Changes between Version 2 and Version 3 of Octet_tcgg

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Nov 3, 2015 4:57:31 PM (2 years ago)
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 v2 == 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.  In this model, the third generation quarks couple differently than the light quarks under an extended The {{{ #!latex $SU(3)_1 \times SU(3)_2$ $SU(3)_1 \times SU(3)_2 \to SU(3)_C$ }}} 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 breaking induced by the expectation value of the {{{ #!latex $b \to \gamma$. ({$\bf 3,\bar{ 3}$}) }}} The extended color symmetry is broken down to scalar field Phi generates color-octet and color-singlet scalars. The most general renormalizable potential for Phi is: {{{ #!latex $SU(3)_C$ $V(\Phi)=-m^2_{\Phi}\text{Tr}(\Phi\Phi^\dagger) -\mu (\text{det }\Phi+\text{H.c.})+\frac{\xi}{2}\left[ \text{Tr}(\Phi\Phi^\dagger) \right]^2+\frac{k}{2}\text{Tr}(\Phi\Phi^\dagger\Phi\Phi^\dagger) \ ,$ }}} by the (diagonal) expectation value, where {{{ #!latex $\langle \Phi \rangle \propto u \cdot {\cal I}$, $\text{det } \Phi = \frac{1}{6}\epsilon^{ijk}\epsilon^{i'j'k'}\Phi_{ii'}\Phi_{jj'}\Phi_{kk'} \ ,$ }}} of a scalar field Phi which transforms as a and where, without loss of generality, one can choose mu > 0. Assuming {{{ #!latex $\bf 3, \bar{3}$ $m^2_\Phi >0$, }}} under the color gauge structure.  It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale. Breaking the color symmetry induces a mixing between the Phi acquires a (positive) diagonal expectation value: {{{ #!latex $SU(3)_1$ \rm{and} $SU(3)_2$ $\langle \Phi \rangle = u \cdot \mathcal{I} \,.$ }}} gauge fields The Phi expansion around the vacuum gives: {{{ #!latex $A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$, $\Phi=u+\frac{1}{\sqrt{6}}\left(\phi_R+i\phi_I\right)+\left(G^a_H+iG^a_G\right)T^a \ ,$ }}} which is diagonalized by a rotation determined by where {{{ #!latex $\cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$, $\phi_R$, $\phi_I$ }}} 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 are singlets under SU(3)_C Additionally, {{{ #!latex $G^{*}_{\mu}=\cos\omega A^{1}_{\mu} - \sin\omega A^{2}_{\mu} \qquad M_{G^{*}} = \frac{g_s u}{\sin\omega \cos\omega}.$ $G^a_G$, $a=1,\dots,8$, }}} In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group. are the Nambu-Goldstone bosons associated with the color-symmetry breaking,  which will be eaten by the {{{ #!latex $g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$ $G^a_H$ }}} as well as a new weak-doublet of vector-like quarks, transform as color octets. $G_H$ can be produced in pairs through its interactions with gluons: {{{ #!latex $({\bf 3,1})$ $\frac{g^2_s}{2}f^{abc}f^{ade}G^b_{\mu}G^{\mu d}G^c_H G^e_H +g_s f^{abc} G^a_{\mu} G^b_H \partial^{\mu} G^c_H \ ,$ }}} under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as or it can be produced singly via gluon-gluon fusion. This occurs at one-loop order through the cubic interaction {{{ #!latex $({\bf 1,3})$ $\frac{\mu}{6} d_{abc} G^a_H G^b_H G^c_H \,,$ }}} The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by which arises from the {{{ #!latex $g_s \left(\cot\omega J^{\mu}_1 - \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$ $\mu(\det\Phi+\text{H.c.})$ }}} term in the potential; where {{{ #!latex $d_{abc}$ }}} is the SU(3) totally symmetric tensor. The single production of GH can be described by the effective coupling {{{ #!latex $-\frac{1}{4} C_{ggG} d_{abc} G^a_{\mu\nu} G^{\mu\nu b} G^c_H$ }}} with {{{ #!latex $C_{ggG}=\sqrt{\frac{1}{6}}\frac{\alpha_s}{\pi }\frac{\mu}{M^2_{G_H}}\left(\frac{\pi^2}{9}-1\right) \ .$ }}} Note that single production is suppressed by a factor {{{ #!latex $(\pi^2/9 -1)^2$, }}} which is an accidental suppression factor coming from the loop. Above 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: {{{ #!latex $\Gamma \left[G_H \to (\bar{c}_L t_R +\bar{t}_R c_L )\right] =\left(V_{cb}\right)^2 \frac{M_{G_H}}{16 \pi} \frac{m^2_t}{u^2}\left(1-\frac{m^2_t}{M^2_{G_H}}\right)^2 \,,$ \newline $\Gamma \left[G_H \to gg \right]=\frac{5 \alpha^2_s}{1536 \pi^3}\frac{\mu^2}{M_{G_H}}\left(\frac{\pi^2}{9}-1\right)^2 \,.$ }}} We set u=mu (the stability of the potential forbids mu>u); and consider for simplicity the set of {{{ #!latex $(M_{G_H}, \mu)$ }}} values 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. == Note == Various Feynman Diagrams for GH processes discussed in [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] are shown below: Need to reread and make sure everything is the same as the paper and that nothing for KKg has been carried over. [[Image(Coloron.png)]] [[Image(Colorong.png)]] [[Image(Colorong2.png)]] [[Image(ColoronDouble1.png)]] [[Image(ColoronDouble2.png)]] See more details in * [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] * [http://arxiv.org/pdf/1412.3094.pdf 1412.3094] == Model Files == * [attachment:proc_card_mg5.dat proc_card]: for generation of 500 GeV coloron (place in Cards/) * [attachment:run_card.dat run_card]: for generation of 500 GeV coloron (place in Cards/) * [attachment:Octet-tcgg-new.zip Octet-tcgg]: the model == Generation specifics == In [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 {{{ p p > GH, GH > b c~ l+ vl @1 GHT=1 QED=2 p p > GH, GH > b~ c l- vl~ @2 GHT=1 QED=2 }}} Specific masses can be generated using the appropriate model from the Octet-tcgg zip file.