& = & 
\frac{ J_{ |c-1/2| } \left( m_n z_v\right) }
{ Y_{|c-1/2| } \left( m_n z_v \right) } 
= \frac{ J_{|c-1/2| \mp 1} \left( m_n z_h \right)  } 
{ Y_{ |c-1/2| \mp 1} \left( m_n z_h \right) } ~,
\label{keyequation}\end{aligned}$$ with upper(lower) signs for $c>-1/2$ ($c<-1/2$). The left-handed $(-,+)$ states satisfy, $$\begin{aligned}
\beta_n & = & 
\frac{ J_{ |c+1/2| } \left( m_n z_h \right) }
{ Y_{|c+1/2| } \left( m_n z_h \right) } 
= \frac{ J_{|c+1/2| \mp 1} \left( m_n z_v \right)  } 
{ Y_{ |c+1/2| \mp 1} \left( m_n z_v \right) } ~.
\label{keyequation2}\end{aligned}$$

Armed with these wave functions, we compute the coupling of these potentially light first KK modes of the custodial partners to the first KK mode of the gluon. The results for both chiralities are presented in Figure \[fig:gffmpcoup\], and indicate that one chirality is always very strongly coupled, $g \sim 6 g_S$, irrespective of the value of $c$.

  -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
   ![\[fig:gffmpcoup\] Coupling of the First KK mode of the gluon to the light KK modes of the custodial partners of the right-handed up-type quark as a function of the bulk mass parameter $c$. The left panel shows the left-handed coupling whereas the right panel 