Discovery prospects of a singly-charged scalar at $μ$TRISTAN

TL;DR

The paper investigates the discovery prospects of a singly-charged scalar Δ^+ within the Type-II seesaw model through associated Δ^+W^+ production at a future $\mu^+\mu^+$ collider (μTRISTAN) at $\sqrt{s}=2$ TeV. Leveraging the lepton-flavor-violating decays $Δ^+ \to e^+/\tau^+$, the authors propose a background-free signature and perform a collider study showing robust $S/\sqrt{S}$ significance (up to 5$\sigma$) across a wide $m_{Δ^+}$ range, for $m_{\nu,\text{lightest}}=0.05$ eV; for $m_{\nu,\text{lightest}}=0.001$ eV the 5$\sigma$ reach is partial. They demonstrate that cross-section shapes alone do not distinguish Normal vs Inverted hierarchy, but that the final-state lepton flavor distributions can differentiate hierarchies when $m_{\nu,\text{lightest}} \leq 0.02$ eV, highlighting a pathway to probe the neutrino-mass ordering with detector-capable LFV signatures. Overall, the study underscores the μ^+μ^+ collider’s potential to discover Δ^+ in the Type-II seesaw scenario and to probe neutrino mass hierarchy via flavor signatures, given suitable detector performance and systematics considerations.

Abstract

In this article, we study the associated production of a singly-charged ($Δ^+$) scalar along with a $W^+$ boson in the newly proposed $μ^+μ^+$ collider (also known as $μ$TRISTAN) at $\sqrt{s} = 2~$ TeV. Such a singly-charged scalar is naturally accommodated in an extremely well-motivated neutrino mass model, namely, the Type-II seesaw model. This model, beside providing a viable explanation of neutrino mass generation, also allows for lepton flavor violating (LFV) processes. Since LFV processes are not allowed in the Standard Model (SM), we focus on the discovery prospect of the singly-charged scalar in the Type-II seesaw model at $μ$TRISTAN through a LFV process, owing to the advantage of this process being free of any SM background. Additionally, this article also proposes a method to indicate if the underlying theory follows a Normal or an Inverted hierarchy depending on the distribution of lepton flavors in the final state.

Figures (19)

• Figure 1: Generic Feynman diagram for signal
• Figure 2: Feynman diagram for lepton flavor violating (LFV) signal processes chosen to get rid of any SM background.
• Figure 3: Cross-Section for the process $\mu^+ \mu^+ \longrightarrow \Delta^+ W^+$ for masses of $\Delta^+$ varying between 101 and 1901 GeV.
• Figure 4: Branching Ratio of $\Delta^+$ for masses of $\Delta^+$ varying between 101 and 1901 GeV.
• Figure 5: Branching Ratio of $\Delta^+$ for masses of the lightest neutrino varying between 0.05 and 0.001 eV for a fixed $m_{\Delta^+} = 101~$ GeV.