A scalar-extended U(1) L mu-L tau explanation of the LUX-ZEPLIN 248 keV excess

The gist The recently observed dark matter (DM) nuclear recoil event at an energy of 248 ± 23 (stat.) ± 23 (syst.) keV at the LUX-ZEPLIN (LZ) experiment, favoring an inelastic scattering interpretation, has motivated various beyond the Standard Model (BSM) scenarios aimed at explaining the observed excess

Model Extension and Mechanism

The work explores an extension of the U(1)Lµ−Lτ-gauged model with two additional complex scalar fields, Φ and S, carrying charges −1 and +2, respectively, under the U(1)Lµ−Lτ gauge symmetry<ref:2610.12443#pg3> These charge assignments allow for a trilinear interaction between the two scalar fields, which is crucial for generating the DM mass splitting Following the spontaneous breaking of the U(1)Lµ−Lτ symmetry, with S acquiring a vacuum expectation value and generating a mass for the BSM gauge boson Zµτ, the real and imaginary components of Φ acquire a mass splitting This naturally gives rise to an inelastic DM scattering scenario that can accommodate the LZ excess

Scalar Sector Dynamics

The extended fields are defined such that S carries Qµτ = +2 and Φ carries QΦµτ = −1 under the U(1)Lµ−Lτ symmetry The spontaneous symmetry breaking induced by ⟨S⟩ = (vµτ / √2) leaves an exact residual Z2 symmetry, under which all SM fields are Z2-even, while the scalar Φ, carrying QΦµτ = −1, is rendered Z2-odd This residual symmetry ensures the stability of Φ The mass terms for the DM states ϕ1 and ϕ2 after electroweak symmetry breaking (EWSB) are given by equations (2.10a) and (2.10b) The DM mass splitting between ϕ1 and ϕ2 can be written as δm = mϕ1 − mϕ2, which in the small splitting approximation is given by δm = 2/√2µvµτ/mϕ2

Phenomenological Constraints

The U(1)Lµ−Lτ model connects to a variety of phenomenological signatures, including tree-level couplings of Zµτ to muons (µ), taus (τ), and their corresponding neutrinos, while couplings to the remaining SM fermions arise only at the one-loop level and are consequently suppressed The characteristic charge assignment leads to constraints from observables in the µ-τ sector, including contributions to the anomalous magnetic moments of the muon and tau The tree-level couplings to muon and tau neutrinos can also be probed through neutrino trident production Conversely, loop-suppressed couplings to other SM fermions significantly weaken constraints from indirect detection and existing collider searches

Direct Detection Analysis

The analysis focuses on DM-nucleus scattering, employing the liquid-xenon detector framework characteristic of the LUX-ZEPLIN (LZ) experiment The differential nuclear recoil rate for elastic DM–nucleus scattering can be expressed as dR/dER = ρ0 mϕ2mA / vmin(ER) d3v fE(v, t) dσA / dER The minimum velocity required to produce a recoil energy ER is given by v el min(ER) = s mA ER2/2µ2ϕ2A, with µϕ2A = mϕ2mA/mϕ2 + mA The differential DM-nucleus elastic scattering cross-section (σϕ2N) is given by σ SI ϕ2N = f2N µ2 ϕ2Nm2/4πv2m2/ϕ2 cos α λh1ϕ2ϕ2 m2/h1 + sin α λh2ϕ2ϕ2 m2/h2!2

Inelastic Scattering and Likelihood Analysis

The generic vmin can be written as vmin = v el min + δm/√2mAER, where δm > 0 corresponds to endothermic (up-scattering) and δm < 0 corresponds to exothermic scattering processes The differential DM-nucleus (ϕ2 − N) scattering cross section is given by dσA ϕ2N→ϕ1N dER d3v = M2 ϕ2N→ϕ1N 32πm2ϕ2mN v2/mA2πv2 Ze ϵγZµτ gµτ m2/Zµτ + 2mAER/n2 F(ER) The expected number of events is obtained by integrating the recoil spectrum over the relevant recoil energy window To statistically quantify the observed excess within the parameter space of our model, we perform a likelihood analysis comparing the predicted nuclear recoil spectrum with the observed event rate For a single observable event at ER = 248 keV, the likelihood function reduces to L (θ) = dN(θ) dER / ER=248 keV e−N(θ)

Conclusion and Prospects

The framework provides a well-motivated realisation of inelastic DM, in which the charge assignments of the extended scalar sector naturally allow the small mass splitting required to account for the observed recoil The viable parameter space accommodating the LZ excess remains largely unconstrained by existing experimental searches, leaving significant room for further exploration Importantly, the parameter space identified in this work can be tested with upcoming LZ data, which can provide crucial evidence for or against our inelastic nuclear recoil interpretation The framework is extremely promising for future validations of the LZ excess and the underlying nature of the dark sector

Metastability of Dark Partner

The heavier real scalar ϕ1 can decay into the leptons and the lightest partner ϕ2, depending on kinetic accessibility If the splitting is smaller than twice the electron mass (δm < 2me), then possible decays only into neutrinos (νµ and ντ) The three-body decay width is strongly suppressed i.e. Γϕ1 ∝ (δm)5, potentially resulting in a lifetime comparable to or longer than the BBN timescale A surviving ϕ1 population can inject non-thermal neutrinos during BBN, modifying primordial light-element abundances The shaded regions in Figure 13 represent the parameter space in which the ϕ1 decay corresponds to a lifetime longer than the corresponding epoch indicated in the legend

Future Probes

Future muon colliders offer a promising avenue for probing the U(1)Lµ−Lτ model due to its tree-level coupling of the initial state muons to the Zµτ boson The presence of the Zµτ boson can lead to deviations in dilepton production processes such as µ+µ− → τ+τ− To estimate the impact of the U(1)Lµ−Lτ model on these processes without performing a detailed collider simulation, we quantify the deviations from the SM prediction through the signal strength (SS), defined as SS = σ − σSM/σSM The sharp increase in the SS corresponds to resonant production of the Zµτ mediator, providing a handle on the sensitivity to the model parameters at future muon colliders

Summary of Findings

The analysis demonstrates that smaller values of vµτ allow for relatively larger mass splittings, δm As the mass splitting increases, smaller values of vµτ are favoured The viable parameter space accommodating the LZ excess remains largely unconstrained by existing experimental searches The framework explored in this work provides a well-motivated realisation of inelastic DM, in which the charge assignments of the extended scalar sector naturally allow the small mass splitting required to account for the observed recoil

Figure Interpretation

In Figure 5, we show the relic abundance satisfied parameter space points in the mϕ2−gµτ plane for different mZµτ/mϕ2 benchmarks while other parameters, mh2 = 2.2 mϕ2, δm = 150 keV, sin α = 0.

1. textbfIncreased Likelihood Analysis Sophistication for Single Events: The improved system can perform a two-parameter analysis by varying two parameters while fixing all others to arbitrary values, using the likelihood ratio test statistic ∆χ2 = −2 h ln L (⃗θ) − ln L (ˆθ) i to determine 1σ and 2σ confidence regions, as described in Eq. (4.25) and Equation (78). This moves beyond asymptotic assumptions to provide a more robust determination of confidence regions using Markov chain Monte Carlo or toy Monte Carlo studies for better statistical rigor, as noted in the text on page 20.

2. textbfEnhanced Kinematic Threshold Modeling for Inelastic Scattering: The system can precisely model the kinematic threshold for endothermic inelastic scattering by calculating vmin(ER) = velmin(ER) + δm / √2mAER (Eq. 4.12). This allows it to accurately translate the DM mass splitting into observable recoil energy windows, differentiating between elastic and inelastic regimes based on whether "δm > 0 corresponds to endothermic (up-scattering) and δm < 0 corresponds to exothermic scattering processes" (Page 17).

3. textbfConstraint Mapping for Parameter Space Navigation: The improved system can navigate the complex parameter space defined by relic density, DM stability, and experimental limits by mapping constraints onto specific planes like the mϕ2 − vµτ plane (Figure 11). It can identify regions where limits become ineffective, such as when the entire white region probed by elastic DD lies within the parameter space excluded by the DM stability condition, simplifying constraint interpretation.

4. textbf Discovery Potential Assessment for Future Facilities: The system can quantitatively assess the sensitivity of future experiments by quantifying the Signal Strength (SS), defined as SS = σ − σSM / σSM (Eq. 5.1) for dilepton production processes at muon colliders, showing how the sharp increase in the SS corresponds to resonant production of the Zµτ mediator. This enables a direct comparison between theoretical predictions and experimental reach in collider settings.

5. textbf Cosmological Consistency Verification: The system can assess constraints from BBN and CMB by examining the decay width expressions, specifically noting that for small mass splittings relevant to DM inelastic DD, the three-body decay width is strongly suppressed i.e. Γϕ1 ∝ (δm)5, which relates to modifying the Hubble expansion rate (∆Neff) and, if the neutrino energy exceeds the 782 keV threshold, directly driving charged-current reactions that alter the neutron-to-proton ratio (Page 28).

The recently observed dark matter (DM) nuclear recoil event at an energy of 248 plus or minus 23,(stat.) plus or minus 23,(syst.), keV at the LUX-ZEPLIN (LZ) experiment, favoring an inelastic scattering interpretation, has motivated various beyond the Standard Model (BSM) scenarios aimed at explaining the observed excess. In particular, this provides an opportunity to probe models that naturally accommodate inelastic DM scattering. In this work, we explore one such possibility by extending the U(1) L μ-L τ model with two complex scalar fields, Φ and S, carrying charges-1 and +2, respectively, under the U(1) L μ-L τ gauge symmetry. These charge assignments allow a trilinear interaction between the two scalar fields, which is crucial for generating the DM mass splitting. Following the spontaneous breaking of the U(1) L μ-L τ symmetry, with S acquiring a vacuum expectation value and generating a mass for the BSM gauge boson Z μτ, the real and imaginary components of Φ acquire a mass splitting. This naturally gives rise to an inelastic DM scattering scenario that can accommodate the LZ excess. We perform a likelihood-based assessment of the sensitivity of the model parameters to the observed event while consistently accounting for other relevant phenomenological constraints. Finally, we discuss the prospects for probing the viable parameter space at future experiments.