The $Delta_{mix}$ parameter in the overlap on domain-wall mixed action

A direct calculation of the mixed-action parameter $Delta_{mix}$ with valence overlap fermions on a domain-wall fermion sea is presented. The calculation is performed on four ensembles of the 2+1-flavor domain-wall gauge configurations: $24^3 times 64$ ($a m_l= 0.005$, $a=0.114fm$) and $32^3 times 64$ ($a m_l = 0.004, 0.006, 0.008$, $a=0.085fm$). For pion masses close to $300MeV$ we find hbox{$Delta_{mix}=0.030(6)GeV^4$} at $a=0.114fm$ and $Delta_{mix}=0.033(12)GeV^4$ at $a=0.085fm$. The results are quite independent of the lattice spacing and they are significantly smaller than the results for valence domain-wall fermions on Asqtad sea or those of valence overlap fermions on clover sea. Combining the results extracted from these two ensembles, we get $Delta_{mix}=0.030(6)(5)GeV^4$, where the first error is statistical and the second is the systematic error associated with the fitting method.