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Exploring top quark FCNC within 2HDM type III in association with flavor physics

The top quark flavor changing neutral current (FCNC) process is an excellent probe to search for new physics in top sector since the Standard Model expectation is extremely suppressed. We explore Higgs-mediated top quark FCNC, focusing on $H$-$t$-$c$ Yukawa coupling $λ_{ct}$ within the general two Higgs doublet model. After electroweak symmetry breaking the top quark FCNC couplings are included in the charged Higgs Yukawa sector so that they contribute to various processes in flavor physics. To probe $λ_{ct}$, we study anomalous single top production and the same sign top pair production at the LHC in association with flavor physics from the tree-level processes $B\to D^{(*)}τν$, $B\to τν$ as well as from the loop-level processes $B_d \to X_s γ$, $B_{d,s}-{\overline B}_{d,s}$ mixing. We perform combined analysis of all the constraints regarding the fine-tuning argument to fit the data and discuss future prospect. The recently updated measurements on $B\to D^{(*)}τν$ still prefer large $λ_{ct}$, but we show that the current bound on the same sign top pair production at the LHC gives the most significant upper bound on $λ_{ct}$ to be less than $10\sim30$ depending on neutral heavy Higgs masses. We also find that for the given upper bound on $λ_{ct}$, $B\to D^{(*)}τν$ put significant lower bound on $H$-$τ$-$τ$ Yukawa coupling, and the bound is proportional to the charged Higgs mass.