| 9 | | Daniel Alva and Tao Han [ [#Alva 1] ]; |
| 10 | | Celine Degrande, Olivier Mattelear, and Jessica Turner [ [#Degrande 2] ]; |
| 11 | | and Silvia Pascoli and Cedric Weiland [ [#Pascoli 3], [#Pascoli2 4] ]. |
| 12 | | |
| 13 | | For detailed instructions and examples on using the HeavyN UFO libraries, see C. Degrande, et al, arXiv:1602.06957 and S. Pascoli, et al, arXiv:1812.08750 |
| 14 | | |
| 15 | | * For studies of heavy Majorana neutrinos, please consider citing [ [#Atre 5] ] for the Lagrangian and [ [#Alva 1], [#Degrande 2] ] for the Majorana FR/UFO files. |
| | 9 | D. Alva and T. Han [ [#Alva 1] ]; C. Degrande, O. Mattelear, and J. Turner [ [#Degrande 2] ]; S. Pascoli and C. Weiland [ [#Pascoli 3], [#Pascoli2 4] ]; and V. Cirigliano, W. Dekens, J. de Vries, K. Fuyuto, E. Mereghetti [ [#Cirigliano 5] ]. |
| | 10 | |
| | 11 | For detailed instructions and examples on using the HeavyN UFO libraries, see C. Degrande, et al, arXiv:1602.06957 and S. Pascoli, et al, arXiv:1812.08750 . For heavy neutrinos in vSMEFT, see V. Cirigliano, et al, arXiv:2021.xxxxx . |
| | 12 | |
| | 13 | * For studies of heavy Majorana neutrinos, please consider citing [ [#Atre 6] ] for the Lagrangian and [ [#Alva 1], [#Degrande 2] ] for the Majorana FR/UFO files. |
| 21 | | This effective/simplified 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 5] ] |
| | 19 | This effective/simplified 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 6] ] |
| | 61 | === vSMEFT === |
| | 62 | In the {{{HeavyN_vSMEFTdim6}}} UFO [ [#Cirigliano 5] ], the {{{HeavyN}}} (Majorana) Lagrangian is extended by the dimension-six EFT operator |
| | 63 | {{{ |
| | 64 | #!latex |
| | 65 | \begin{equation} |
| | 66 | \mathcal{L}_{H\nu e}^{(6)} = \frac{1}{\Lambda^2} \left(i \tilde{\varphi}^{\dagger} D_{\mu} \varphi\right) \, \bar \nu_R \gamma^\mu \,C_{H\nu l} ~ l_R |
| | 67 | + \mathrm{H.c.}\, , |
| | 68 | \end{equation} |
| | 69 | }}} |
| | 70 | where {{{D_\mu}}} is the usual SM covariant derivative. {{{\Lambda}}} is the EFT cutoff in GeV scale, {{{ C_{H\nu l} }}} is the dimensionless Wilson coefficient, and {{{$l=e,\mu,\tau$}}}. Note that in Ref. [ [#Cirigliano 5] ], {{{ C_{H\nu l} }}} has dimension {{{GeV^-2}}}. In the unitary gauge after and EW symmetry breaking, the leading contribution of this operator can be written in the neutrino mass basis as |
| | 71 | {{{ |
| | 72 | #!latex |
| | 73 | \begin{equation} |
| | 74 | \mathcal{L}_{H\nu e}^{(6)} \approx |
| | 75 | \frac{g v^2}{2\sqrt{2}\Lambda^2} |
| | 76 | \sum_{\ell=e}^{\tau} |
| | 77 | \sum_{k=1}^{3} \,\overline{N_k} |
| | 78 | \left[\bar{C}_{H\nu l}\right]_{k \ell} \gamma^\mu P_R \ell_{R}\,W_\mu^+ |
| | 79 | \left(1+\frac{h}{v}\right)^2 +\text{H.c.} |
| | 80 | \end{equation} |
| | 81 | }}} |
| | 82 | Here {{{k=1,\dots,3}}} runs over all three heavy neutrino mass eigenstates and {{{$\ell=e,\mu,\tau$}}} runs over all lepton flavors. For the precise definition of the effective Wilson coefficient {{{$\bar{C}_{H\nu l}$}}}, see Ref. [ [#Cirigliano 5] ]. |
| | 83 | |
| | 84 | |
| 135 | | * For Majorana file, particle identification (PID) codes for N1,...,N3, follow standard HEP MCPID codes: 9900012, 9900014, 9900016 |
| 136 | | |
| 137 | | * For Dirac file, to avoid conflict with Pythia8, where the above PIDs are reserved for Majorana fields, the nonstandard HEP MCPID codes for N1,...,N3 are:9990012, 9990014, 9990016 |
| 138 | | |
| 139 | | |
| | 173 | * For the Majorana file, particle identification (PID) codes for N1,...,N3, follow standard HEP MCPID codes: 9900012, 9900014, 9900016 |
| | 174 | |
| | 175 | * For the Dirac file, to avoid conflict with Pythia8, where the above PIDs are reserved for Majorana fields, the nonstandard HEP MCPID codes for N1,...,N3 are:9990012, 9990014, 9990016 |
| | 176 | |
| | 177 | * For vSMEFT file, 10 additional model parameters are introduced: |
| | 178 | * One EFT cutoff scale {{{Lambda}}} in units of GeV. |
| | 179 | * Nine Wilson coefficients coupling {{{N_k}}} to {{{l}}}: {{{CeN1, CeN2, CeN3, CmuN1, CmuN2, CmuN3, CtaN1, CtaN2, CtaN3}}} |
| | 180 | * '''Note''': Default parameters are set such that {{{Lambda=1000}}} (GeV), {{{CeN1=CmuN2=CtaN3=1}}}, and all other coefficients are zero |
| | 181 | |
| 175 | | |
| 176 | | [=#Atre] [5] A. Atre, T. Han, S. Pascoli and B. Zhang, ''The Search for Heavy Majorana Neutrinos,'' JHEP '''0905''', 030 (2009), arXiv:0901.3589 [hep-ph] |
| 177 | | |
| 178 | | [=#Ruiz] [6] R. Ruiz, ''A quantitative study on helicity inversion in Majorana neutrino decays at the LHC,'' arXiv:2008.01092 [hep-ph] |
| | 217 | [=#Cirigliano] [5] |
| | 218 | |
| | 219 | [=#Atre] [6] A. Atre, T. Han, S. Pascoli and B. Zhang, ''The Search for Heavy Majorana Neutrinos,'' JHEP '''0905''', 030 (2009), arXiv:0901.3589 [hep-ph] |
| | 220 | |
| | 221 | [=#Ruiz] [7] R. Ruiz, ''A quantitative study on helicity inversion in Majorana neutrino decays at the LHC,'' arXiv:2008.01092 [hep-ph] |
