A $B-$anomaly motivated $Z^\prime$ boson at the energy and precision frontiers

TL;DR

The paper investigates a TeV-scale $Z'$ from a kinetically mixed $U(1)_{B_3-L_2}$ extension as a concrete link between $B$-meson flavour anomalies and collider signals. It analyzes a multi-channel discovery program at the HL-LHC and explores the precision potential of FCC-ee, while also projecting the reach of a future 100 TeV collider (FCC-hh) to cover the full flavour-preferred parameter space. The study finds that HL-LHC can improve direct sensitivity in several channels, FCC-ee can constrain oblique corrections that arise from kinetic mixing, and FCC-hh would robustly probe the entire region, providing coherent cross-channel tests of the model. Collectively, the results emphasize the complementary roles of high-energy and high-precision facilities in validating flavour-mmotivated new physics scenarios with a $Z'$ mediator.

Abstract

TeV-scale $Z^\prime$ bosons with family-dependent couplings can explain some anomalies inferred from $B-$meson measurements of processes involving the $b \rightarrow s \ell^+\ell^-$ transition. A $Z^\prime$ originating from kinetically-mixed spontaneously broken $U(1)_{B_3-L_2}$ gauge symmetry has been shown to greatly ameliorate global fits~\cite{Allanach:2024ozu} in a `flavour-preferred' region of parameter space. We provide an exploration of this region at the high luminosity (HL-)LHC with particular attention to which signals could be verified across different discovery modes. Even if the HL-LHC does not discover the $Z^\prime$ boson in a resonant di-lepton channel, a FCC-ee $Z$-pole run would detect oblique corrections to the electroweak precision observables (EWPOs). Changes due to $Z^\prime$-induced non-oblique corrections are unlikely to be detected, to within experimental precision. In any case, the extended discovery potential offered by a 100 TeV $pp-$collider would afford sensitivity to the entire flavour-preferred region and enable a fine-grained and forensic analysis of the~model.

Figures (9)

• Figure 1: Representative loop-induced decays compared to the unsupressed decay modes exploited further in this work.
• Figure 2: Bump-hunt bounds on the flavour-motivated malaphoric $B_3-L_2$ model parameter space for $M_{Z^\prime} = 2,3,4~\text{TeV}$. The region below each contour is sensitive to the 95$\%$ CL. 139 fb$^{-1}$ curves are LHC bounds whereas the 3 and 6 ab$^{-1}$ curves are the projected sensitivities at HL-LHC. For $M_{Z^\prime}=2~\mathrm{TeV}$, the $Z^\prime \rightarrow \tau^+\tau^-$ constraints are shown as an additional channel; higher-mass $\tau^+\tau^-$ limits are not included due to the absence of cross-section upper bounds. $Z^\prime \rightarrow \mu^+\mu^-$ curves in the left panel are in the $\hat{\epsilon} > 0$ region. The region of 95$\%$CL resulting from the global fit in Ref. Allanach:2024ozu is shown as the coloured region.
• Figure 3: 95% CL sensitivity for a di-jet invariant mass bump hunt at the FCC-hh for 100 TeV collisions at an integrated luminosity $\mathcal{L} = 30~\text{ab}^{-1}$. The entire 95$\%$ CL global-fit parameter space can be probed.
• Figure 4: Representative Feynman diagrams contributing to the $Z$ pole forward-backward asymmetry at $e^+ e^-$ colliders (a) and helicity asymmetries (b) at a comparable order in the $M_{Z^\prime}^{-2}$ expansion.
• Figure 5: Projected FCC-$ee$ constraints on the model parameter space from the oblique $T$-parameter, and four fermion operators corresponding to $Z^\prime$ mediated $e^+ e^- \to q \bar{q}$ ($2 \ell 2 q$ operators), and $e^+ e^- \to \ell^+ \ell^-$ ($4 \ell$ operators) processes. The shaded regions (excluding the global fit region) represent the FCC-ee sensitive regions at $95 \%$ confidence level.