Implications of Generalized Z − Z ′ Mixing

We discuss experimental implications of extending the gauge structure of the Standard Model to include an additional U(1) interaction broken at or near the weak scale. We work with the most general, renormalizable Lagrangian for the SU(2)×U(1)×U(1) sector, with emphasis on the phenomenon of gauge kinetic mixing between the two U(1) gauge fields, and do not restrict ourselves to any of the “canonical” Z ′ models often discussed in the literature. Low-energy processes and Z0-pole precision measurements are specifically addressed. Email: [email protected] Email: [email protected] Email: [email protected] One of the simplest, and most well-motivated, extensions of the Standard Model (SM) is the addition of an extra U(1) gauge factor to its SU(3) × SU(2) × U(1) structure. Traditionally [1], the most studied such extensions were motivated by grand unified theories (GUT’s) of rank higher than that of the SM (SO(10), E6 or larger), or by geometric compactifications of heterotic string models which possessed a low-energy spectrum sharing many features with E6 GUT’s. Examples of the resulting Z ′ gauge bosons include the χ and ψ models whose couplings to the SM fermions are defined by the decompositions SO(10) → SU(5)×U(1)χ and E6 → SO(10)×U(1)ψ. However, it has recently become clear that these models are not especially favored, and that a larger class of Z ′ models is more naturally considered. There are two reasons for this change of view: first, even in “traditional” GUTlike models, the phenomenon of kinetic mixing [2, 3, 4] can significantly shift the predicted couplings of the Z ′ to SM states away from their canonical values, as well as changing the relationship between other SM observables [5]; furthermore, kinetic mixing is in general generated by renormalization group (RG) running down from the high (i.e., GUT) scale to the weak scale [3, 4]. Second, from the string perspective, a much broader class of models with additional U(1) factors now looks reasonable; this is due both to the construction of many non-geometrical string models in weak coupling perturbation theory (e.g., those arising from free-fermionic techniques) which share very little resemblence to GUT-like models, and to the recent developements in strongly-coupled string theory which show that additional gauge factors can arise non-perturbatively. It is also worth mentioning that string models naturally lead to non-zero kinetic mixing as a threshold effect at the string scale [6]. In either case the traditional parameterization in terms of the U(1) combinations in E6 is inadequate. Our intention in this paper is to explore the experimental consequences of the most general U(1) extensions of the SM. Consistent with the effective field theory philosophy, we study the full set of additional renormalizable operators generated by the interactions of the Z , and allowed by SM and U(1) gauge symmetries. One expects that additional matter fields would also arise in extended gauge models in order to cancel possible anomalies; however we will not study their effects here as the spectrum and charges of extra matter would be highly model-dependent. For a generic Z , one usually find that direct experimental searches, via, for example, Drell-Yan Z ′ production at a pp collider, will provide the strongest constraints on the existence of these new interactions. Such searches have been considered many times both in the theoretical and experimental literatures. However there exist a number of low-energy processes which are sensitive to extra gauge interactions, as well as Z-pole processes sensitive to Z −Z ′ mixing. These processes can provide the most useful mechanisms for searching for and/or measuring Z ′ physics, particularly if the extra Z ′ is either leptophobic [4, 7] or close in mass to the Z. It is on these indirect and mixing bounds that we will concentrate in this work. Finally, we wish to make note of previous related works which considered many of these same issues in particular limits: Kim, et al. [8] on low-energy observables;