Changes between Version 1 and Version 2 of WZPrimeAtNLO


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Timestamp:
Jan 19, 2017, 3:30:24 PM (8 years ago)
Author:
Richard Ruiz
Comment:

Copy new page from HeavyNnlo and add equations from the Jet Veto paper by Fuks and Ruiz

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  • WZPrimeAtNLO

    v1 v2  
    1 blabla
     1= SM + W' and W' at NLO in QCD =
     2
     3=== Contact Author ===
     4Benjamin Fuks
     5* UPMC Univ. Paris, LPTHE
     6* fuks AT lpthe.jussieu.fr
     7
     8Richard Ruiz
     9* University of Durham (IPPP)
     10* richard.ruiz AT durham.ac.uk
     11
     12
     13
     14== Model Description ==
     15This 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}}}
     22The 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}}}
     29
     30and its interactions with the Weak gauge and Higgs bosons are given by
     31{{{
     32#!latex
     33\begin{eqnarray}
     34 \mathcal{L}^q_{\rm NP} =
     35    - \frac{g}{\sqrt{2}} \sum_{i,j} \Big[
     36       \overline{u}_i V_{ij}^{\rm CKM}~W_\mu^{\prime+}~\gamma^\mu
     37       \Big(\kappa_L^{q} P_L + \kappa_R^{q}P_R\Big)~ d_j + \text{H.c.}\Big]
     38\\
     39    - \frac{g}{\cos\theta_W} \sum_{q=u,d}\sum_i \Big[
     40      \overline{q}_i ~Z_\mu^\prime \gamma^\mu
     41      \Big(\zeta_{L}^{q}P_L + \zeta_{R}^{q}P_R\Big)q_i\Big] \ ,
     42+{\rm H.c.}
     43\end{eqnarray}
     44}}}
     45$i$ and $j$ denote flavor indices, $P_{L/R}=\frac12 (1\mp\gamma_5)$ and
     46are the usual left/right-handed
     47chirality projectors, $V^{\rm CKM}$ is the Cabbibo-Kobayashi-Maskawa (CKM) matrix,
     48and $g$ and $\theta_W$ are the weak coupling constant and mixing angle respectively.
     49We choose coupling normalizations facilitating the mapping to the reference SSM
     50Lagrangian ${\cal L}_{\rm SSM}$~\cite{Altarelli:1989ff}.
     51The real-valued quantities $\kappa_{L,R}^q$ and $\zeta_{L,R}^q$
     52
     53
     54{{{
     55#!latex
     56\begin{eqnarray}
     57  \mathcal{L}^\ell_{\rm NP} =
     58   - \frac{g}{\sqrt{2}}\sum_i\Big[
     59       \overline{\nu}_{\ell_i} W_\mu^{\prime+}~\gamma^\mu
     60        \kappa_L^{\ell} P_L\ell_i^- + \text{H.c.}\Big]
     61\\
     62    - \frac{g}{\cos\theta_W} \sum_{f=\ell,\nu_\ell}\sum_i \Big[
     63      \overline{f}_i ~Z_\mu^\prime \gamma^\mu
     64      \Big(\zeta_{L}^{f}P_L + \zeta_{R}^{f}P_R\Big)f_i\Big] \ .
     65+{\rm H.c.}
     66\end{eqnarray}
     67}}}
     68The quantities $\kappa_L^\ell$ are real-valued and serve as normalizations for
     69leptonic coupling strengths.
     70As no right-handed neutrinos are present in the SM, the corresponding
     71right-handed leptonic new physics couplings are omitted ($\zeta_R^\nu =
     72\kappa_R^\ell = 0$).
     73We assume that leptonic interactions are flavor diagonal.
     74
     75
     76
     77{{{
     78#!latex
     79\begin{eqnarray}
     80  \zeta_{R,L}^{f} = \zeta_{Z_{\rm SSM}}^f \Big( g_V^f \pm g_A^f\Big)
     81  \qquad\text{with}\qquad
     82  g_V^f = \frac{1}{2}T_L^{3,f} - Q^f\sin^2\theta_W
     83  \qquad\text{and}\qquad
     84  g_A^f=-\frac{1}{2}T_L^{3,f},
     85\end{eqnarray}
     86}}}
     87
     88In
     89the canonical SSM, the overall normalizations are further trivially fixed as
     90{{{
     91#!latex
     92\begin{eqnarray}
     93 \kappa^{q,\ell}_L=1, \qquad
     94 \kappa_R^q=0,
     95 \qquad\text{and}\qquad
     96 \zeta_{Z_{\rm SSM}}^{f}=1 \ .
     97\end{eqnarray}
     98}}}
     99
     100
     101
     102== QCD Corrections ==
     103The above Lagrangian 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.
     104In the UFO file, five massless quarks are assumed as are zero off-diagonal CKM matrix entries.
     105For additional details, see [ [#Fuks 2] ] and references therein.
     106These additions permit tree-level calculations at LO and NLO in QCD, loop-induced calculations at LO in QCD, and NLO matched to NNLL(Veto) resummation using MadGraph_aMC@NLO.
     107
     108
     109== Model Files ==
     110 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz SM_HeavyN_NLO_UFO.tgz]: Standalone UFO folder.
     111
     112 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/heavyN.fr heavyN.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
     113
     114 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/heavyN_NLO.nb heavyN_NLO.nb]: Mathematica notebook file that generates UFO file from FeynRules model files. Allows user to also run quick sanity checks (optional) on model.
     115
     116 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_Files.tgz SM_HeavyN_Files.tgz]: Standalone package containing heavyN.fr, heavyN_NLO.nb, massless.rst (default FR file), diagonalCKM.rst (default FR file), and sm.fr (default FR file).
     117
     118 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz SM_HeavyN_FilesWithUFO.tgz]: Combination of SM_HeavyN_NLO_UFO.tgz and SM_HeavyN_Files.tgz.
     119
     120
     121
     122== Notes ==
     123 * To download any of the packages and unpack via the terminal, use the commands:
     124
     125~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_NLO_UFO.tgz
     126
     127~/Path $ tar -zxvf SM_HeavyN_NLO_UFO.tgz
     128
     129~/Path $ wget http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HeavyN/SM_HeavyN_FilesWithUFO.tgz
     130
     131~/Path $ tar -zxvf SM_HeavyN_FilesWithUFO.tgz
     132
     133 * This model contains 15 free parameters:
     134  * Three masses: mN1, mN2, mN3. Defaults are 300 GeV, 500 GeV, and 1 TeV, respectively.
     135  * Three widths: WN1, WN2, WN3. Defaults are 0.303 GeV, 1.50 GeV, and 12.3 GeV, respectively.
     136  * Nine real (no CP violation) mixing parameters: V''lk'' for ''l'' = ''e, mu, tau'' and ''k'' = 1,2,3. Default values are V''lk'' = Identity(3x3), i.e., Ve1 = Vmu2 = Vta3 = 1 and all others zero.
     137  * '''Note''': VlN are restricted to be real in the model file.
     138  * '''Note''': Default parameters are set so "out-of-the-box" checks can be made with [ [#Alva 1] ] and [ [#Degrande 2] ].
     139
     140
     141== Validation ==
     142* The model file was validated at NLO in [ [#Fuks 2] ] by comparing against Standard Model predictions and {{{$W'}}}$ predictions from [ [#Sullivan ] ], as well as private LO and NLO calculations. See Table III of [ [#Fuks 2] ] for representative total widths that have been checked against analytic computation.
     143
     144
     145=== List of studies that have used the model file ===
     146* Please email to update this space.
     147
     148== References ==
     149* Please cite [  ] for the model file, [] for NLO corrections, and [] for automated veto resummation.
     150
     151[=#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]
     152
     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.
     154
     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].