Neutral B Mixing in Staggered Chiral Perturbation Theory

TL;DR

This paper calculates B meson mixing matrix elements at one loop in staggered chiral perturbation theory, addressing lattice computation representations and the role of wrong-spin operators in the continuum limit.

Contribution

It provides a comprehensive one-loop chiral perturbation theory calculation for all five operators relevant to B mixing, clarifying the impact of lattice operator representations and wrong-spin effects.

Findings

Wrong-spin operator contributions vanish in the continuum limit.

All five operators' matrix elements can be computed without extra low energy constants.

The operator representation influences the chiral calculation and lattice results.

Abstract

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 4-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.