Changes between Version 1 and Version 2 of kkg_FV


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Timestamp:
10/28/15 16:15:57 (21 months ago)
Author:
druekeel
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  • kkg_FV

    v1 v2  
    1 bla 
     1= A Kaluza-Klein Gluon Model = 
     2 
     3== Authors == 
     4 
     5* Elizabeth Drueke (Michigan State University) 
     6* Joseph Nutter (Michigan State University) 
     7* Reinhard Schwienhorst (Michigan State University) 
     8* Natascia Vignaroli (Michigan State University) 
     9* Devin G. E. Walker (SLAC National Accelerator Laboratory) 
     10* Jiang-Hao Yu (The University of Texas at Austin) 
     11 
     12== Description of the Model == 
     13 
     14Colored 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/pdf/1409.7607v2.pdf 1409.7607v2] analyzes the tc decay as depicted below: 
     15[[Image(wiki:KKg.png)]] 
     16In this model, the third generation quarks couple differently than the light quarks under an extended  
     17{{{ 
     18#!latex 
     19$SU(3)_1 \times SU(3)_2$ 
     20}}} 
     21color 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 vector0like 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  
     22{{{ 
     23#!latex 
     24$b \to \gamma$. 
     25}}} 
     26The extended color symmetry is broken down to  
     27{{{ 
     28#!latex 
     29$SU(3)_C$ 
     30}}} 
     31by the (diagonal) expectation value, 
     32{{{ 
     33#!latex 
     34$\langle \Phi \rangle \propto u \cdot {\cal I}$, 
     35}}} 
     36of a scalar field Phi which transforms as a  
     37{{{ 
     38#!latex 
     39$\bf 3, \bar{3}$ 
     40}}} 
     41under the color gauge structure.  It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale. 
     42 
     43Breaking the color symmetry induces a mixing between the  
     44{{{ 
     45#!latex 
     46$SU(3)_1$ \rm{and} $SU(3)_2$ 
     47}}} 
     48gauge fields 
     49{{{ 
     50#!latex 
     51$A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$, 
     52}}} 
     53which is diagonalized by a rotation determined by  
     54{{{ 
     55#!latex 
     56$\cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$, 
     57}}} 
     58where g_s is the QCD strong coupling and g_1 and 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 
     59{{{ 
     60#!latex 
     61$G^{*}_{\mu}=\cos\omega A^{1}_{\mu} - \sin\omega A^{2}_{\mu} \qquad M_{G^{*}} = \frac{g_s u}{\sin\omega \cos\omega}.$ 
     62}}} 
     63In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group.   
     64{{{ 
     65#!latex 
     66$g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$ 
     67}}} 
     68as well as a new weak-doublet of vector-like quarks, transform as  
     69{{{ 
     70#!latex 
     71$({\bf 3,1})$ 
     72}}} 
     73under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as 
     74{{{ 
     75#!latex 
     76$({\bf 1,3})$ 
     77}}} 
     78The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by 
     79{{{ 
     80#!latex 
     81$g_s \left(\cot\omega J^{\mu}_1 - \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$ 
     82}}} 
     83 
     84 
     85G*'s form an extended color group and can be produced at the LHC by quark-antiquark fusion determined by the G* coupling to light quarks  
     86{{{ 
     87#!latex 
     88$g_s \tan\omega$ 
     89}}} 
     90Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance.  
     91 
     92The G* decay widths are: 
     93{{{ 
     94#!latex 
     95$\Gamma[G^{*} \to t\bar t] = \frac{g^2_s}{24\pi} M_{G^{*}}\cot^2\omega \sqrt{1-4 \frac{m^2_t}{M^2_{G^{*}}}} (1+2\frac{m^2_t}{M^2_{G^{*}}}),$ \newline 
     96$\Gamma[G^{*} \to b\bar b] = \frac{g^2_s}{24\pi} M_{G^{*}}\cot^2\omega,$ \newline 
     97$\Gamma[G^{*} \to j j] = \frac{g^2_s}{6\pi} M_{G^{*}}\tan^2\omega.$ 
     98}}} 
     99Additionally, the NMFV flavor structure of the model generates a G* to tc flavor violating decay with rate 
     100{{{ 
     101#!latex 
     102$\Gamma[G^{*} \to t_L \bar c_L]=\Gamma[G^{*} \to c_L \bar t_L]\simeq \left(V_{cb}\right)^2 \frac{g^2_s}{48\pi} M_{G^{*}} \left( \cot\omega+\tan\omega \right)^2,$ 
     103}}} 
     104where 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  
     105{{{ 
     106#!latex 
     107$(U_L)_{23}$ 
     108}}} 
     109element. The CKM mixing matrix is given by  
     110{{{ 
     111#!latex 
     112$V_{CKM}=U^{\dagger}_L D_L$. 
     113}}} 
     114At first order in the mixing parameters,  
     115{{{ 
     116#!latex 
     117$(U_L)_{23}\equiv V_{cb} - (D_L)_{23}$. 
     118}}} 
     119The non-diagonal elements of D_L are strongly constrained by the data on  
     120{{{ 
     121#!latex 
     122$b\to s \gamma$. \rm{So } $(D_L)_{23}$ 
     123}}} 
     124is thus forced to be small and, as a consequence,  
     125{{{ 
     126#!latex 
     127$(U_L)_{23}\simeq V_{cb}$. 
     128}}} 
     129 
     130== Note == 
     131 
     132Need to reread and make sure everything is the same as paper.