Zeros of amplitude in the associated production of photon and leptoquark at $$\varvec{e}$$ e - $$\varvec{p}$$ p collider

Though various extensions of the Standard Model with higher gauge group predict the existence of leptoquarks, none of them has been observed yet at any of the colliders. In this paper, we study the prospect of several past and future $$e$$\n -\n $$p$$\n colliders like HERA, LHeC and FCC-he to detect them through radiation amplitude zero. We find that the leptoquarks showing zeros in the tree-level single-photon amplitudes at $$e$$\n -\n $$p$$\n collider lie within the complementary set of those exhibiting zeros at e-\n $$\\gamma $$\n collider. We present a PYTHIA-based analysis for HERA, LHeC and FCC-he (run II) to detect the leptoquarks with masses 70 GeV, 900 GeV and 1.5 TeV (2.0 TeV) respectively through radiation amplitude zero.