| 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 | | }}} |
| | 27 | 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. |
| | 28 | |
