Changes between Version 2 and Version 3 of Octet_tcgg
 Timestamp:
 Nov 3, 2015 4:57:31 PM (3 years ago)
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Octet_tcgg
v2 v3 12 12 == Description of the Model == 13 13 14 Colored vector bosons from new strong dynamics, KaluzaKlein gluons or KKg’s (G*) in a dual 5D picture, have been searched for mainly in the ttbar channel. In this model, the third generation quarks couple differently than the light quarks under an extended14 The 15 15 {{{ 16 16 #!latex 17 $SU(3)_1 \times SU(3)_2 $17 $SU(3)_1 \times SU(3)_2 \to SU(3)_C$ 18 18 }}} 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 flavorchanging neutral currents (FCNCs) from nonstandard 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 on19 breaking induced by the expectation value of the 20 20 {{{ 21 21 #!latex 22 $b \to \gamma$. 22 ({$\bf 3,\bar{ 3}$}) 23 23 }}} 24 The extended color symmetry is broken down to 24 scalar field Phi generates coloroctet and colorsinglet scalars. The most general renormalizable potential for Phi is: 25 25 {{{ 26 26 #!latex 27 $ SU(3)_C$27 $V(\Phi)=m^2_{\Phi}\text{Tr}(\Phi\Phi^\dagger) \mu (\text{det }\Phi+\text{H.c.})+\frac{\xi}{2}\left[ \text{Tr}(\Phi\Phi^\dagger) \right]^2+\frac{k}{2}\text{Tr}(\Phi\Phi^\dagger\Phi\Phi^\dagger) \ ,$ 28 28 }}} 29 by the (diagonal) expectation value, 29 where 30 30 {{{ 31 31 #!latex 32 $\ langle \Phi \rangle \propto u \cdot {\cal I}$,32 $\text{det } \Phi = \frac{1}{6}\epsilon^{ijk}\epsilon^{i'j'k'}\Phi_{ii'}\Phi_{jj'}\Phi_{kk'} \ ,$ 33 33 }}} 34 of a scalar field Phi which transforms as a34 and where, without loss of generality, one can choose mu > 0. Assuming 35 35 {{{ 36 36 #!latex 37 $ \bf 3, \bar{3}$37 $m^2_\Phi >0$, 38 38 }}} 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 39 Phi acquires a (positive) diagonal expectation value: 42 40 {{{ 43 41 #!latex 44 $ SU(3)_1$ \rm{and} $SU(3)_2$42 $\langle \Phi \rangle = u \cdot \mathcal{I} \,.$ 45 43 }}} 46 gauge fields 44 The Phi expansion around the vacuum gives: 47 45 {{{ 48 46 #!latex 49 $ A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$,47 $\Phi=u+\frac{1}{\sqrt{6}}\left(\phi_R+i\phi_I\right)+\left(G^a_H+iG^a_G\right)T^a \ ,$ 50 48 }}} 51 wh ich is diagonalized by a rotation determined by49 where 52 50 {{{ 53 51 #!latex 54 $\ cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$,52 $\phi_R$, $\phi_I$ 55 53 }}} 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 massless SM gluon and a new massive coloroctet vector boson G* given by 54 are singlets under SU(3)_C Additionally, 57 55 {{{ 58 56 #!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 $G^a_G$, $a=1,\dots,8$, 60 58 }}} 61 In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group.59 are the NambuGoldstone bosons associated with the colorsymmetry breaking, which will be eaten by the 62 60 {{{ 63 61 #!latex 64 $ g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$62 $G^a_H$ 65 63 }}} 66 as well as a new weakdoublet of vectorlike quarks, transform as 64 color octets. 65 66 $G_H$ can be produced in pairs through its interactions with gluons: 67 67 {{{ 68 68 #!latex 69 $ ({\bf 3,1})$69 $\frac{g^2_s}{2}f^{abc}f^{ade}G^b_{\mu}G^{\mu d}G^c_H G^e_H +g_s f^{abc} G^a_{\mu} G^b_H \partial^{\mu} G^c_H \ ,$ 70 70 }}} 71 under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as 71 or it can be produced singly via gluongluon fusion. This occurs at oneloop order through the cubic interaction 72 72 {{{ 73 73 #!latex 74 $ ({\bf 1,3})$74 $\frac{\mu}{6} d_{abc} G^a_H G^b_H G^c_H \,,$ 75 75 }}} 76 The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by 76 which arises from the 77 77 {{{ 78 78 #!latex 79 $ g_s \left(\cot\omega J^{\mu}_1  \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$79 $\mu(\det\Phi+\text{H.c.})$ 80 80 }}} 81 term in the potential; where 82 {{{ 83 #!latex 84 $d_{abc}$ 85 }}} 86 is 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 }}} 91 with 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 }}} 96 Note that single production is suppressed by a factor 97 {{{ 98 #!latex 99 $(\pi^2/9 1)^2$, 100 }}} 101 which is an accidental suppression factor coming from the loop. 102 Above the threshold for decays into a single top quark, GH has two main decay modes: the decay into gluons, which occurs at looplevel similar to single coloron production, and the flavorviolating 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 }}} 108 We 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 }}} 113 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. 81 114 82 == Note == 115 Various Feynman Diagrams for GH processes discussed in [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] are shown below: 83 116 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)]] 122 123 See 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:Octettcggnew.zip Octettcgg]: the model 133 134 == Generation specifics == 135 136 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 preincluded !MadGraph cuts as demonstrated in the run_card.dat for 500 GeV mass included above. The specific generations run were 137 {{{ 138 p p > GH, GH > b c~ l+ vl @1 GHT=1 QED=2 139 p p > GH, GH > b~ c l vl~ @2 GHT=1 QED=2 140 }}} 141 Specific masses can be generated using the appropriate model from the Octettcgg zip file.