Changes between Version 2 and Version 3 of WZPrimeAtNLO


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Timestamp:
01/19/17 16:10:01 (10 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]