= A Kaluza-Klein Gluon Model with FCNC Decay to a Single Top Quark =

This model allows for FCNC interactions of the Kaluza-Klein gluon and in particular focuses on the flavor-violating decay of the KKg to a top quark and a charm quark.

== Corresponding Authors ==

* Elizabeth Drueke (Michigan State University)
* Reinhard Schwienhorst (Michigan State University)
* Natascia Vignaroli (Michigan State University)

== Other Contributors ==

* Joseph Nutter (Michigan State University)
* Devin G. E. Walker (SLAC National Accelerator Laboratory)
* Jiang-Hao Yu (The University of Texas at Austin)
* R. Sekhar Chivukula (Michigan State University)
* Elizabeth H. Simmons (Michigan State University)

== Description of the Model ==

Colored vector bosons from new strong dynamics, Kaluza-Klein gluons or KKg’s (G*) in a dual 5D picture, have been searched for mainly in the t-tbar channel.  The analysis in [http://arxiv.org/abs/1409.7607v2 1409.7607v2] analyzes the tc decay as depicted below:
[[Image(KKg.png)]]
The benchmark adopted here is a simple renormalizable model of an
extended color gauge sector, which realizes next-to-minimal flavor violation (NMFV). In this model, the third generation quarks couple differently than the light quarks under an extended 
{{{
#!latex
$SU(3)_1 \times SU(3)_2$
}}}
color gauge group.  The mixing between light and third generation quarks is induced by the interactions of all three generation quarks with a set of new heavy vector-like quarks. Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance. 

The G* decay widths are:
{{{
#!latex
$\Gamma[G^{*} \to t\bar t] = \frac{g^2_s}{24\pi} M_{G^{*}}\cot^2\omega \sqrt{1-4 \frac{m^2_t}{M^2_{G^{*}}}} (1+2\frac{m^2_t}{M^2_{G^{*}}}),$ \newline
$\Gamma[G^{*} \to b\bar b] = \frac{g^2_s}{24\pi} M_{G^{*}}\cot^2\omega,$ \newline
$\Gamma[G^{*} \to j j] = \frac{g^2_s}{6\pi} M_{G^{*}}\tan^2\omega.$
}}}
Additionally, the NMFV flavor structure of the model generates a G* to tc flavor violating decay with rate
{{{
#!latex
$\Gamma[G^{*} \to t_L \bar c_L]=\Gamma[G^{*} \to c_L \bar t_L]\simeq \left(V_{cb}\right)^2 \frac{g^2_s}{48\pi} M_{G^{*}} \left( \cot\omega+\tan\omega \right)^2,$
}}}
where 
{{{
#!latex
$V_{cb}=0.0415$
}}}
is the CKM matrix element. 

The default value is
{{{
#!latex
$\cot\omega=2.6$,
}}}
which corresponds to a width of about 25% of the KKg mass.

See more details in
* [http://arxiv.org/abs/1409.7607v2 1409.7607v2]
* [http://arxiv.org/abs/1412.3094 1412.3094]

== Model Files ==

* [attachment:proc_card_mg5.dat proc_card]: for generation of 500 GeV KKg (place in Cards/)
* [attachment:run_card.dat run_card]: for generation of 500 GeV KKg (place in Cards/)
* [attachment:kkg_FV.zip kkg_FV]: the model and parameter cards for specific mass generations

== Generation specifics ==
   
In [http://arxiv.org/abs/1409.7607v2 1409.7607v2], the samples were generated with the KKg mass as the scale, dsqrt_q2fact1, and dsqrt_q2fact2 in the run_card.dat file.  These samples were also generated without !MadGraph cuts as demonstrated in the run_card.dat file for 500 GeV mass included above.  The specific generations run were 
{{{
p p > kkg > b~ c l- vl~ @1
p p > kkg > b c~ l+ vl @2
}}}
To generate the settings for a specific KKg mass, change the param_card.dat in the generation directory to the card of the appropriate mass in the param_cards directory (included as part of the model zip file).  It is important to do this immediately before generating events.

== Related Models ==

* [wiki:modcolorS_trip modcolorS_trip]
* [wiki:Octet_tcgg Octet_tcgg]
* [wiki:Wprime W-prime]