Search for Vector-Like Singlet Top ($T$) Quark in a Future Muon-Proton ($μp$) Collider at $\sqrt{s} = 5.29, 6.48,$ and $9.16$ TeV using Advanced Machine Learning Architectures

TL;DR

This work investigates single production of a vector-like top quark $T$ at a future μp collider with $\sqrt{s}_{\mu p} = 5.29$, 6.48, and 9.16 TeV, focusing on the $T\to Wb$ decay in hadronic and leptonic channels across $m_T = 2$–5 TeV. It combines detector-level simulations (MadGraph5, Pythia, Delphes) with TMVA-based multivariate classifiers (BDT, BDTG, MLP, Likelihood) to maximize signal discrimination against SM backgrounds. A key finding is the crossover between hadronic and leptonic channels: hadronic channels excel at intermediate $m_T$ due to larger BRs, while leptonic channels offer higher purity at high $m_T$, with Asimov significance $Z_A$ showing a systematic-limited ceiling at high luminosity. At $\sqrt{s}=9.16$ TeV, the study demonstrates discovery reach up to $m_T \sim 4$–$5$ TeV depending on $g^*$ and channel, underscoring the μp collider’s potential to probe VLQs beyond the reach of the LHC. The results motivate staged discovery strategies and further exploration of systematic uncertainties, alternative decay channels, and collider infrastructure for a μp facility.

Abstract

In this work, we explore the discovery potential of Vector-Like Singlet Top quarks ($T$) at a future $μp$ collider with center-of-mass energies of 5.29, 6.48, and 9.16 TeV, providing a unique environment to probe beyond Standard Model limits. We analyze the $T \to Wb$ decay mode in both fully hadronic ($bjj$) and leptonic ($blν$) final states, offering a multi-channel assessment of $T$-quark sensitivity across a mass range of 2 to 5 TeV. Our methodology employs multivariate classifiers such as Boosted Decision Trees (BDTs) and Multi-Layer Perceptrons (MLP) to optimize signal-to-background discrimination in complex final states. The results demonstrate that the 9.16 TeV benchmark acts as a definitive discovery machine; even with 100 fb$^{-1}$ of data, the statistical significance exceeds $5σ$ up to 4 TeV masses. We identify a crossover effect where hadronic channels provide superior reach at intermediate masses due to higher branching ratios, while leptonic channels offer robustness at 5 TeV where purity limits detection. Incorporating a 20\% systematic uncertainty via Asimov significance ($Z_A$), we quantify the transition from fluctuation-dominated to systematic-dominated regimes at high luminosities. At 3000 fb$^{-1}$, regions with $g^{*} \in [0.20, 0.50]$ and $m_T$ up to 4 TeV are discoverable via the hadronic channel with MLP, and regions with $g^{*} \in [0.10, 0.50]$ and $m_T$ up to 5 TeV are accessible through the leptonic channel with BDT, highlighting the collider's potential to probe new physics beyond the Standard Model.

Figures (11)

• Figure 1: Representative leading-order (LO) Feynman diagram for the single production of a vector-like singlet top quark in the hadronic channel at a $\mu p$ collider: $\mu^- p \to \nu_\mu\, T\, b$, followed by $T \to W^+ b$ and $W^+ \to j j$.
• Figure 2: Representative leading-order (LO) Feynman diagram for single production of a vector-like singlet top quark in the leptonic channel at a $\mu p$ collider: $\mu^- p \to \nu_\mu\, T\, b$, followed by $T \to W^+ b$ and $W^+ \to e^+ \nu_e$.
• Figure 3: The Hadronic and Leptonic Signal efficiency $\epsilon$(%) versus $m_T$ evaluated at the collider energies of $\sqrt{s}=5.29$, $6.48$, and $9.16$ TeV. It can be observed that the efficiency monotonically decreases for both channels at higher mass points. It is clear that the signature of Leptonic Signal is relatively clear across all collider energies; whereas, the Hadronic channel gets high jet signatures at higher center of mass energy due to jet substructure algorithm.
• Figure 4: The Output Distribution Score and Overtraining Evaluation of all ML Classifiers (BDTs, MLP, Likelihood) for Hadronic Analysis after Multivariate Training conducted at $\sqrt{s} = 9.16TeV$ for $m_{T}= 3000GeV$.
• Figure 5: The Output Distribution Score and Overtraining Evaluation of all ML Classifiers (BDTs, MLP, Likelihood) after the Multivariate Training in Leptonic Analysis conducted at $\sqrt{s} = 9.16TeV$ for $m_{T}= 3000GeV$.