Chiral behavior of the B0d,s−B̄0d,s mixing amplitude in the Standard Model and beyond

We compute the chiral logarithmic corrections to the B0d−0d and B0s−0s mixing amplitudes in the Standard Model and beyond. We then investigate the impact of the inclusion of the lowest-lying scalar heavy-light states to the decay constants and bag-parameters and show that this does not modify the pion chiral logarithms, but it does produce corrections which are competitive in size with the K- and η-meson chiral logarithms. This conclusion is highly relevant to the lattice studies since the pion chiral logarithms represent the most important effect in guiding the chiral extrapolations of the lattice data for these quantities. It is also important to stress that the pion chiral logarithmic corrections are useful in guiding those chiral extrapolations as long as mπ ΔS, where ΔS stands for the mass difference between the heavy-light mesons belonging to ½+ and ½− doublets.