Exploring the Top-Higgs FCNC Couplings at Polarized Linear Colliders with Top Spin Observables

We study the nature of the flavor changing neutral couplings of the top quark with the Higgs boson and the up/charm quark in the $t\bar{t}$ production at linear colliders. There are previous bounds on such tqH couplings at both, linear and hadronic colliders, with the assumption that it couples equally to the left and the right handed fermions. In this paper we examine the chirality of the tqH coupling and construct different observables which will be sensitive to it. The kinematics of the emitted q from t $\rightarrow$ qH in $t\bar{t}$ production is discussed and it was found that the polar angle distribution of q is sensitive to the chiral nature of tqH couplings. The observables in the context of top-antitop spin correlations, which are sensitive to new physics in the top decay are considered using different spin-quantization bases. It was found that in particular the off-diagonal basis can be useful to distinguish among the chiral tqH couplings. The sensitivity of the unpolarized ILC in probing the couplings at the 3$\sigma$ level at $\sqrt{s}$ = 500 GeV and L = 500 fb$^{-1}$ is also studied, resulting in predicted BR(t $\rightarrow$ qH) < 1.19 $\times 10^{-3}$. This limit is further improved to BR(t $\rightarrow$ qH) < 8.84 $\times 10^{-4}$ with the inclusion of initial beam polarization of left handed electrons and right handed positrons.