Changes between Version 3 and Version 4 of ZeeBabu


Ignore:
Timestamp:
Jun 30, 2022, 3:19:27 PM (3 years ago)
Author:
Richard Ruiz
Comment:

updated QCD corrections

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  • ZeeBabu

    v3 v4  
    1 = {{{SM_ZeeBabu}}}: The Standard Model + Zee-Babu scalars at NLO in QCD =
     1= [[span(style=color: #FF0000, '''*New*''' )]] {{{SM_ZeeBabu}}}: The Standard Model + Zee-Babu scalars at NLO in QCD [[span(style=color: #FF0000, '''*New*''' )]] =
    22
    33=== Contact Author ===
    … …  
    99==== Usage resources ====
    1010
    11 * [[span(style=color: #FF0000, '''*New*''' )]] For detailed instructions and examples on using the SM_ZeeBabu UFO libraries, see R. Ruiz arXiv:2207.qwerty .
     11* For detailed instructions and examples on using the {{{SM_ZeeBabu}}} UFO libraries, see R. Ruiz arXiv:2207.qwerty .
    1212* See '''Validation''' section below for additional information
    1313
    … …  
    1818
    1919== Model Description ==
    20 === Majorana N ===
     20
    2121This 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] ]
    2222{{{
    … …  
    5252The 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.
    5353
    54 === Dirac N ===
    55 The Dirac variant of the HeavyN model file contains the same interaction Lagrangian as the Majorana case. The heavy Dirac neutrinos' kinetic and mass terms are [ [#Pascoli2 4] ]
    56 {{{
    57 #!latex
    58 \begin{equation}
    59 \mathcal{L}_{N} = \overline{N_k} i\!\not\!\partial N_k - m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3.
    60 \end{equation}
    61 }}}
    62 
    63 === [[span(style=color: #FF0000, '''*New*''' )]] vSMEFT at dimension six ===
    64 In the {{{HeavyN_vSMEFTdim6}}} UFO [ [#Cirigliano 5] ], the {{{HeavyN}}} (Majorana) Lagrangian is extended by the dimension-six EFT operator
    65 {{{
    66 #!latex
    67 \begin{equation}
    68 \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
    69 +  \mathrm{H.c.}\, ,
    70 \end{equation}
    71 }}}
    72 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
    73 {{{
    74 #!latex
    75 \begin{equation}
    76 \mathcal{L}_{H\nu e}^{(6)} \approx
    77 \frac{g v^2}{2\sqrt{2}\Lambda^2}
    78 \sum_{\ell=e}^{\tau}
    79 \sum_{k=1}^{3} \,\overline{N_k} 
    80  \left[\bar{C}_{H\nu l}\right]_{k \ell} \gamma^\mu P_R \ell_{R}\,W_\mu^+ 
    81 \left(1+\frac{h}{v}\right)^2 +\text{H.c.}
    82 \end{equation}
    83 }}}
    84 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] ].
    85 
    8654
    8755== QCD Corrections ==
    88 The above Lagrangian with Goldstone boson couplings and in the Feynman Gauge was implemented into FeynRules  2.3.10. QCD renormalization and R2 rational counter terms were determined using NLOCT 1.02 and FeynArts 3.8. Feynman rules were collected into a single UFO, available below.
    89 In the UFO file, five massless quarks are assumed as are zero off-diagonal CKM matrix entries.
    90 For additional details, see [ [#Degrande 2] ] and references therein.
     56The above Lagrangian with Goldstone boson couplings and in the Feynman Gauge was implemented into FeynRules  2.3.36. QCD renormalization and R2 rational counter terms were determined using NLOCT 1.02 and FeynArts 3.11. Feynman rules were collected into a single UFO, available below.
     57In the default UFO, five massless quarks are assumed as well as a CKM matrix equal to the identity matrix.
     58For additional details, see [ [#Ruiz 4] ] and references therein.
    9159These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO.
    9260
    … …  
    9664
    9765
    98 ==== Majorana ====
     66==== Default UFO (massless charged leptons) ====
    9967 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz SM_HeavyN_NLO_UFO.tgz]: Standalone UFO folder. Assumes massless bottom quark and tau lepton, diagonal CKM.
    10068
    … …  
    11280 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz SM_HeavyN_FilesWithUFO.tgz]: Combination of SM_HeavyN_NLO_UFO.tgz and SM_HeavyN_Files.tgz.
    11381
    114 ==== Dirac ====
     82==== Alternative UFO (massive charged leptons) ====
    11583 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_Dirac_NLO_UFO.tgz SM_HeavyN_Dirac_NLO_UFO.tgz]: Standalone NLO UFO libraries
    11684
    … …  
    12189 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/heavyN_Dirac.fr heavyN_Dirac.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
    12290
    123 ==== [[span(style=color: #FF0000, '''*New*''' )]] vSMEFT ====
    124 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_vSMEFTdim6_NLO.tgz SM_HeavyN_vSMEFTdim6_NLO.tgz]: Standalone NLO UFO folder. Assumes massless bottom quark and tau lepton, diagonal CKM.
    12591
    126 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_vSMEFTdim6_XLO.tgz SM_HeavyN_vSMEFTdim6_XLO.tgz]: Standalone LO UFO folder. Assumes massless bottom quark and tau lepton, diagonal CKM.
    127 
    128 * [https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/heavyN_vSMEFTdim6.fr heavyN_vSMEFTdim6.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
    12992
    13093== Download and Unpack ==
    … …  
    151114~/Path $ tar -zxvf SM_HeavyN_Dirac_LO_UFO.tgz
    152115
    153 ==== vSMEFT NLO ====
    154 ~/Path $ wget https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_vSMEFTdim6_NLO.tgz
    155 
    156 ~/Path $ tar -zxvf SM_HeavyN_vSMEFTdim6_NLO.tgz
    157 
    158 ==== vSMEFT LO ====
    159 ~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_vSMEFTdim6_XLO.tgz
    160 
    161 ~/Path $ tar -zxvf SM_HeavyN_vSMEFTdim6_XLO.tgz
    162 
    163 
    164116
    165117== Notes ==
    … …  
    184136
    185137== Validation ==
    186 * The model file was validated at LO in  [ [#Alva 1] ]; see Tables 2 and 5 for further validation checks.
    187 * The model file was validated at NLO in [ [#Degrande 2] ]; see Table 1 for further validation checks.
    188 * For very large masses, this model has been constructed to satisfy the Goldstone Equivalence Theorem:
    189 {{{
    190 #!latex
    191 \begin{eqnarray}
    192 \text{BR}(N_i \rightarrow W^+ \ell^-) &=& \text{BR}(N_i \rightarrow W^- \ell^+) =
    193 \\
    194 \text{BR}(N_i \rightarrow Z \nu_\ell + Z \overline{\nu_\ell} ) &=&
    195 \text{BR}(N_i \rightarrow h \nu_\ell + h \overline{\nu_\ell} ) = 25\%.
    196 \end{eqnarray}
    197 }}}
    198 * Helicity dependence of LNV and LNC decay rates of Majorana neutrino decays was validated in [ [#Ruiz 7] ]
     138* The model file was checked and validated against partonic results in [ [#Gunion 99] ]
     139* The cross sections of Table 2 of [ [#Ruiz 4] ] can be generated using the script available from https://gitlab.cern.ch/riruiz/public-projects/-/tree/master/ZeeBabu_LHC_Update/LHC_XSec_Table2
     140
    199141
    200142== Studies that have used the above model files ==
    201143Please email to update this space.
    202 * Golling, et al., ''Physics at a 100 TeV pp collider: beyond the Standard Model phenomena'', arXiv:1606.00947
    203 * CMS, ''Search for heavy neutral leptons in events with three charged leptons in proton-proton collisions at 13 TeV'', arXiv:1802.02965 [hep-ex]
    204 * CMS, ''Search for heavy Majorana neutrinos in same-sign dilepton channels in proton-proton collisions at 13 TeV'', arXiv:1806.10905 [hep-ex]
     144* ...
    205145
    206146== References ==
    207 * For studies of Majorana neutrinos, please consider citing [ 6 ] for the Lagrangian and [ 1-2 ] for the Majorana FR/UFO files.
    208 * For studies of heavy Dirac neutrinos, please also consider citing [ 4 ].
    209 * For studies of heavy neutrinos in vSMEFT, please consider citing [ 5 ].
    210 
    211 
    212 [ [#Zee1 1], [#Zee2 2] ] and Babu  [ [#Babu 3] ].
    213 * If using any of the UFOs, please cite the companion paper [ [#Ruiz 4] ]
     147* For the Lagrangian, please cite the original papers by Zee [ [#Zee1 1], [#Zee2 2] ] and Babu  [ [#Babu 3] ].
     148* If using any of the UFOs, please cite the companion paper [ [#Ruiz 4] ].
    214149
    215150[=#Zee1] [1] A. Zee, ''Charged Scalar Field and Quantum Number Violations,'' Phys. Lett. '''B161''' (1985) 141, https://inspirehep.net/literature/214241
    … …  
    224159arXiv:2207.qwerty [hep-ph]
    225160
     161[=#Gunion] [99] J.F. Gunion, C. Loomis, K.T. Pitts, ``Searching for Doubly-Charged Higgs Bosons at Future Colliders,'' arXiv:hep-ph/9610237
     162
     163