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In this work we study the constraints on the anomalous $tq\gamma$ ($q=u$, $c$) couplings by photon-produced leading single top production and single top jet associated production through the main reaction $pp\rightarrow p\gamma p\rightarrow pt\rightarrow pW(\rightarrow\ell \nu_\ell) b+X$ and $pp\rightarrow p\gamma p\rightarrow ptj\rightarrow pW(\rightarrow\ell \nu_\ell) bj+X$ assuming a typical LHC multipurpose forward detectors in a model independent effective lagrangian approach.
- Our results show that: for the typical detector acceptance $0.0015<\xi_1<0.5$, $0.1<\xi_2<0.5$ and $0.0015<\xi_3<0.15$ with a luminosity of 2 $\rm{fb}^{-1}$, the lower bounds of $\kappa_{tq\gamma}$ through leading single top channel (single top jet channel) are 0.0096 (0.0115), 0.0162 (0.0152) and 0.0098 (0.0122), respectively, correspond to $\rm{Br}(t\rightarrow q\gamma)\sim 3\times 10^{-5}$.
- With a luminosity of 200 $\rm{fb}^{-1}$, the lower bounds of $\kappa_{tq\gamma}$ are 0.0031 (0.0034), 0.0051 (0.0047) and 0.0031(0.0038), respectively, correspond to $\rm{Br}(t\rightarrow q\gamma)\sim 4\times 10^{-6}$.
- We conclude that both channels can be used to detect such anomalous $tq\gamma$ couplings and the detection sensitivity on $\kappa_{tq\gamma}$ can be improved.
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