Single production of vectorlike top partner decaying to Wb in the leptonic channel at ep colliders in the littlest Higgs model with T-parity

In the littlest Higgs model with T-parity (LHT), we study the single production of a vectorlike top partner with the subsequent decay T+ -> Wb in the leptonic channel at the ep colliders. Focusing on the LHeC (root s = 1.98 TeV) and FCC-eh (root s = 5.29 TeV), we investigate the observability of the single top partner production with the unpolarized and polarized electron beams, respectively. As a result, the statistical significance can be enhanced by the polarized electron beams. Under the current constraints, the search for T+ in the Wb channel at the LHeC cannot provide a stronger limit on the top partner mass. By contrast, the search for the T+ in this channel at the FCC-eh with polarized e(-) beams can exclude the top partner mass up to 1350 GeV, 1500 GeV, and 1565 GeV with integrated luminosities of 100 fb(-1), 1000 fb(-1), and 3000 fb(-1) at the 2 sigma level, which is an improvement with respect to the current indirect searches and the LHC direct searches. Furthermore, we also give an extrapolation to the high-luminosity LHC with root s = 14 TeV and L = 3000 fb(-1). Our results show that the LHT model is still a natural solution to the shortcomings of the electroweak and scalar sector although it has been constrained severely.