# Rare top decay and CP violation in THDM

## Abstract

We discuss the formalism of two Higgs doublet model type III with CP violation from CP-even CP-odd mixing in the neutral Higgs bosons. The flavor changing interactions among neutral Higgs bosons and fermions are presented at tree level in this type of model. These assumptions allow the study rare top decays mediated by neutral Higgs bosons, particularly we are interested in . For this process we estimated upper bounds of the branching ratios of the order of for a neutral Higgs boson mass of 125 GeV and , 1.5, 2, 2.5. For the case of the number of possible events is estimated from 1 to 10 events which could be observed in future experiments at LHC with a luminosity of 300 and 14 GeV for the energy of the center of mass. Also we estimate that the number of events for the process in different scenarios is of order of .

## I Introduction

The last results from LHC have confirmed the observation of one scalar particle with mass on the electro-weak scale. The ATLAS atlas125gev () and CMS cms125gev () collaborations have been reported the observation of a new particle with mass of around to 125 GeV. The observation has an important significance of more than 5 standard deviations. Even with this research it is not yet possible for us to name this particle as the Standard Model Higgs boson. However if this result is confirmed by future analysis, it will be one of the greatest discoveries of mankind. On the other hand, the SM is often considered as an effective theory, valid up to an energy scale of , that eventually will be replaced by a more fundamental theory, which will explain, among other things, the physics behind electro-weak symmetry breaking and perhaps even the origin of flavor. Many examples of candidate theories, which range from supersymmetry susyrev1 (); susyrev2 () to strongly interacting models ArkaniHamed:2001nc () as well as some extra dimensional scenarios Chang:2010et (), include a multi-scalar Higgs sector. In particular, models with two scalar doublets have been studied extensively BrancoReport (), as they include a rich structure with interesting phenomenology.

First versions of the two Higgs doublet model (2HDM) are known as 2HDM-I 2hdmI1 (); 2hdmI2 () and 2HDM-II 2hdmII (). These versions involve natural flavor conservation and CP conservation in the potential through the introduction of a discrete symmetry. A general version which is named as 2HDM-III allows the presence of flavor-changing scalar interactions (FCNSI) at a three level 2hdmIII (). There are also some variants (known as top, lepton, neutrino), where one Higgs doublet couples predominantly to one type of fermion BrancoReport (), while in other models it is even possible to identify a candidate for dark matter 2hdm:darkmatter1 (); 2hdm:darkmatter2 (). The definition of all these models, depends on the Yukawa structure and symmetries of the Higgs sector, whose origin is still not known. The possible appearance of new sources of CP violation is another characteristic of these models 2dhmCPV ().

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 Glashow:1976nt (), and its phenomenology will be similar to the 2HDM-I, although in this case the SM couplings are shared not only because of mixing, but also because of the Yukawa structure. The distinctive characteristic of 2HDM-III is the presence of FCNSI, which require a certain mechanism in order to suppress them, for instance one can imposes a certain texture for the Yukawa couplings Fritzsch:1977za (), which will then predict a pattern of FCNSI Higgs couplings 2hdmIII (). Within all those models (2HDM I,II,III) Carcamo:2006dp (), the Higgs doublets couple, in principle, with all fermion families, with a strength proportional to the fermion masses, modulo other parameters.

With higher energy, as planned, the LHC will also become an amazing top factory, allowing to test the top properties, its couplings to SM channels and rare decays roberto:top (). One of the interesting rare decays for the top is , which is a clear signal of new physics. In literature this type of top decay is often known as rare top decay and it could be mediated at three level by neutral gauge bosons in the context of physics beyond SM. For instance, models with additional gauge symmetries introduces an neutral gauge boson which allows the rare top decay Zprime1 (); Zprime5 (); Zprime6 (). The obtained results for branching ratios with flavor changing neutral currents are extremely suppressed due to the mass of additional gauge boson which must be of the order of TeV. However, in the framework of the 2HDM-III these rare top decay are possible at three level through neutral Higgs bosons in the framework of general 2HDM with upper bounds of branching ratio less suppressed.

In this work we discuss the flavor changing neutral Higgs interactions due to Yukawa couplings and a CP violation source from Higgs sector in the framework of 2HDM-III. Our analysis is devoted to the study of decay at tree level with basic goal of identifying effects of new physics. The organization of the paper goes as follows: Section II describes the CP violation source in Higgs sector. The flavor changing interaction between neutral Higgs bosons and fermions are introduced in section III. Section IV contains the analysis of the branching ratio for rare top decay. Finally section 5 we present our conclusion and discussion.

## Ii Neutral Higgs bosons spectrum

Let and denote two complex doublet scalar fields with hypercharge-one. The most general gauge invariant and renormalizable Higgs scalar potential in a covariant form with respect to global transformation is given by oneil ()

(1) |

where and are labels with respect to two dimensional Higgs flavor space. The index conventions means that replacing an unbarred index with a barred index is equivalent to complex conjugation and barred-unbarred indices denote a sum. The most general -conserving vacuum expectation values are

(2) |

where and GeV.

After spontaneous symmetry breaking, an orthogonal transformation is used to diagonalize the squared mass matrix for neutral Higgs fields. The mass-eigenstates of the neutral Higgs bosons are

(3) |

where can be written down as:

(4) |

and , for and . The denote the real parts of the complex scalar field in weak-eigenstate, , whereas is written in terms of the imaginary parts and is orthogonal to the Goldstone boson, such as . The neutral Higgs bosons are defined to satisfy the masses hierarchy given by the inequalities rot (); moretti ().

## Iii Yukawa interactions with neutral scalar-pseudoscalar mixing

Now, we will describe the interactions between fermions and neutral Higgs bosons. The most general structure of the Yukawa interactions for fermions fields can be written as follows:

(5) | |||||

where are the Yukawa matrices. The and denote the left handed fermions doublets meanwhile , , correspond to the right handed singlets. The zero superscript in fermions fields stands for weak eigenstates. After getting a correct spontaneous symmetry breaking by using (2), the mass matrices become

(6) |

where for . The matrices are used to diagonalize the fermions mass matrices and relate the physical and weak states. If general scalar potential is considered, the neutral Higgs fields are CP-even and CP-odd mixing states as we discussed previously. In order to study the rare top decay we are interested in up-quarks and charged leptons fields. By using equations (3), 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 and contain flavor change. In order to simplify the notation we will omit the subscript 1 in Yukawa couplings. Explicitly we write the interactions for up-type quarks and neutral Higgs bosons as

(7) | |||||

meanwhile the interactions for charged leptons and neutral Higgs bosons are

(8) | |||||

The fermion spinors are denoted as and . The down-type quarks are analogous to charged leptons sector. We note that (7) and (8) generalize expressions obtained by rot (); moretti (); roberto1 (); roberto2 (). The CP conserving case is obtained if only two neutral Higgs bosons are mixed with well-defined CP states, for instance for and is the usual limit.

## Iv Rare top decay through neutral Higgs bosons

We assume that the flavor neutral changing Higgs interactions are responsible for rare top decay at tree level. The mass of the lightest physical Higgs boson is identified with the observed particle by ATLAS and CMS with a mass value of the order of 125 GeV, meanwhile the masses of are considered in region of more than 600 GeV. Then, contributions of physical neutral Higgs bosons are neglected in the amplitude for the width of rare top decay and only the contributions of the lightest neutral Higgs boson are taken into account. Therefore, width for rare top decay at tree level is given by

(9) |

where

(10) |

and

(11) | |||||

In the expression for width decay (9) we have used the usual notation for dimensionless parameters, , , , and . We note that can be of the same order as the square of transferred momentum, then our result is computed without approximation in the propagator. By integrating the expression (9) we can estimate the branching ratio for . We use the experimental mean value for full width of the top quark given by GeV and the width of the Higgs field given by GeVwidth-top (). Additionally, we assume that the Yukawa matrices have the structure based in Sher-Cheng ansatz 2hdmIII (); Fritzsch:1977za (), that is, . Therefore, the resulting branching ratio only has dependence on and . The mixing angle is absent in the physical state for . Allowed regions for the parameter space are obtained through the bounds of the , defined by

(12) |

For charged Higgs boson with mass of the order of GeV - GeV, the contains an important contribution from charged Higgs boson at one level loop, which affects the allowed regions for . Thus, it is possible to find allowed values in the parameter space if the parameters and are fixed. A process used to set and charged Higgs boson mass is, for instance, the flavor changing process misiak2012 () that receives a contribution from 2HDM through charged Higgs boson. This contribution is comparable to the contribution of from SM. For small values of this process gives a bound to the charged Higgs boson mass of the order of 300 GeV ref67 (); ref65 (). Contributions from other processes such as , , , and ; set bounds for the mass of and as GeV and .

Therefore, allowed regions f the parameter space are obtained by experimental and theoretical constrains in the framework of the 2HDM type II with CP violation for fixed and . For , GeV and , the - regions are moretti ()

(13) |

and

(14) |

For the same settings but with GeV,

(15) |

In order to reduce - parameter space we consider these regions as an approximation. In addition, we will consider and in the final state. The Figure 1 shows the branching ratio of rare top decay for regions and meanwhile figure 2 is obtained for . For , GeV and the allowed parameter regions in - plane in the framework of 2HDM with potential but softly broken discrete symmetry are Arhrib2012 ()

(16) |

and

(17) |

For the regions are

(18) |

and

(19) |

Finally, for the region is

(20) |

and

(21) |

The figures 3, 4 and 5 show the branching ratio for previous regions. We note that the branching ratio of rare top decay for and GeV is bounded as for any . For and pair in final state we find that with same . If mixing angle is fixed with values greater than , the branching ratio does not vary drastically over all - region; for instance when then . The table 1 contains the upper bounds for the considered regions.

Regions | Upper bound | Events |
---|---|---|

0 | ||

0 | ||

10 | ||

2 | ||

4 | ||

1 | ||

1 | ||

0 | ||

1 |

## V Discussion and conclusion

From 2015 to 2017 the experiment is expected to reach 100 of data with a energy of the center of mass of 14 TeV. In the year 2021 is expected to reach a luminosity of the order of 300 of data. Experiments with this luminosity could find evidence of new physics beyond SM. Then, Run 3 in LHC could observe events for the neutral flavor changing process such that , which can be explained in a naive form as

(22) | |||||

Then, we estimate the number of events using the upper bound for branching ratio with pdg2012 (). The table 1 contains this estimation for the considered regions.

Finally, we compare our result with reported results in others framework, such as effective theories and 2HDM type I or II. Based on (7) we can write the branching ratio for as

(23) | |||||

where is the usual function. We find that with GeV and . Despite the absence of flavor changing neutral Higgs interactions in SM, decay can occur at one loop level. The reported result for the branching ratio is of the order of - for mele (). More recently, in the framework of general 2HDM with CP-even and CP-odd neutral Higgs bosons the branching ratios are estimated as and for GeV and GeV kao2012 (). By using effective operator formalism the flavor changing neutral Higgs interactions are introduced. An upper bound is estimated as for neutral Higgs mass of 125 GeV Craig2012 (). Top decays with effective theories is also studied, for the case of the for GeV are obtained Toscano2010 (). In reference Roberto2005 () has been estimated upper bound for GeV through the one loop contributions of effective flavor changing neutral couplings on the electroweak precision observables in SM. For Yukawa complex couplings and CP effects in 2HDM type III the is predicted by iltan ().

From reference 1205 () fugure 3 can be estimated the branching ratio of the into ’s which is the order of for any value of and . Using this BR and taking into account for different scenarios of models, we obtain

(24) |

which is two order of magnitude bigger than the value obtain for us for different regions of parameters, table 1. The number of events, in the best scenario, at LHC with of luminosity and TeV for the energy of the center of mass is the order of .

## Acknowledgments

This work is supported in part by PAPIIT project IN117611-3, Sistema Nacional de Investigadores (SNI) in México. J.H. Montes de Oca Y. is thankful for support from the postdoctoral DGAPA-UNAM grant. R. M. thanks to COLCIENCIAS for the financial support.

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