15 | | This effective model extends the Standard Model (SM) field content by introducing three right-handed (RH) neutrinos, which are singlets under the SM gauge symmetry (no color, weak isospin, or weak hypercharge charges). Each RH neutrino possesses one RH Majorana mass. After electroweak symmetry breaking, the Lagrangian with three heavy Majorana neutrinos ''N''i (for i=1,2,3) is given by [ [#Atre 3] ] |
16 | | {{{ |
17 | | #!latex |
18 | | \begin{equation} |
19 | | \mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}} |
20 | | \end{equation} |
21 | | }}} |
22 | | The first term is the Standard Model Lagrangian. In the mass basis, i.e., after mixing with active neutrinos, the heavy Majorana neutrinos' kinetic and mass terms are |
23 | | {{{ |
24 | | #!latex |
25 | | \begin{equation} |
26 | | \mathcal{L}_{N} = \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3, |
27 | | \end{equation} |
28 | | }}} |
| 15 | This effective model extends the Standard Model (SM) field content by introducing the massive vector fields {{{$W^{'#pm}$}}} and {{{$Z'$}}} bosons, and are electrically charged and neutral, respectively. To remain model independence, couplings to SM gauge bosons and scalars are omitted. |
45 | | $i$ and $j$ denote flavor indices, $P_{L/R}=\frac12 (1\mp\gamma_5)$ and |
46 | | are the usual left/right-handed |
47 | | chirality projectors, $V^{\rm CKM}$ is the Cabbibo-Kobayashi-Maskawa (CKM) matrix, |
48 | | and $g$ and $\theta_W$ are the weak coupling constant and mixing angle respectively. |
49 | | We choose coupling normalizations facilitating the mapping to the reference SSM |
50 | | Lagrangian ${\cal L}_{\rm SSM}$~\cite{Altarelli:1989ff}. |
51 | | The real-valued quantities $\kappa_{L,R}^q$ and $\zeta_{L,R}^q$ |
| 32 | Here, {{{$i$}}} and {{{$j$}}} denote flavor indices, {{{$P_{L/R}=(1/2)(1\mp\gamma_5)$}}} and |
| 33 | are the usual left/right-handed chirality projectors, {{{$V^{\rm CKM}$}}} is the CKM matrix, |
| 34 | and {{{$g$}}} and {{{$\theta_W$}}} are the weak coupling constant and mixing angle respectively. |
| 35 | We choose coupling normalizations facilitating the mapping to the reference Sequential Standard Model |
| 36 | Lagrangian {{{${\cal L}_{\rm SSM}$}}} [ [#Altarelli X] ]. |
| 37 | The real-valued quantities {{{$\kappa_{L,R}^q$}}} and {{{$\zeta_{L,R}^q$}}} |
68 | | The quantities $\kappa_L^\ell$ are real-valued and serve as normalizations for |
69 | | leptonic coupling strengths. |
70 | | As no right-handed neutrinos are present in the SM, the corresponding |
71 | | right-handed leptonic new physics couplings are omitted ($\zeta_R^\nu = |
72 | | \kappa_R^\ell = 0$). |
| 54 | The quantities {{{$\kappa_L^\ell$}}} are real-valued and serve as normalizations for |
| 55 | leptonic coupling strengths. As no right-handed neutrinos are present in the SM, the corresponding |
| 56 | right-handed leptonic new physics couplings are omitted ({{{$\zeta_R^\nu = \kappa_R^\ell = 0$}}}). |
155 | | [=#Becher] [] T. Becher, R. Frederix, M. Neubert and L. Rothen, ''Automated NNLL $+$ NLO resummation for jet-veto cross sections,'' EPJC'''75''', no. 4, 154 (2015) arXiv:1412.8408 [hep-ph]. |
| 141 | [=#Becher] [] T. Becher, R. Frederix, M. Neubert and L. Rothen, ''Automated NNLL $+$ NLO resummation for jet-veto cross sections,'' EPJC'''75''', no. 4, 154 (2015) arXiv:1412.8408 [hep-ph] |
| 142 | |
| 143 | [=#Gopalakrishna] [] S. Gopalakrishna, T. Han, I. Lewis, Z.-G. Si and Y. F. Zhou, ''Chiral Couplings of {{{$W'$}}} and Top Quark Polarization at the LHC,'' PRD'''82''', 115020 (2010) arXiv:1008.3508 [hep-ph] |
| 144 | |
| 145 | [=#Han] [] T. Han, I. Lewis, R. Ruiz and Z.-G. Si, ''Lepton Number Violation and {{{$W^\prime$}}} Chiral Couplings at the LHC,'' PRD'''87''', no. 3, 035011 (2013) arXiv:1211.6447 [hep-ph] |