Changes between Version 2 and Version 3 of WZPrimeAtNLO


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Timestamp:
Jan 19, 2017 4:10:01 PM (19 months ago)
Author:
richardphysics
Comment:

Updated Lagrangian Still in Progress

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  • WZPrimeAtNLO

    v2 v3  
    1313
    1414== Model Description ==
    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 }}}
     15This 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.
    2916
    30 and its interactions with the Weak gauge and Higgs bosons are given by
     17Following Refs. [ [#Gopalakrishna X], [#Han Y] ], the Lagrangian parameterizing the new vector bosons' couplings to up-type and down-type quark fields {{{$u_i$}}} and {{{$d_j$}}} is given by
    3118{{{
    3219#!latex
    3320\begin{eqnarray}
    34  \mathcal{L}^q_{\rm NP} =
     21 \mathcal{L}^q  =
    3522    - \frac{g}{\sqrt{2}} \sum_{i,j} \Big[
    3623       \overline{u}_i V_{ij}^{\rm CKM}~W_\mu^{\prime+}~\gamma^\mu
     
    4330\end{eqnarray}
    4431}}}
    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 $\zeta_{L,R}^q$
     32Here, {{{$i$}}} and {{{$j$}}} denote flavor indices, {{{$P_{L/R}=(1/2)(1\mp\gamma_5)$}}} and
     33are the usual left/right-handed chirality projectors, {{{$V^{\rm CKM}$}}} is the CKM matrix,
     34and {{{$g$}}} and {{{$\theta_W$}}} are the weak coupling constant and mixing angle respectively.
     35We choose coupling normalizations facilitating the mapping to the reference Sequential Standard Model
     36Lagrangian {{{${\cal L}_{\rm SSM}$}}} [ [#Altarelli X] ].
     37The real-valued quantities {{{$\kappa_{L,R}^q$}}} and {{{$\zeta_{L,R}^q$}}}
    5238
    5339
     
    6652\end{eqnarray}
    6753}}}
    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 ($\zeta_R^\nu =
    72 \kappa_R^\ell = 0$).
     54The quantities {{{$\kappa_L^\ell$}}} are real-valued and serve as normalizations for
     55leptonic coupling strengths. As no right-handed neutrinos are present in the SM, the corresponding
     56right-handed leptonic new physics couplings are omitted ({{{$\zeta_R^\nu = \kappa_R^\ell = 0$}}}).
    7357We assume that leptonic interactions are flavor diagonal.
    7458
     
    149133* Please cite [  ] for the model file, [] for NLO corrections, and [] for automated veto resummation.
    150134
     135[=#Altarelli] [] G. Altarelli, B. Mele and M. Ruiz-Altaba, ''Searching for New Heavy Vector Bosons in $p \bar{p}$ Colliders,''   Z. Phys. C'''45''', 109 (1989), doi:10.1007/BF01556677
     136
    151137[=#Fuks] [] B. Fuks, R. Ruiz, ''A Comprehensive Framework for Studying {{{$W'$}}} and {{{$Z'$}}} Bosons at Hadron Colliders with Automated Jet Veto Resummation,''  arXiv:1701.xxxx [hep-ph]
    152138
    153 [=#Sullivan] [] Z. Sullivan, ''Fully differential {{{$W'$}}} production and decay at next-to-leading order in QCD,'' PRD'''66''', 075011 (2002),   arXiv:hep-ph/0207290.
     139[=#Sullivan] [] Z. Sullivan, ''Fully differential {{{$W'$}}} production and decay at next-to-leading order in QCD,'' PRD'''66''', 075011 (2002),   arXiv:hep-ph/0207290
    154140
    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]