A Kaluza-Klein Gluon Model

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 ​1409.7607v2 analyzes the tc decay as depicted below: 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

$SU(3)_1 \times SU(3)_2$

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. The model reproduces the CKM mixing and generates flavor-changing neutral currents (FCNCs) from non-standard interactions. Due to the specific structure of the model, dangerous FCNCs are naturally suppressed and a large portion of the model parameter space is allowed by the data on meson mixing process and on

$b \to s\gamma$.

The model has the color gauge structure

$SU(3)_1 \times SU(3)_2$

The extended color symmetry is broken down to

$SU(3)_C$

by the (diagonal) expectation value,

$\langle \Phi \rangle \propto u \cdot {\cal I}$,

of a scalar field Phi which transforms as a

$(\bf 3, \bar{3})$

under the color gauge structure. It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale, u>>v.

Breaking the color symmetry induces a mixing between the

$SU(3)_1$ \rm{and} $SU(3)_2$

gauge fields

$A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$,

which is diagonalized by a rotation determined by

$\cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$,

where g_s is the QCD strong coupling and g_1, g_2 are the SU(3)_1 and SU(3)_2 gauge couplings, respectively. The mixing diagonalization reveals two color vector boson mass eigenstates: the mass-less SM gluon and a new massive color-octet vector boson G* given by

$G^{*}_{\mu}=\cos\omega A^{1}_{\mu} - \sin\omega A^{2}_{\mu} \qquad M_{G^{*}} = \frac{g_s u}{\sin\omega \cos\omega}.$

In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group.

$g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$

as well as a new weak-doublet of vector-like quarks, transform as

$({\bf 3,1})$

under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as

$({\bf 1,3})$

The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by

$g_s \left(\cot\omega J^{\mu}_1 - \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$

The G* can be produced at the LHC by quark-antiquark fusion determined by the G* coupling to light quarks

$g_s \tan\omega$

Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance.

The G* decay widths are:

$\Gamma[G^{*} \to t\bar t] = \frac{g^2_s}{24\pi} M_{G^{*}}\cot^2\omega \sqrt{1-4 \frac{m^2_t}{M^2_{G^{*}}}} (1+2\frac{m^2_t}{M^2_{G^{*}}}),$ \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

$\Gamma[G^{*} \to t_L \bar c_L]=\Gamma[G^{*} \to c_L \bar t_L]\simeq \left(V_{cb}\right)^2 \frac{g^2_s}{48\pi} M_{G^{*}} \left( \cot\omega+\tan\omega \right)^2,$

where

$V_{cb}=0.0415$

is the CKM matrix element. Note here that G* FCNCs are induced by the mixing among left-handed quarks generated by the exchange of heavy vector-like quarks. This mixing is controlled by the 3x3 matrices U_L and D_L in the up- and down-quark sectors, respectively. In particular, the

$G* \to tc$

flavor violating decay is controlled by the

$(U_L)_{23}$

element. The CKM mixing matrix is given by

$V_{CKM}=U^{\dagger}_L D_L$.

At first order in the mixing parameters,

$(U_L)_{23}\equiv V_{cb} - (D_L)_{23}$.

The non-diagonal elements of D_L are strongly constrained by the data on

$b\to s \gamma$. 

So

$(D_L)_{23}$

is thus forced to be small and, as a consequence,

$(U_L)_{23}\simeq V_{cb}$.

See more details in

• ​1409.7607v2
• ​1412.3094

Model Files

• proc_card​: for generation of 500 GeV KKg (place in Cards/)
• run_card​: for generation of 500 GeV KKg (place in Cards/)
• kkg_FV​: the model and parameter cards for specific mass generations

Generation specifics

In ​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, 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).