Probing Flavor-Violating Higgs Decays in the Type-III Two-Higgs-Doublet Model at the LHC and HL-LHC

We present a comparative collider study of three flavor-violating Higgs signatures in the Type-III Two-Higgs-Doublet Model (\ddHmIII) at $\sqrt{s}=14$~TeV: $pp\to H\to t\bar{c}(\bar{t}c)$, $pp\to H^{\pm }\to c\bar{b}(\bar{c}b)$, and $pp\to H^{\pm }\to t\bar{b}(\bar{t}b)$. Using a common cut-based analysis and realistic detector simulation, we identify a clear phenomenological hierarchy. The neutral mode and the heavy charged mode emerge as the most robust signatures, containing parameter regions that already exceed the $5\sigma$ benchmark at an integrated luminosity of $300{\text{fb}}^{-1}$. In contrast, the light charged channel $H^{\pm }\to c\bar{b}$ is considerably more sensitive to the event-selection strategy because of large QCD backgrounds, although one competitive benchmark survives. Our results single out the neutral and heavy charged flavor-violating channels as the most promising targets for discovery-oriented searches and for constraining the \ddHmIII\ parameter space at the LHC and HL-LHC. All quoted significances are purely statistical and do not include systematic uncertainties.