Higgs decay mediated by top-quark with flavor-changing neutral scalar interactions

We explore the flavor-changing parameters mediated by a Higgs boson within the THDM-III context. In particular, the $h\to t^* c$ processes, and check the high suppression for the FC in the THDM-III context for the low $t_\beta$ parameters. Our exploration in the $\chi_{ij}^{u}-\chi_{ij}^{d}-$parameter space shows the allowed regions for different $t_\beta^{}$ values. We explored different modes for Higgs decays, considered the experimental constraints to get scattering plots for the FC parameters and some relevant decay modes. We expect future results to figure out the FC and its implications in the scalar sector.


Introduction
Different experiments have examined the Standard Model observables which have good agreement with the theoretical results. Currently LHC explores the nature at energy scale of order TeV s and the SM works very well to analyze the structure of the matter. However we have some questions to solve: the matter-antimatter asymmetry, the CP violation and flavorchanging neutral currents (FCNC) mediated by gauge and scalar bosons. In this document, we shall discuss the last one where the neutral scalar boson can change the fermion flavor.
This letter is organized as follows: section 2 shows the models and methods in the THDM-III context, section 3 we expose a results for the h → t * c process and section 4 contains the conclusions.

Models and Methods
We shall consider the THDM-III where the most general potential is [7] In a general way, the Yukawa sector for the THDM-III is given by [8] L T HDM −III Where the (2) is the Lagrangian density for the fermion-fermion-φ; and φ = A 0 , H 0 , h 0 which are the pseudoscalar, heavy Higgs and standard model Higgs, and the superscript (zero) labels the mass eigenstates.
One can rewrite the Yukawa couplings as because we explore a simple model where the flavor-changing is due to the χ i f -parameters, and it is simple if we reduce the number of those parameters, which are associated to the Yukawa couplings; namely where the m i and m j are the fermion masses and χ f ij are the dimensionless parameters that will probe the flavor-changing mediated by scalar bosons.
We explore the THDM-III because it is possible to have mixing between the fermion flavors at tree level. For the purpose of this paper, we introduce B → X s γ processes considering Γ(B → X s γ) Γ(b → sγ), since the non-perturbative effects are small [9]. We consider the constraints coming from t → cV, b → sγ, h → l i l j , h → γZ, to show the correlation between branching ratios b → sγ and h → γZ, and found excluded regions (e. g. figs. 3-4). Figs. 3 and 4 show a correlation between parameters of the model, considering different constraints coming from t and b-quark and h decays [10]. The process that is represented in fig. 2 was proposed by ref. [2] to explore the flavor-changing modes.

Results
Our analysis shows that it could be possible to have FC if we consider the quark type separately, since the parameter space is wider for the u-quark type. We find that if t β  4 ) show that χ d ij − t β is more suppressed than the χ u ij − t β for the lowest t β values. In figs 5-6, the dark regions represent the highly allowed region. We generated randomly the parameter set, as follow, −200 ≤ χ u,d ij ≤ 200, 0 ≤ t β ≤ 100, 350 GeV ≤ m H,H ± ≤ 1000 GeV, as well considering the experimental bounds for the t, b and h branching ratios at tree and one-loop level.
If we consider the W − decays to ν l l then we obtain Br(h → llqq) of order 10 −4 , therefore our results are interesting if we compare to the experimental results Br(h → llqq) ∼ 10 −2 − 10 −3 as is shown in ref. [11] for m h = 125 GeV . We found Br(h → t * c) ∼ 10 −3 for the 1 t β 20 ( fig. 7), which is a very interesting channel to explore in the LHC or the next generation of colliders. Fig. 7 shows an interesting channel (Br(h → t * c) ) to probe new physics and we expect the     Br (h → γ Z) Figure 6. Scattering plot for the branching ratios of the processes b → sγ versus h → γZ.
next experimental results to test the THDM-III as the simplest SM extension.

Conclusions
We have explored the h → t * c processes, and checked the high suppression considering FC mediated by Higgs boson. Our exploration in the χ u ij − χ d ij −parameter space showed the allowed regions for different t β values (see figs. 3-4). Besides we explore the different modes for Higgs decays to (see figs. 5-6). Our results showed Br(h → µτ ) 10 −5 and Br(h → γZ) ∼ 10 −6 as long as Br(b → sγ) 10 −4 as is shown in figs. 5-6, those engaging values for exploring in LHC. Besides we predicted Br(h → t * c) ∼ 10 −3 for 1 t β 20, this a feasible channel to explore our model in the LHC.