Electroweak precision data and the Lee-Wick standard model

Abstract

We investigate the electroweak precision constraints on the recently proposed Lee-Wick standard model at tree level. We analyze low-energy, Z-pole (LEP1/SLC) and LEP2 data separately. We derive the exact tree-level low-energy and Z-pole effective Lagrangians from both the auxiliary field and higher derivative formulation of the theory. For the LEP2 data we use the fact that the Lee-Wick standard model belongs to the class of models that assumes a so-called ''universal'' form which can be described by seven oblique parameters at leading order in m 2 W =M 2 1;2 . At tree level we find that Y ¼ Àm 2 W =M 2 1 and W ¼ Àm 2 W =M 2 2 , where the negative sign is due to the presence of the negative norm states. All other oblique parameters ðŜ; XÞ and ðT;Û; VÞ are found to be zero. In the addendum we show how our results differ from previous investigations, where contact terms, which are found to be of leading order, have been neglected. The LEP1/SLC constraints are slightly stronger than LEP2 and much stronger than the low-energy ones. The LEP1/SLC results exclude gauge boson masses of M 1 ' M 2 $ 3 TeV at the 99% confidence level. Somewhat lower masses are possible when one of the masses assumes a large value. Loop corrections to the electroweak observables are suppressed by the standard $1=ð4Þ 2 factor and are therefore not expected to change the constraints on M1 and M 2 . This assertion is most transparent from the higher derivative formulation of the theory.

Particle Physics-Final Report

“…Lee and Wick argued that this class of theories can be made consistent if the would-be negative metric states are unstable. This "Lee-Wick Standard Model" (LWSM) is consistent with electroweak precision data [12,35,37,140] and with flavor physics constraints provided M is at least a few TeV [49]. Such low values for M have observable effects, resonances associated with would-be negative metric states, roughly one per SM particle.…”

Theory and phenomenology of two-Higgs-doublet models

“…While one does have microcausality violation, no logical paradoxes arise macroscopically [182,184]. There is now an extensive literature on the LWSM [185,186,187,188,189,190,191,192,193,194,195,196,197] .…”

Precision electroweak constraints on theN=3Lee-Wick standard model

“…In addition, one can easily compute the tree-level oblique electroweak parameters as done for the N = 2 model in Ref. [11]:…”

“…[7,8] find that N = 2 LW gauge bosons, for example, can readily be produced at the LHC, but may be difficult to distinguish from novel states from other scenarios such as extra-dimension models. Precision observables in the N = 2 theory, on the other hand, have been examined in a succession of improvements [9][10][11][12] (by scanning the LW parameter space in [9]; by including only LW masses for the fields most important for the hierarchy problem [10]; by using not just oblique parameters S, T , but also the "post-LEP" parameters W , Y [11]; by including bounds from the Zbb direct correction [12]), with the consensus conclusion that LW gauge boson masses must be well over 2 TeV, and in such cases, the LW fermion masses must be substantially higher (perhaps as much as 10 TeV). If all LW masses are comparable, then the lower bound on this scale is typically ∼ 7 TeV.…”