Measuring anomalous $Wtb$ couplings at $e^-p$ collider

We study the accuracy with which the lowest order $CP$ conserving anomalous $Wtb$ couplings in the single top quark production at the proposed large hadron electron collider (LHeC) can be probed. The one dimensional distribution of various kinematic observables at the parton level MC and their asymmetries arising due to the presence of anomalous couplings both in the hadronic and leptonic $W$ decay is examined. \par We find that at 95 \% C.L. the anomalous coupling associated with the left handed vector current can be measured at an accuracy of the order of $\sim 10^{-2}-10^{-3}$, while those associated with the right handed vector and left as well as right handed tensor currents have sensitivity at the order of $\sim 10^{-1}-10^{-2}$ for the systematic uncertainty varying between 10\%-1\% at an integrated luminosity of 100 fb$^{-1}$. A comprehensive analysis of the combined covariance matrix derived from all one dimensional distributions of kinematical observables is used to compute the errors in anomalous couplings.

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