will provide a useful analytic tool for investigating the effect of broken hierarchy on the structure formation .