Constraints on Vector-Like Top Dipole Interactions from Top-Associated Photon Measurements at the LHC

Vector-like top partners with electric charge $+2/3$ are predicted in many extensions of the Standard Model and are actively searched for at the LHC through their electroweak decays $T\to Wb$, $Zt$, and $Ht$. More general scenarios, however, allow dipole interactions that induce radiative decays $T\to t\gamma$ and $T\to tg$. We reinterpret precision measurements of top-associated photon production to constrain such dipole operators. This approach provides a complementary probe to traditional resonance searches, which rely on direct reconstruction of heavy states, by instead exploiting distortions in precision observables. Using unfolded differential cross sections for $t\bar{t}\gamma$ production measured by CMS and the fiducial $t\bar{t}\gamma\gamma$ cross section reported by ATLAS, we derive constraints on the electromagnetic and chromomagnetic dipole couplings of a vector like $T$ quark within an effective field theory framework. We present limits in terms of the effective couplings $c_{t\gamma}$ and $c_{tg}$, as well as the corresponding branching fractions $BR(T \to t\gamma)$ and $BR(T \to tg)$, for masses in the range $500~GeV \le m_T \le 2.0~TeV$. For $m_T = 500~GeV$, the analysis reaches sensitivity to the electromagnetic dipole coupling as small as $c_{t\gamma} \simeq 0.005~TeV^{-1}$ in the gluon dominated scenario $B_{\gamma} = 0.1$, while the sensitivity degrades to $O(1)~TeV^{-1}$ at $m_T = 2.0~TeV$. We find that the $t\bar{t}\gamma$ and $t\bar{t}\gamma\gamma$ measurements provide complementary sensitivity, probing different regions of parameter space and lifting degeneracies between electromagnetic and chromomagnetic dipole interactions. These results demonstrate that precision measurements of top-associated photon final states provide a powerful and complementary probe of vector-like quarks in scenarios where radiative decays dominate.