Flavor changing effects in theories with a heavyZ′boson with family nonuniversal couplings

There are theoretical and phenomenological motivations that there may exist additional heavy $Z^{\prime }$ bosons with family nonuniversal couplings. Flavor mixing in the quark and lepton sectors will then lead to flavor changing couplings of the heavy $Z^{\prime },$ and also of the ordinary Z when ${Z-Z}^{\prime }$ mixing is included. The general formalism of such effects is described, and applications are made to a variety of flavor changing and CP-violating tree and loop processes. Results are described for three specific cases motivated by a specific heterotic string model and by phenomenological considerations, including cases in which all three families have different couplings, and those in which the first two families, but not the third, have the same couplings. Even within a specific theory the results are model dependent because of unknown quark and lepton mixing matrices. However, assuming that typical mixings are comparable to the Cabibbo-Kobayashi-Maskawa matrix, processes such as coherent μ-e conversion in a muonic atom, $K^0-K^0$ and $B-\overline{B}$ mixing, ε, and ${\epsilon }^{\prime }/\epsilon$ lead to significant constraints on $Z^{\prime }$ bosons in the theoretically and phenomenologically motivated range $M_{Z^{\prime }}\sim 1\mathrm{TeV}.$