[Paper Review] The CDF W-mass, muon g-2, and dark matter in a $U(1)_{L_μ-L_τ}$ model with vector-like leptons

Quan Zhou, Xiao-Fang Han|arXiv (Cornell University)|Apr 27, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a $U(1)_{L_\mu - L_\tau}$ gauge model with vector-like leptons to simultaneously explain the CDF $W$-boson mass anomaly, the muon $g-2$ discrepancy, and viable dark matter. It shows that a large mass splitting between vector-like leptons $E_1$ and $E_2$, along with asymmetric mixing parameters $s_L$ and $s_R$, is required to fit the $W$-mass and $g-2$ data, while dark matter relic density is achieved via $Z'$ or $S$ pair production or co-annihilation when the lightest vector-like lepton is near the dark matter mass.

ABSTRACT

We study the CDF $W$-mass, muon $g-2$, and dark matter observables in a local $U(1)_{L_μ-L_τ}$ model in which the new particles include three vector-like leptons ($E_1,~ E_2,~ N$), a new gauge boson $Z'$, a scalar $S$ (breaking $U(1)_{L_μ-L_τ}$), a scalar dark matter $X_I$ and its partner $X_R$. We find that the CDF $W$-mass disfavors $m_{E_1}= m_{E_2}={m_N}$ or $s_L=s_R=0$ where $s_{L(R)}$ is mixing parameter of left (right)-handed fields of vector-like leptons. A large mass splitting between $E_1$ and $E_2$ is favored when the differences between $s_L$ and $s_R$ becomes small. The muon $g-2$ anomaly can be simultaneously explained for appropriate difference between $s_L$ $(m_{E_1})$ and $s_R$ $(m_{E_2})$, and some regions are excluded by the diphoton signal data of the 125 GeV Higgs. Combined with the CDF $W$-mass, muon $g-2$ anomaly and other relevant constraints, the correct dark matter relic density is mainly obtained in two different scenarios: (i) $X_IX_I o Z'Z',~ SS$ for $m_{Z'}(m_S)

Motivation & Objective

• To address the $7\sigma$ discrepancy in the CDF $W$-boson mass measurement compared to the Standard Model.
• To explain the $4.2\sigma$ anomaly in the muon anomalous magnetic moment ($g-2$) using new physics beyond the Standard Model.
• To realize a viable dark matter candidate $X_I$ with correct relic density within the same model framework.
• To constrain the model using direct LHC searches for $2\ell + E_T^{\text{miss}}$ events and Higgs diphoton data.
• To identify viable parameter regions where all three anomalies—$W$-mass, $g-2$, and dark matter—can be simultaneously satisfied.

Proposed method

• Introduces a local $U(1)_{L_\mu - L_\tau}$ gauge symmetry with a new $Z'$ gauge boson, a scalar $S$ for spontaneous symmetry breaking, and a complex scalar $X$ for dark matter.
• Adds three vector-like lepton states: a singlet $N$, a doublet $E$, and a primed state $E'$, with chiral mixing parameters $s_L$ and $s_R$.
• Computes oblique $S$, $T$, $U$ parameters via loop corrections from vector-like leptons to explain the CDF $W$-mass shift.
• Evaluates contributions to muon $g-2$ via $Z'$ and scalar $X$ exchange, dependent on $s_L$ and $s_R$ mixing.
• Calculates dark matter relic density via $X_I X_I \to Z'Z'$, $SS$, and co-annihilation processes involving $E_1$, $E_2$, $N$, and $X_R$.
• Applies constraints from LHC $2\ell + E_T^{\text{miss}}$ searches and the 125 GeV Higgs diphoton signal to exclude certain parameter regions.

Experimental results

Research questions

• RQ1 Can a $U(1)_{L_\mu - L_\tau}$ model with vector-like leptons simultaneously explain the CDF $W$-mass anomaly and the muon $g-2$ discrepancy?
• RQ2 What are the required mass splittings and mixing parameters ($s_L$, $s_R$) in the vector-like lepton sector to fit both the $W$-mass and $g-2$ data?
• RQ3 Which dark matter annihilation or co-annihilation mechanisms can produce the correct relic density under the combined constraints?
• RQ4 How do direct LHC searches for $2\ell + E_T^{\text{miss}}$ events constrain the masses of vector-like leptons and the dark matter candidate?
• RQ5 Which regions of the parameter space are excluded by the 125 GeV Higgs diphoton signal or other experimental bounds?

Key findings

• The CDF $W$-mass measurement disfavors degenerate masses for $E_1$, $E_2$, and $N$, or vanishing mixing parameters $s_L = s_R = 0$.
• A large mass splitting between $E_1$ and $E_2$ is favored when the differences in $s_L$ and $s_R$ become small.
• The muon $g-2$ anomaly can be explained for appropriate differences between $s_L$ (linked to $m_{E_1}$) and $s_R$ (linked to $m_{E_2}$), but regions with large $Z'$ couplings are excluded by Higgs diphoton data.
• The correct dark matter relic density is achieved in two main scenarios: (1) $X_I X_I \to Z'Z'$ or $SS$ when $m_{Z'}$ or $m_S < m_{X_I}$, and (2) co-annihilation when $\min(m_{E_1}, m_{E_2}, m_N, m_{X_R})$ is nearly degenerate with $m_{X_I}$.
• LHC direct searches for $2\ell + E_T^{\text{miss}}$ events impose strong bounds: for $\min(m_{E_1}, m_{E_2}) - m_{X_I} > 300$ GeV, the lightest vector-like lepton mass must exceed 500 GeV.
• Dark matter mass $m_{X_I}$ can be as low as 100 GeV if $\min(m_{E_1}, m_{E_2}) - m_{X_I} < 60$ GeV or $> 400$ GeV, depending on the co-annihilation regime.