| 27 | | 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 vector-like 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 |
| 28 | | {{{ |
| 29 | | #!latex |
| 30 | | $b \to s\gamma$. |
| 31 | | }}} |
| 32 | | The model has the color gauge structure |
| 33 | | {{{ |
| 34 | | #!latex |
| 35 | | $SU(3)_1 \times SU(3)_2$ |
| 36 | | }}} |
| 37 | | The extended color symmetry is broken down to |
| 38 | | {{{ |
| 39 | | #!latex |
| 40 | | $SU(3)_C$ |
| 41 | | }}} |
| 42 | | by the (diagonal) expectation value, |
| 43 | | {{{ |
| 44 | | #!latex |
| 45 | | $\langle \Phi \rangle \propto u \cdot {\cal I}$, |
| 46 | | }}} |
| 47 | | of a scalar field Phi which transforms as a |
| 48 | | {{{ |
| 49 | | #!latex |
| 50 | | $(\bf 3, \bar{3})$ |
| 51 | | }}} |
| 52 | | under the color gauge structure. It is assumed that color gauge breaking occurs at a scale much higher than the electroweak scale, u>>v. |
| 53 | | |
| 54 | | Breaking the color symmetry induces a mixing between the |
| 55 | | {{{ |
| 56 | | #!latex |
| 57 | | $SU(3)_1$ \rm{and} $SU(3)_2$ |
| 58 | | }}} |
| 59 | | gauge fields |
| 60 | | {{{ |
| 61 | | #!latex |
| 62 | | $A^{1}_{\mu}$ \rm{and} $A^{2}_{\mu}$, |
| 63 | | }}} |
| 64 | | which is diagonalized by a rotation determined by |
| 65 | | {{{ |
| 66 | | #!latex |
| 67 | | $\cot\omega = \frac{g_1}{g_2} \qquad g_s = g_1 \sin\omega = g_2 \cos\omega$, |
| 68 | | }}} |
| 69 | | where g_s is the QCD strong coupling and g_1, 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 |
| 70 | | {{{ |
| 71 | | #!latex |
| 72 | | $G^{*}_{\mu}=\cos\omega A^{1}_{\mu} - \sin\omega A^{2}_{\mu} \qquad M_{G^{*}} = \frac{g_s u}{\sin\omega \cos\omega}.$ |
| 73 | | }}} |
| 74 | | In the NMFV model, the third generation quarks couple differently than the light quarks under the extended color group. |
| 75 | | {{{ |
| 76 | | #!latex |
| 77 | | $g_L=(t_L, b_L),$ \rm{ } $t_R,$ \rm{ and } $b_R,$ |
| 78 | | }}} |
| 79 | | as well as a new weak-doublet of vector-like quarks, transform as |
| 80 | | {{{ |
| 81 | | #!latex |
| 82 | | $({\bf 3,1})$ |
| 83 | | }}} |
| 84 | | under the color gauge group, while the light generation quarks are charged under SU(3)_2 and transform as |
| 85 | | {{{ |
| 86 | | #!latex |
| 87 | | $({\bf 1,3})$ |
| 88 | | }}} |
| 89 | | The G* interactions with the color currents associated with SU(3)_1 and SU(3)_2 are given by |
| 90 | | {{{ |
| 91 | | #!latex |
| 92 | | $g_s \left(\cot\omega J^{\mu}_1 - \tan\omega J^{\mu}_2 \right)G^{*}_{\mu}.$ |
| 93 | | }}} |
| 94 | | |
| 95 | | |
| 96 | | The G* can be produced at the LHC by quark-antiquark fusion determined by the G* coupling to light quarks |
| 97 | | {{{ |
| 98 | | #!latex |
| 99 | | $g_s \tan\omega$ |
| 100 | | }}} |
| 101 | | Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance. |
| | 29 | 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 vector-like quarks. Gluon-gluon fusion production is forbidden at tree level by SU(3)_C gauge invariance. |
| 123 | | $G* \to tc$ |
| 124 | | }}} |
| 125 | | flavor violating decay is controlled by the |
| 126 | | {{{ |
| 127 | | #!latex |
| 128 | | $(U_L)_{23}$ |
| 129 | | }}} |
| 130 | | element. The CKM mixing matrix is given by |
| 131 | | {{{ |
| 132 | | #!latex |
| 133 | | $V_{CKM}=U^{\dagger}_L D_L$. |
| 134 | | }}} |
| 135 | | At first order in the mixing parameters, |
| 136 | | {{{ |
| 137 | | #!latex |
| 138 | | $(U_L)_{23}\equiv V_{cb} - (D_L)_{23}$. |
| 139 | | }}} |
| 140 | | The non-diagonal elements of D_L are strongly constrained by the data on |
| 141 | | {{{ |
| 142 | | #!latex |
| 143 | | $b\to s \gamma$. |
| 144 | | }}} |
| 145 | | So |
| 146 | | {{{ |
| 147 | | #!latex |
| 148 | | $(D_L)_{23}$ |
| 149 | | }}} |
| 150 | | is thus forced to be small and, as a consequence, |
| 151 | | {{{ |
| 152 | | #!latex |
| 153 | | $(U_L)_{23}\simeq V_{cb}$. |
| | 51 | $ct\eta \neq \omega$ |
