Changes between Version 7 and Version 8 of ZeeBabu


Ignore:
Timestamp:
Jun 30, 2022, 4:12:49 PM (2 years ago)
Author:
Richard Ruiz
Comment:

updated Lagrangian (finished)

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  • ZeeBabu

    v7 v8  
    1919== Model Description ==
    2020
    21 The Zee-Babu model extends the Standard Model (SM) by two complex scalars, $k$ and $h$.
    22 Neither carries color or weak isospin but both are charged under weak hypercharge.
    23 $k$ and $h$ are assigned lepton number $L=+2$, which is normalized such that SM leptons carry $L=+1$.
    24 In terms of the SM Lagrangian $(\mathcal{L}_{\rm SM})$, the Lagrangian of the Zee-Babu model  $(\mathcal{L}_{\rm ZB})$ is
     21The Zee-Babu model extends the Standard Model (SM) by two complex scalars, {{{k--}}} and {{{h-}}}.
     22Neither carries color or weak isospin but both are charged under weak hypercharge. {{{k--}}} and {{{h-}}} carry the electric charges {{{Q_k=-2}}} and {{{Q_h=-1}}}, respectively, and both are assigned lepton number {{{L=+2}}}. This is normalized such that SM leptons carry {{{L=+1}}}.
     23
     24In terms of the SM Lagrangian {{{L_SM}}}}, the Lagrangian of the Zee-Babu model  {{{LZB}}} is
    2525{{{
    2626#!latex
    … …  
    3333\end{align}
    3434}}}
    35 Here, the weak hypercharge operator is normalized such that the electromagnetic charge operator is $\hat{Q}=\hat{T}_L^3+\hat{Y}$, and $Y_k = -2\ (Y_h = -1)$.
    36 The weak hypercharge coupling is denoted by $g_Y\approx 0.36$.
    37 As neither $k$ nor $h$ mix with SM states, the mass eigenstates, denoted by $k^{--}$ and $h^-$, are aligned with their gauge states and carry the electric charges $Q_k=-2$ and $Q_h=-1$, respectively.
     35
    3836
    3937
    … …  
    4947\end{align}
    5048}}}
    51 
    52 The Yukawa part of $\mathcal{L}_{\rm ZB}$ describes the coupling of SM leptons to $k$ and $h$. It is given by
     49Here, the weak hypercharge operator is normalized such that the electromagnetic charge operator is
     50{{{Q=T+Y}}} and {{{Y_k = -2 (Y_h = -1)}}}.
     51'''Note''' that {{{k^dagger = k++}}} and {{{h^dagger = h+}}}.
     52
     53
     54The Yukawa part describes the coupling of SM leptons to {{{k--}}} and {{{h-}}}. It is given by
    5355{{{
    5456#!latex
    … …  
    6365}}}
    6466
    65 The scalar potential of $k$ and $h$, including couplings to the SM Higgs doublet $\Phi$, is given by
     67The scalar potential for {{{k--}}} and {{{h-}}}, including couplings to the SM Higgs doublet {{{Phi}}}, is given by
    6668{{{
    6769#!latex
    … …  
    8486\end{align}
    8587}}}
    86 After EWSB, the physical masses of $k$ and $h$ are, respectively,
     88After EWSB, the physical masses of {{{k--}}} and {{{h-}}} are, respectively,
    8789{{{
    8890#!latex
    … …  
    9496\end{align}
    9597}}}
    96 
    97 
    98 Neutrino masses (mNk) and mixing parameters (Vlk) between heavy mass eigenstate and (active) flavor eigenstates are taken to be independent, phenomenological parameters. This allows for maximum flexibility and model independence when calculating rates. Therefore, some care is required by the user.
    99 The lepton number- and flavor-violating interactions of the Lagrangian allow for modeling of the Type I, Inverse, and Linear seesaw mechanisms at both lepton, hadron, and lepto-hadron colliders.
     98The parameter {{{mu}}} has mass dimension {{{GeV}}} and the {{{h-h-k}}} vertex violates lepton number conservation.
     99
     100Light neutrino masses are generated at two loops. They are described by {{{\delta\mathcal{L}_\nu}}}.
     101To phenomenologically parameterize the Lagrangian, neutrinos are assumed to be massless in the UFO. This allows all {{{f}}} and {{{g}}} to be taken independently from one another.
     102
     103'''Note''' that this model permits lepton flavor violation and lepton number violation.
     104
    100105
    101106