Z' models for the LHCb and g-2 muon anomalies

Abstract: We revisit a class of Z' explanations of the anomalies found by the LHCb collaboration in $B$ decays, and show that the scenario is tightly constrained by a combination of constraints: (i) LHC searches for di-muon resonances, (ii) pertubativity of the Z' couplings; (iii) the $B_s$ mass difference, and (iv) and electro-weak precision data. Solutions are found by suppressing the Z' coupling to electrons and to light quarks and/or by allowing for a Z' decay width into dark matter. We also present a simplified framework where a TeV-scale Z' gauge boson that couples to standard leptons as well as to new heavy vector-like leptons, can simultaneously accommodate the LHCb anomalies and the muon g-2 anomaly.

$Z^{\prime}$ Models for the LHCb and $g-2$ Muon Anomalies

The paper presents a meticulous examination of $Z^{\prime}$ models as potential explanations for anomalies observed in $B$ decays by the LHCb collaboration and the long-standing muon $g-2$ anomaly. It delves into the complex interplay between these anomalies and constraints from various experimental and theoretical sources.

Overview of $Z^{\prime}$ Models

$Z^{\prime}$ models extend the Standard Model (SM) by including an additional ${\rm U}(1)' $ gauge symmetry, positing a new $Z^{\prime}$ gauge boson that interacts with SM particles. This framework is motivated by discrepancies between observed and predicted phenomena, suggesting new physics beyond the SM. Notably, the paper targets anomalies in the $B \to K^{(*)} \mu^+ \mu^-$ decay processes and discrepancies in the measured and theoretical values of the muon anomalous magnetic moment $(g-2)$.

Constraints on $Z^{\prime}$ Models

The exploration of $Z^{\prime}$ models is bounded by several experimental constraints:

1. Di-muon Resonance Searches: LHC searches for di-muon resonances provide substantial constraints on the parameter space of potential $Z^{\prime}$ explanations, especially concerning the coupling strengths to muons and quarks.

2. $B_s$ Mass Difference: The mass difference $\Delta M_{B_s}$ offers additional limits, which exclude models where the $Z^{\prime}$ contributes too heavily to this observable unless appropriately weighted by coupling constants.

3. Perturbativity: To maintain theoretical consistency, the $Z^{\prime}$ must not have excessively large couplings that would violate perturbative unitarity.

4. Electroweak Precision Data: The impacts on precision electroweak measurements are examined, particularly the implications on the vectorial couplings to leptons.

Implications and Extensions

The analysis indicates that accommodating both the LHCb and $g-2$ anomalies simultaneously is challenging under tight constraints. Solutions require suppressing $Z^{\prime}$ couplings to light quarks and electrons or introducing new decay channels into dark matter, effectively reducing visible resonance signatures.

An exciting facet introduced in the paper is an extended model incorporating vector-like leptons, which modifies the muon interactions with the $Z^{\prime}$. This addition paves the way for resolving the $g-2$ anomaly without conflicting with other constraints, offering intriguing phenomenological avenues, including novel LHC signatures.

Future Directions

The paper suggests that further exploration into non-standard decay pathways and broader parameter scans in light of new experimental data, particularly from ongoing LHC operations, could validate or invalidate these models. Importantly, the interplay between direct collider searches and indirect precision measurements will continue to serve as a critical foundation for probing the validity of $Z^{\prime}$ models in explaining observed anomalies.

In summary, by stringently analyzing $Z^{\prime}$ models under current constraints, this paper contributes significantly to our understanding of potential extensions to the Standard Model, emphasizing the need for precise measurement and innovative model-building to uncover the nature of possible new physics.