Changes between Version 8 and Version 9 of modcolorS_trip


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Timestamp:
Nov 3, 2015 11:22:12 PM (3 years ago)
Author:
druekeel
Comment:

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  • modcolorS_trip

    v8 v9  
    11
    2 = A Color Triplet Model =
     2= A Color Triplet Model with Decay to Top and Bottom Quark =
     3
     4This model introduces a heavy hadronic resonance with fractional electric charge (color triplet). The color triplet is produced in quark-quark collisions (not quark-antiquark) and decays to a top quark and a bottom quark.
    35
    46== Corresponding Authors ==
     
    2325[[Image(ColorResSig1.png)]]
    2426
    25 In particular, it is possible to produce triplet, anti-triplet, and sextet particles; but the LHC is a proton-proton machine and so the triplet production is enhanced by the parton-parton luminosity of the quark-quark initial state.  The contributing quark-quark initial states are QQ, QU, QD, and UD, where Q, U, and D denote the SM quark doublet, up-type singlet, and down-type singlet, respectively.  The diquark particles could be the spin-0 scalars with
    26 {{{
    27 #!latex
    28 $SU(3) \times SU(2)_L \times U(1)_Y$
    29 }}}
    30 quantum numbers
    31 {{{
    32 #!latex
    33 $\Phi \simeq (6 \oplus \overline{3}, 3, \frac13), \quad \Phi_U \simeq (6 \oplus \overline{3}, 1, \frac13),$
    34 }}}
    35 and the spin-1 vectors
    36 {{{
    37 #!latex
    38 $V^\mu_U \simeq  (6 \oplus \overline{3}, 2, \frac56), \quad V^\mu_D \simeq  (6 \oplus \overline{3}, 2, -\frac16).$
    39 }}}
    40 To produce the tb final state, the charge of the colored particle needs to be 1/3. The gauge-invariant Lagrangian can be written as:
    41 {{{
    42 #!latex
    43 $\mathcal{L}_{\rm diquark} = K^j_{ab} [\kappa_{\alpha\beta} \overline{Q^C_{\alpha a}}i\sigma_2 \Phi^{j} Q_{\beta b} + \lambda_{\alpha\beta} \Phi_U \overline{D^C_{\alpha a}}U_{\beta b} + \lambda^U_{\alpha\beta} \overline{Q^C_{\alpha a}}i\sigma_2\gamma_\mu{V^{j}_U}^\mu U_{\beta b} +$
    44 }}}
    45 {{{
    46 #!latex
    47 $\lambda^D_{\alpha\beta} \overline{Q^{C}_{\alpha a}}i\sigma_2\gamma_\mu{V^{j}_D}^\mu D_{\beta b}] + \rm{h.c.}$
    48 }}}
    49 where
    50 {{{
    51 #!latex
    52 $\Phi^j = {1\over 2}\sigma_{k} \Phi_{k}^{j}$
    53 }}}
    54 with the
    55 {{{
    56 #!latex
    57 $SU(2)_{L}$
    58 }}}
    59 Pauli matrices
    60 {{{
    61 #!latex
    62 $\sigma_{k}$
    63 }}}
    64 and color factor
    65 {{{
    66 #!latex
    67 $K^j_{ab}$.
    68 }}}
    69 The couplings to QQ, and to U and D, are given, respectively, by
    70 {{{
    71 #!latex
    72 $\kappa_{\alpha\beta}$ \rm{ and } $\lambda_{\alpha\beta}$.
    73 }}}
    74 Here a, and b are quark color indices, and j is the diquark color index with
    75 {{{
    76 #!latex
    77 $j=1-N_D$,
    78 }}}
    79 where N_D is the dimension of the (N_D=3) antitriplet or (N_D=6) sextet representation. C denotes charge conjugation, and alpha and beta are the fermion generation indices. After electroweak symmetry breaking, all of the SM fermions are in the mass eigenstates. The relevant couplings of the colored diquark to the top quark and the bottom quark are then given by
    80 {{{
    81 #!latex
    82 $\mathcal{L}_{qqD} = K_{ab}^{j} \left[  \kappa^\prime_{\alpha\beta} \Phi \overline{u^c}_{\alpha a} P_\tau d_{\beta b} + \lambda^\prime_{\alpha\beta} V_{D}^{j\mu} \overline{u^c}_{\alpha a} \gamma_{\mu}P_\tau d_{\beta b} \right]+ \mathrm{h.c.},$
    83 }}}
    84 where
    85 {{{
    86 #!latex
    87 $P_\tau = \frac{1\pm \gamma_5}{2}$
    88 }}}
    89 are the chiral projection operators. Assuming that the flavor-changing neutral coupling is small, the third-generation couplings are
    90 {{{
    91 #!latex
    92 $\mathcal{L}_{\rm top} = K_{ab}^{j} \Phi \overline{t^c}_\alpha P_\tau b_\beta +
    93 K_{ab}^{j} V^\mu \overline{t^c}_\alpha \gamma_\mu P_\tau b_\beta + h.c.$
    94 }}}
     27In particular, it is possible to produce triplet, anti-triplet, and sextet particles; but the LHC is a proton-proton machine and so the triplet production is enhanced by the parton-parton luminosity of the quark-quark initial state.  The contributing quark-quark initial states are QQ, QU, QD, and UD, where Q, U, and D denote the SM quark doublet, up-type singlet, and down-type singlet, respectively. 
     28
    9529The decay width of the color~triplet to tb is given by
    9630{{{
     
    10842$g_{\Phi}$.
    10943}}}
     44Here, q3trip is the
     45{{{
     46#!latex
     47$g_{\Phi}$
     48}}}
     49coupling to tb.
     50
    11051See more details in
    11152* [http://arxiv.org/abs/1409.7607v2 1409.7607v2]
     
    12970
    13071To generate the settings for a specific color triplet mass, change the MSIX parameter to the mass of the particle in GeV and the WSIX parameter as described above in the parameters.py file of the model.
     72
     73== Related Models ==
     74
     75* [wiki:kkg_FV kkg_FV]
     76* [wiki:Octet_tcgg Octet_tcgg]
     77* [wiki:Wprime W-prime]