Custodial isospin violation in the Lee-Wick standard model

We analyze the tension between naturalness and isospin violation in the Lee-Wick standard model (LW SM) by computing tree-level and fermionic one-loop contributions to the post-LEP electroweak parameters (S-circumflex, T-circumflex, W, and Y) and the ZbLb-barL coupling. The model is most natural when the LW partners of the gauge bosons and fermions are light, but small partner masses can lead to large isospin violation. The post-LEP parameters yield a simple picture in the LW SM: the gauge sector contributes to Y and W only, with leading contributions arising at tree level, while the fermion sector contributes to S-circumflex and T-circumflex only, with leading corrections arising at one loop. Hence, W and Y constrain the masses of the LW gauge bosons to satisfy M1, M2 > or approx. 2.4 TeV at 95% C.L. Likewise, experimental limits on T-circumflex reveal that the masses of the LW fermions must satisfy Mq, Mt > or approx. 1.6 TeV at 95% C.L. if the Higgs mass is light and tend to exclude the LW SM for any LW fermion masses if the Higgs mass is heavy. Contributions from the top-quark sector to the ZbLbL coupling can be even more stringent, placing a lower bound of 4 TeV on the LW fermion masses at 95% C.L.