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 | $ct\eta \neq \omega$ |