^{1}

^{*}

^{1}

^{2}

We study the decay
t → cγ with flavor-changing neutral interactions in scalar sector of the type III Two Higgs Doublet Model (THDM-III) with mixing between neutral scalar fields as a result of considering the most general scalar potential. The branching ratio of the decay
*Br* (
t → cγ) is calculated as function of the mixing parameters and masses of the neutral scalar fields. We obtain a
*Br*
(t → cγ)
of the order of 10
^{−8} for the considered regions of the mixing parameters. Finally, one upper bound for the possible events is estimated to be n=18 by assuming an expected luminosity of the order of 300 fb
^{−1}.

A sensitive test for new physics is the processes of the top quark due to large mass. The predictions of the Standard Model (SM) for the top quark in flavor changing neutral (FCN) transitions are strongly suppressed [^{−5} - 10^{−6} may be detectable, depending on the signal. Any hint for new top quark physics at LHC would motivate further study at the next generation of collider experiments [

Within 2HDM-I where only one Higgs doublet generates all gauge and fermion masses, while the second doublet only knows about this through mixing, and thus the Higgs phenomenology will share some similarities with the SM, although the SM Higgs couplings will now be shared among the neutral scalar spectrum. The presence of a charged Higgs boson is clearly the signal beyond the SM. Within 2HDM-II, one also has natural flavor conservation [

In the present work, we calculate the the BR for the decay

Given

where

Now, the most general

where we choose a basis in which

In the literature, the sign of the vev is chosen positive for convenience, however it could also take negative sign. The mass of the gauge fields are proportional to the square of the vev. The fermions have proportional masses to the vev then to be defined positively would take Yukawa couplings negative. In this way we would obtain consistent models and equal prediction regardless of the sign of the vev.

In Equation (2), the phase of

in the interaction basis can be written as

denote the real part. The third neutral scalar field in the interaction basis defined as

where R can be written down as:

and

Higgs bosons

For the THDM with no CP violation in scalar sector the

where

where

In order to study the rare top decay we are interested in up-type quarks fields. By using Equations (5), the interactions between neutral Higgs bosons and fermions can be written in the form of the 2HDM type II with additional contributions which arise from Yukawa couplings

where

and

The fermion spinors are denoted as

We are interested in the contributions of the flavor changing neutral scalar interactions to the rare top decay

where

with

The above expression contains too many free parameters of the model, such as the masses Last expression contains several free parameters of the THDM, such as the masses of neutral Higgs bosons and the mixing parameter

First we will discuss the free parameters involved in the process. The Yukawa couplings in the THDM-III are responsible for the FCNSI as shown the expression (9). One possible option to suppress these FCNSI is obtained by assuming an ansantz for the Yukawa couplings. We take into account the ansantz proposed by Cheng-Sher [

THDM type III in Yukawa Lagrangian has two sectors: in one of them the couplings are proportional to the masses of the fermions and does not generate flavor changing. The other sector generates flavor changing at tree level. This situation occurs because the two Yukawa matrices can not be diagonalized simultaneously with one rotation. The mass of the fermions and the factor that generates flavor changing are a linear combination of the two Yukawa matrices of the Lagrangian. Depending on this linear combination to generate the fermion masses, THDM type I or THDM type II can be generated plus additional terms that produce the flavor changes. In general THDM type III produces four different types of Lagrangians making linear combinations of type I and II for the up and down quarks. Then, in THDM type III we can choose the sector without flavor changing as type II and add the respective flavor changing that appear in this model. For this reason, a sector of parameters THDM type II in the various processes analyzed in the literature as

For the masses of neutral scalar

and

Figures 1-3 show the behavior of the branching ratio for

The obtained

From 2015 to 2017, the experiment is expected to reach 100 fb^{−1} of data with a energy of the center of mass of 14 TeV. In the year 2021, it is expected to reach a luminosity of the order of 300 fb^{−1} of data. Experiments with this luminosity could find evidence of new physics beyond SM. Then, Run 3 in LHC could

observe events for the flavor changing neutral processes, which can be explained in a naive form as^{−1} and ^{−8},

Last experimental results have obtained a bound for these branching ratios such as

This work is supported in part by PAPIIT Project IN113916, Sistema Nacional de Investigadores (SNI) in México, and PIAPI 1628 Project. R. M. thanks to COLCIENCIAS for the financial support.

Gaitán-Lozano, R., de Oca, J.H.M. and Martinez, R. (2017) Rare Top Decay t ® cg in General THDM- III. Journal of Quantum Information Science, 7, 57-66. https://doi.org/10.4236/jqis.2017.72006