Leptophobic U(1)'s and the R_b - R_c Crisis

TL;DR

The paper addresses the LEP-era R_b excess and R_c deficit by proposing leptophobic $U(1)'$ extensions that induce $Z$-$Z'$ mixing. By enforcing gauge-coupling unification, vector-like beyond-MSSM matter, and generation-independent leptophobic charges, the authors construct anomaly-free, perturbative models, highlighting the $ ext{η}$-model from $E_6$ as particularly natural in string-inspired contexts. Importantly, they show that kinetic mixing between $U(1)'$s, captured by the parameter $oldsymbol{ extdelta}$, is essential and, under RG running with a specific spectrum, predicts $oldsymbol{ extdelta}$ values that yield good fits to LEP data for a light $Z'$ with $M_{Z'}$ in the few-hundred GeV range. Among the explored classes, the $ ext{η}$-model and two related C-type models (C$(7/5)$ and C$(1)$) emerge as the most viable, predicting observable but challenging-to-detect new states below the TeV scale and motivating further consideration of low-energy constraints and collider signatures.

Abstract

In this paper, we investigate the possibility of explaining both the R_b excess and the R_c deficit reported by the LEP experiments through Z-Z' mixing effects. We have constructed a set of models consistent with a restrictive set of principles: unification of the Standard Model (SM) gauge couplings, vector- like additional matter, and couplings which are both generation-independent and leptophobic. These models are anomaly-free, perturbative up to the GUT scale, and contain realistic mass spectra. Out of this class of models, we find three explicit realizations which fit the LEP data to a far better extent than the unmodified SM or MSSM and satisfy all other phenomenological constraints which we have investigated. One realization, the η-model coming from E_6, is particularly attractive, arising naturally from geometrical compactifications of heterotic string theory. This conclusion depends crucially on the inclusion of a U(1) kinetic mixing term, whose value is correctly predicted by renormalization group running in the E_6 model given one discrete choice of spectra.

Figures (5)

• Figure 1: 99% C.L. contours for the four basic classes of models labeled by their $Q/u^c$ charge ratio in the $(\overline{\xi},\Delta\overline{\rho})$ plane. The cross represents the SM.
• Figure 2: $\chi^2$ contours for the C(7/5) Model in the $(\overline{\xi},\Delta\rho_M)$ plane. The solid ellipses represent the 95% and 99% C.L. bounds on the fit. The dashed ellipses represent the corresponding bounds if $\Delta\rho_{\rm extra} =-0.001$. The three solid lines are contours of $M_{Z'}$ arising from the theoretical constraint of perturbativity of the $U(1)'$ coupling up to the GUT scale, and are labeled in GeV.
• Figure 3: $\chi^2$ contours for the C(1) Model in the $(\overline{\xi},\Delta\rho_M)$ plane. See caption of Figure \ref{['fig:C75']} for explanation.
• Figure 4: $\chi^2$ contours for general $E_6$ models. The two contours represent confidence levels of 95% and 99%. Three canonical $E_6$ models are labeled at the bottom. The two points highlight the $\eta$-model with $\delta=1/3$ (${\bf\times}$) and $\delta=0.29$ (${\bf\triangle}$).
• Figure 5: $\chi^2$ contours for the $\eta$-model with $\delta=0.29$ in the $(\overline{\xi},\Delta\rho_M)$ plane. See caption of Figure \ref{['fig:C75']} for explanation. Additional positive contributions to $\Delta\overline{\rho}$ reduce the best fit value of the $Z'$ mass.