[Paper Review] $b ightarrow s \mu^+ \mu^-$ anomalies and related phenomenology in $U(1)_{B_3 - x_\mu L_\mu - x_ au L_ au}$ flavor gauge models

Pyungwon Ko, Takaaki Nomura+1 more|arXiv (Cornell University)|Feb 16, 2019

Particle physics theoretical and experimental studies73 references9 citations

TL;DR

This paper proposes a U(1)_{B₃−xₘLₘ−xₜLₜ} flavor gauge model to explain the b → sμ⁺μ⁻ anomalies observed in B-meson decays. By assigning lepton-flavor non-universal U(1)X charges—specifically xₘ = −1/3—it generates a TeV-scale Z′ boson that induces a large negative shift in the Wilson coefficient ∆Cₘ⁹ ≈ −1, consistent with LHCb data. The minimal model also accounts for neutrino masses via Type-I seesaw, dark matter through a Dirac fermion, and satisfies constraints from LFV, Bs–B̄s mixing, and relic density.

ABSTRACT

We propose a generation dependent lepton/baryon gauge symmetry, $U(1)_{B_3 - x_\mu L_\mu - x_ au L_ au} \equiv U(1)_X$ (with $x_\mu + x_ au =1$ for anomaly cancellation), as a possible solution for the $b ightarrow s \mu^+ \mu^-$ anomalies. By introducing two Higgs doublet fields, we can reproduce the observed CKM matrix, and generate flavor changing $Z'$ interactions in the quark sector. Thus one can explain observed anomalies in $b o s \ell^+ \ell^-$ decay with the lepton non-universal $U(1)_X$ charge assignments. We show the minimal setup explaining $b o s \ell^+ \ell^-$ anomalies, neutrino masses and mixings and dark matter candidate, taking into account experimental constraints of flavor physics such as charged lepton flavor violations and the $B_s$--$\bar B_s$ mixing. Finally we discuss collider physics focusing on $Z'$ production at the Large Hadron Collider and relic density of our dark matter candidate.

Motivation & Objective

• To explain the persistent b → sμ⁺μ⁻ anomalies in B-meson decays, including the P′₅ and RK/RK* deviations observed by LHCb.
• To construct a minimal, anomaly-free U(1)X gauge model with lepton-flavor non-universal charges that naturally generate the required Z′-mediated FCNCs.
• To unify explanations for b → sμ⁺μ⁻ anomalies, neutrino masses via Type-I seesaw, and a Dirac fermion dark matter candidate within a single framework.
• To constrain the model using experimental limits from charged lepton flavor violation (μ → eγ), Bs–B̄s mixing, and relic density, while ensuring consistency with flavor physics.
• To predict observable signatures at the LHC, including Z′ production in di-lepton and mono-jet + missing energy channels, and assess the viability of the dark matter candidate.

Proposed method

• Introduces a U(1)_{B₃−xₘLₘ−xₜLₜ} gauge symmetry with xₘ + xₜ = 1 to ensure anomaly cancellation, assigning flavor-dependent U(1)X charges to SM fermions.
• Uses two Higgs doublets to generate the realistic CKM matrix, with the second Higgs (Φ₁) carrying U(1)X charge to induce small off-diagonal terms in quark mass matrices.
• Derives the effective Z′-mediated interaction for b → sμ⁺μ⁻ via Z′ exchange, showing that a negative xₘ (e.g., xₘ = −1/3) leads to ∆Cₘ⁹ ≈ −1, matching global fits.
• Constructs the neutrino mass matrix via Type-I seesaw mechanism using two SM singlet scalar fields, with Majorana masses generated through U(1)X symmetry breaking.
• Computes contributions to charged lepton flavor violation (μ → eγ), Bs–B̄s mixing, and Z′ contributions to muon g−2, applying experimental bounds.
• Evaluates Z′ production cross sections at the LHC (pp → Z′ → μ⁺μ⁻, τ⁺τ⁻, νν̄) and relic density of the Dirac fermion dark matter candidate using micrOMEGAs, including resonant annihilation effects.

Experimental results

Research questions

• RQ1 Can a U(1)_{B₃−xₘLₘ−xₜLₜ} gauge model with lepton-flavor non-universal charges explain the b → sμ⁺μ⁻ anomalies, particularly the observed ∆Cₘ⁹ ≈ −1?
• RQ2 How do the Z′ and scalar contributions to Bs–B̄s mixing cancel to satisfy the stringent experimental bound while still explaining the b → sμ⁺μ⁻ anomalies?
• RQ3 What are the constraints from charged lepton flavor violation (μ → eγ) and future μ → e conversion experiments on the model’s parameter space?
• RQ4 Can the model simultaneously account for neutrino masses, a viable Dirac fermion dark matter candidate, and LHC phenomenology?
• RQ5 What are the viable parameter regions for Z′ production at the LHC and dark matter relic density, and how do they constrain the {mZ′, gX} parameter space?

Key findings

• A negative U(1)X charge assignment for muons (xₘ = −1/3) leads to ∆Cₘ⁹ ≈ −1, which is consistent with global fits to LHCb data on P′₅ and RK/RK*.
• The model satisfies the experimental bound on Bs–B̄s mixing only when the Z′ and scalar contributions to the mixing amplitude cancel, requiring fine-tuning of parameters.
• The branching ratio for Z′ → νₜν̄ₜ is approximately 16% of Z′ → νₘν̄ₘ, enabling detection via mono-jet + missing transverse momentum at the LHC.
• Z′ production cross sections are estimated at ~1 fb for mZ′ = 1.5 TeV and gX = 0.6, with di-lepton modes (μ⁺μ⁻, τ⁺τ⁻) constrained by LHC dijet resonance searches.
• The relic density of the Dirac fermion dark matter candidate is consistent with Planck observations (Ωh² = 0.1206 ± 0.0063) in a region where mZ′ ≈ 2mX, due to resonant annihilation via Z′.
• The model is safe from indirect detection constraints (e.g., Fermi-LAT) because the dominant annihilation channel (χχ̄ → Z′ → τ⁺τ⁻) has a cross section well below the gamma-ray limits for mZ′ > 500 GeV.