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 | |
| 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. The analysis in [http://arxiv.org/pdf/1409.7607v2.pdf 1409.7607v2] analyzes the tc decay as depicted below: |
| 15 | [[Image(wiki:KKg.png)]] |
| 16 | In 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 | }}} |
| 21 | 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 |
| 22 | {{{ |
| 23 | #!latex |
| 24 | $b \to \gamma$. |
| 25 | }}} |
| 26 | The extended color symmetry is broken down to |
| 27 | {{{ |
| 28 | #!latex |
| 29 | $SU(3)_C$ |
| 30 | }}} |
| 31 | by the (diagonal) expectation value, |
| 32 | {{{ |
| 33 | #!latex |
| 34 | $\langle \Phi \rangle \propto u \cdot {\cal I}$, |
| 35 | }}} |
| 36 | of a scalar field Phi which transforms as a |
| 37 | {{{ |
| 38 | #!latex |
| 39 | $\bf 3, \bar{3}$ |
| 40 | }}} |
| 41 | under the color gauge structure. It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale. |
| 42 | |
| 43 | Breaking the color symmetry induces a mixing between the |
| 44 | {{{ |
| 45 | #!latex |
| 46 | $SU(3)_1$ \rm{and} $SU(3)_2$ |
| 47 | }}} |
| 48 | gauge fields |
| 49 | {{{ |
| 50 | #!latex |
| 51 | $A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$, |
| 52 | }}} |
| 53 | which 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 | }}} |
| 58 | 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 |
| 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 | }}} |
| 63 | In 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 | }}} |
| 68 | as well as a new weak-doublet of vector-like quarks, transform as |
| 69 | {{{ |
| 70 | #!latex |
| 71 | $({\bf 3,1})$ |
| 72 | }}} |
| 73 | under 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 | }}} |
| 78 | The 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 | |
| 85 | G*'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 | }}} |
| 90 | Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance. |
| 91 | |
| 92 | The 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 | }}} |
| 99 | Additionally, 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 | }}} |
| 104 | where 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 | }}} |
| 109 | element. The CKM mixing matrix is given by |
| 110 | {{{ |
| 111 | #!latex |
| 112 | $V_{CKM}=U^{\dagger}_L D_L$. |
| 113 | }}} |
| 114 | At first order in the mixing parameters, |
| 115 | {{{ |
| 116 | #!latex |
| 117 | $(U_L)_{23}\equiv V_{cb} - (D_L)_{23}$. |
| 118 | }}} |
| 119 | The 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 | }}} |
| 124 | is thus forced to be small and, as a consequence, |
| 125 | {{{ |
| 126 | #!latex |
| 127 | $(U_L)_{23}\simeq V_{cb}$. |
| 128 | }}} |
| 129 | |
| 130 | == Note == |
| 131 | |
| 132 | Need to reread and make sure everything is the same as paper. |