Collider Probes of Four-Lepton Final States in Maximally Flavor-Violating $U(1)_{L_μ-L_τ}$ Model

TL;DR

Charged lepton flavor violation in the muon-tau sector is explored within a maximally flavor-violating $U(1)_{L_\mu-L_\tau}$ model that introduces a $Z'$ boson and scalar triplets. The authors construct the model with mass-coupling relation $m_{Z'}=\tilde{g} v_S$ and flavor-changing $Z'$ interactions in the $\mu-\tau$ sector, supplemented by a type-II seesaw sector to generate neutrino masses. They analyze four-lepton final states at future high-energy muon and electron-positron colliders, computing cross sections, forward-backward asymmetries, and polarization effects, and identifying parameter regions where signals exceed backgrounds. They show that observable cross sections scale with $m_{Z'}$ and $\tilde{g}/m_{Z'}$, while triplet Yukawas are subdominant in viable regions; polarization and $A_{FB}$ provide robust handles for discovery. The results provide concrete guidance for upcoming collider searches of LFV in the $L_\mu-L_\tau$ sector.

Abstract

We investigate the collider signatures of the maximally flavor-violating $U(1)_{L_μ-L_τ}$ model, where a new gauge boson $Z^\prime$ and scalar triplets induce lepton flavor-changing interactions in the $μ$-$τ$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $m_{Z^\prime}$ and the effective parameters $\tilde{g}/m_{Z^\prime}$, while remaining largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $m_{Z^\prime}$, and beam polarization can significantly suppress Standard Model backgrounds while enhancing new physics contributions. We find that over the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results demonstrate that multi-lepton final states are powerful probes of the $U(1)_{Lμ- L_τ}$ framework and offer valuable guidance for future searches at muon and electron-positron colliders.

Figures (8)

• Figure 1: The allowed model parameter spaces in the $\tilde{g}/m_{Z'}$-$y/m_{\Delta}$ plane. Different constraints are indicated using distinct colors: green for $\tau \to \mu\nu\bar{\nu}$; yellow for neutrino trident process; and blue for muon $(g-2)$. Here the red markers denote the selected benchmark points, chosen to represent both typical and extreme parameter ratios of the $Z'$ boson and triplet scalars.
• Figure 2: Representative Feynman diagrams for the four-lepton processes
• Figure 3: (a) The cross section $\sigma(\mu^-\mu^+ \rightarrow \mu^\pm \mu^\mp + \tau^\pm \tau^\mp)$ as a function of $m_{Z'}$ at a muon collider with $\sqrt{s}=3$ TeV. (b) The signal cross-section in the plane $\tilde{g}-m_{Z'}$.
• Figure 4: The forward-backward asymmetry $A_{FB}$ as the function with $m_{Z^\prime}$ for $\tilde{g}=0.1$ with $m_{\Delta}=500$ GeV and $Y_{22}=0.415$.
• Figure 5: (a) The angular distribution at a center-of-mass energy of 3 TeV for different channels. (b) The angular distribution with different collider energies.