I calculate, at one loop in staggered chiral perturbation theory, the matrix elements of the complete set of five local operators that may contribute to $B$ mixing both in the standard model and in beyond-the-standard-model theories. Lattice computations of these matrix elements by the Fermilab Lattice/MILC collaborations (and earlier by the HPQCD collaboration) convert a light staggered quark into a naive quark, and construct the relevant four-quark operators as local products of two local bilinears, each involving the naive light quark and the heavy quark. This particular representation of the operators turns out to be important in the chiral calculation, and it results in the presence of “wrong-spin” operators, whose contributions however vanish in the continuum limit. If the matrix elements of all five operators are computed on the lattice, then no additional low-energy constants are required to describe wrong-spin chiral effects.

• Received 15 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.114503