## Top Quark Decay to a Higgs and a Light Quark Operator

### Motivation

Neutral Flavor Changing couplings are absent in the Standard Model at tree level. Moreover, at next-to-leading order they are supressed by the GIM mechanism. Therefore a detection of such processes would be a strong hint at new physics. Here we focus Neutral Flavor Change mediated by the Higgs boson following [@zhang2013top].

The lowest dimensional operators compatible with the symmetries of the Standard Model are the following six-dimensional operators (for a comprehensive list of all six-dimensional operators compatible with Standard Model symmetries consult [@grzadkowski2010dimension]):

- chromomagnetic operator $O_{uG}$

- dimension-six Yukawa interaction $O_{u\phi}$

- To each (1,3) operator corresponds a (3,1) operator where the flavors are reversed.

- To each operator (e.g. (1,3)) corresponds another where the up quark is exchanged for a charm quark (e.g. (2,3)).

- The hermitian conjugates of the above-mentioned operators contributing with the opposite chirality.

Where we denoted:

- $\phi$ is the Higgs doublet;
- $Q$ and $q$ are respectively the 1st (or 2nd) and the 3th left-handed quark doublet;
- $u$ (or $c$) and $t$ are the right-handed quarks;
- $\bar{\phi} = i \sigma
^{2 \phi$ } - $y_t = \sqrt{2}\frac{m_t}{v}$ the top quark Yukawa coupling.

The complete Lagrangian takes the form:

where $\Lambda$ is the new physics energy scale, $O_i$ is for the various six-dimensional operators in consideration and $c_i$ are relative couplings.

The normalizations for the six-dimensional operators were chosen such that for
any new SM-like vertices the ratio of the new couplings to the SM couplings is
of the form $c_i\frac{m_t^{2}{\Lambda}2}$.

### Implementation and Validation

The implementation is a straightforward transcription of the Lagrangian into
`FeynRules` format as no new fields need to be defined.

The model was validated using the build-in checks in `FeynRules` and
`MadGraph5`. Moreover the decay widths were confirmed through `MadGraph5` and
compared to the analytical results.