Changes between Version 1 and Version 2 of kkg_FV


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Timestamp:
Oct 28, 2015 4:15:57 PM (2 years ago)
Author:
druekeel
Comment:

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  • kkg_FV

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    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.