Changes between Version 2 and Version 3 of Octet_tcgg


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Timestamp:
Nov 3, 2015 4:57:31 PM (2 years ago)
Author:
druekeel
Comment:

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  • Octet_tcgg

    v2 v3  
    1212== Description of the Model ==
    1313
    14 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.  In this model, the third generation quarks couple differently than the light quarks under an extended
     14The
    1515{{{
    1616#!latex
    17 $SU(3)_1 \times SU(3)_2$
     17$SU(3)_1 \times SU(3)_2 \to SU(3)_C$
    1818}}}
    19 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 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
     19breaking induced by the expectation value of the
    2020{{{
    2121#!latex
    22 $b \to \gamma$.
     22({$\bf 3,\bar{ 3}$})
    2323}}}
    24 The extended color symmetry is broken down to
     24scalar field Phi generates color-octet and color-singlet scalars. The most general renormalizable potential for Phi is:
    2525{{{
    2626#!latex
    27 $SU(3)_C$
     27$V(\Phi)=-m^2_{\Phi}\text{Tr}(\Phi\Phi^\dagger) -\mu (\text{det }\Phi+\text{H.c.})+\frac{\xi}{2}\left[ \text{Tr}(\Phi\Phi^\dagger) \right]^2+\frac{k}{2}\text{Tr}(\Phi\Phi^\dagger\Phi\Phi^\dagger) \ ,$
    2828}}}
    29 by the (diagonal) expectation value,
     29where
    3030{{{
    3131#!latex
    32 $\langle \Phi \rangle \propto u \cdot {\cal I}$,
     32$\text{det } \Phi = \frac{1}{6}\epsilon^{ijk}\epsilon^{i'j'k'}\Phi_{ii'}\Phi_{jj'}\Phi_{kk'} \ ,$
    3333}}}
    34 of a scalar field Phi which transforms as a
     34and where, without loss of generality, one can choose mu > 0. Assuming
    3535{{{
    3636#!latex
    37 $\bf 3, \bar{3}$
     37$m^2_\Phi >0$,
    3838}}}
    39 under the color gauge structure.  It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale.
    40 
    41 Breaking the color symmetry induces a mixing between the
     39Phi acquires a (positive) diagonal expectation value:
    4240{{{
    4341#!latex
    44 $SU(3)_1$ \rm{and} $SU(3)_2$
     42$\langle \Phi \rangle = u \cdot \mathcal{I} \,.$
    4543}}}
    46 gauge fields
     44The Phi expansion around the vacuum gives:
    4745{{{
    4846#!latex
    49 $A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$,
     47$\Phi=u+\frac{1}{\sqrt{6}}\left(\phi_R+i\phi_I\right)+\left(G^a_H+iG^a_G\right)T^a \ ,$
    5048}}}
    51 which is diagonalized by a rotation determined by
     49where
    5250{{{
    5351#!latex
    54 $\cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$,
     52$\phi_R$, $\phi_I$
    5553}}}
    56 where 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
     54are singlets under SU(3)_C Additionally,
    5755{{{
    5856#!latex
    59 $G^{*}_{\mu}=\cos\omega A^{1}_{\mu} - \sin\omega A^{2}_{\mu} \qquad M_{G^{*}} = \frac{g_s u}{\sin\omega \cos\omega}.$
     57$G^a_G$, $a=1,\dots,8$,
    6058}}}
    61 In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group.
     59are the Nambu-Goldstone bosons associated with the color-symmetry breaking,  which will be eaten by the
    6260{{{
    6361#!latex
    64 $g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$
     62$G^a_H$
    6563}}}
    66 as well as a new weak-doublet of vector-like quarks, transform as
     64color octets.
     65
     66$G_H$ can be produced in pairs through its interactions with gluons:
    6767{{{
    6868#!latex
    69 $({\bf 3,1})$
     69$\frac{g^2_s}{2}f^{abc}f^{ade}G^b_{\mu}G^{\mu d}G^c_H G^e_H +g_s f^{abc} G^a_{\mu} G^b_H \partial^{\mu} G^c_H \ ,$
    7070}}}
    71 under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as
     71or it can be produced singly via gluon-gluon fusion. This occurs at one-loop order through the cubic interaction
    7272{{{
    7373#!latex
    74 $({\bf 1,3})$
     74$\frac{\mu}{6} d_{abc} G^a_H G^b_H G^c_H   \,,$
    7575}}}
    76 The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by
     76which arises from the
    7777{{{
    7878#!latex
    79 $g_s \left(\cot\omega J^{\mu}_1 - \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$
     79$\mu(\det\Phi+\text{H.c.})$
    8080}}}
     81term in the potential; where
     82{{{
     83#!latex
     84$d_{abc}$
     85}}}
     86is the SU(3) totally symmetric tensor. The single production of GH can be described by the effective coupling
     87{{{
     88#!latex
     89$-\frac{1}{4} C_{ggG} d_{abc} G^a_{\mu\nu} G^{\mu\nu b} G^c_H$
     90}}}
     91with
     92{{{
     93#!latex
     94$C_{ggG}=\sqrt{\frac{1}{6}}\frac{\alpha_s}{\pi }\frac{\mu}{M^2_{G_H}}\left(\frac{\pi^2}{9}-1\right) \ .$
     95}}}
     96Note that single production is suppressed by a factor
     97{{{
     98#!latex
     99$(\pi^2/9 -1)^2$,
     100}}}
     101which is an accidental suppression factor coming from the loop.
     102Above the threshold for decays into a single top quark, GH has two main decay modes: the decay into gluons, which occurs at loop-level similar to single coloron production, and the flavor-violating decay into tc. The corresponding rates are:
     103{{{
     104#!latex
     105$\Gamma \left[G_H \to (\bar{c}_L t_R +\bar{t}_R c_L )\right] =\left(V_{cb}\right)^2 \frac{M_{G_H}}{16 \pi} \frac{m^2_t}{u^2}\left(1-\frac{m^2_t}{M^2_{G_H}}\right)^2 \,, $ \newline
     106$\Gamma \left[G_H \to gg \right]=\frac{5 \alpha^2_s}{1536 \pi^3}\frac{\mu^2}{M_{G_H}}\left(\frac{\pi^2}{9}-1\right)^2 \,.$
     107}}}
     108We set u=mu (the stability of the potential forbids mu>u); and consider for simplicity the set of
     109{{{
     110#!latex
     111$(M_{G_H}, \mu)$
     112}}}
     113values that give a 50% GH decay into tc and 50% into gg. GH is a very narrow resonance, with a width of the order of 10^-4 GeV.
    81114
    82 == Note ==
     115Various Feynman Diagrams for GH processes discussed in [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] are shown below:
    83116
    84 Need to reread and make sure everything is the same as the paper and that nothing for KKg has been carried over.
     117[[Image(Coloron.png)]]
     118
     119[[Image(Colorong.png)]] [[Image(Colorong2.png)]]
     120
     121[[Image(ColoronDouble1.png)]] [[Image(ColoronDouble2.png)]]
     122 
     123See more details in
     124
     125* [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2]
     126* [http://arxiv.org/pdf/1412.3094.pdf 1412.3094]
     127
     128== Model Files ==
     129
     130* [attachment:proc_card_mg5.dat proc_card]: for generation of 500 GeV coloron (place in Cards/)
     131* [attachment:run_card.dat run_card]: for generation of 500 GeV coloron (place in Cards/)
     132* [attachment:Octet-tcgg-new.zip Octet-tcgg]: the model
     133
     134== Generation specifics ==
     135   
     136In [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2], the samples were generated with the mass as the scale, dsqrt_q2fact1, and dsqrt_q2fact2 in the run_card.  These samples were also generated without the pre-included !MadGraph cuts as demonstrated in the run_card.dat for 500 GeV mass included above.  The specific generations run were
     137{{{
     138p p > GH, GH > b c~ l+ vl @1 GHT=1 QED=2
     139p p > GH, GH > b~ c l- vl~ @2 GHT=1 QED=2
     140}}}
     141Specific masses can be generated using the appropriate model from the Octet-tcgg zip file.