Effects of Universal Extra Dimensions on $B^0 - {\bar B^0}$ Mixing

We study contributions coming to $\Delta m_B$ from one or more universal extra dimensions (UED) in which all the Standard Model fields can propagate. In the model with a single UED, the box diagrams for mixing are convergent and therefore insensitive to the cutoff scale of the theory. In the case of two UEDs, the contributions are divergent and have to be regulated by a cut-off scale $M_s$ of the order of a few TeV. Within the present range of the parameters, the lower bound on the compactification scale 1/R has been estimated to be 200 GeV for one UED and 390 GeV for two UEDs. The bound increases drastically if one can have a better determination of the $B$ meson decay constant $f_B$ and the QCD correction parameter $B_B$. For example, it rises to 600 GeV (for one UED) if the error in the determination of $f_B\sqrt{B_B}$ from quenched lattice calculation is reduced to one-third from its present value. The UED contributions to the $K$ system are strongly suppressed.