Probing Inert Triplet Model at a multi-TeV muon collider via vector boson fusion with forward muon tagging

This study investigates the potential of a multi-TeV Muon Collider (MuC) for probing the Inert Triplet Model (ITM), which introduces a triplet scalar field with hypercharge $Y=0$ to the Standard Model. The ITM stands out as a compelling Beyond the Standard Model scenario, featuring a neutral triplet $T^0$ and charged triplets $T^\pm$. Notably, $T^0$ is posited as a dark matter (DM) candidate, being odd under a $Z_2$ symmetry. Rigorous evaluations against theoretical, collider, and DM experimental constraints corner the triplet scalar mass to a narrow TeV-scale region, within which three benchmark points are identified, with $T^\pm$ masses of 1.21 TeV, 1.68 TeV, and 3.86 TeV, for the collider study. The ITM's unique $TTVV$ four-point vertex, differing from fermionic DM models, facilitates efficient pair production through Vector Boson Fusion (VBF). This characteristic positions the MuC as an ideal platform for exploring the ITM, particularly due to the enhanced VBF cross-sections at high collision energies. To address the challenge of the soft decay products of $T^\pm$ resulting from the narrow mass gap between $T^\pm$ and $T^0$, we propose using Disappearing Charged Tracks (DCTs) from $T^\pm$ and Forward muons as key signatures. We provide event counts for these signatures at MuC energies of 6 TeV and 10 TeV, with respective luminosities of 4 ab$^{-1}$ and 10 ab$^{-1}$. Despite the challenge of beam-induced backgrounds contaminating the signal, we demonstrate that our proposed final states enable the MuC to achieve a $5\sigma$ discovery for the identified benchmark points, particularly highlighting the effectiveness of the final state with one DCT and one Forward muon.