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Single production of $X_{\pm 5/3}$ and $Y_{\mp 4/3}$ vectorlike quarks at the LHC

Two triplet vector-like quarks (VLQs) with hypercharges of $Y=2/3, -1/3$ and one singlet scalar boson are embedded in the standard model (SM) to resolve the 750 GeV diphoton excess. The constraints on the tree-level Higgs- and $Z$-mediated flavor-changing neutral currents are discussed in detail. Besides the resolution of excess, it is found that the signal strength of diphoton Higgs decay can have a $10\%$ deviation from the SM prediction and that the upper limits of the branching ratios for rare top-quark decays are $BR(t\to c (h, Z)) < (6.8, 0.48) \times 10^{-5}$. We find that the production cross section of a single VLQ by electroweak processes is larger than that of VLQ-pair by QCD processes. To explore the signals of the heavy VLQs at the LHC, we throughly analyze the production of single $X_{\pm 5/3}$ and $Y_{\mp 4/3}$ via $q_i q'_j$ annihilations in $pp$ collisions at $\sqrt{s}=13$ TeV. It is found that the electroweak production cross sections for $d X_{5/3}$, $u Y_{-4/3} $, and $d Y_{4/3} $ channels with $m_X=m_Y=1$ TeV can be $84.3$, $72.3$, and $157.8$ fb, respectively; and the dominant decay modes are $X_{5/3} \to (c,t) W^+$ and $Y_{-4/3} \to (s,b) W^-$. With adopting kinematic cuts, the significance for $pp\to d W^+ t$ channel can be over $5σ$.