Changes between Initial Version and Version 1 of EffLRSM.


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Timestamp:
Oct 31, 2016, 10:39:05 AM (8 years ago)
Author:
Mattelaer Olivier
Comment:

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  • EffLRSM.

    v1 v1  
     1= Effective Left-Right Symmetric Model at NLO in QCD =
     2
     3=== Contact Author ===
     4Richard Ruiz
     5* University of Durham (IPPP)
     6* richard.ruiz AT durham.ac.uk
     7
     8In collaboration with
     9Olivier Mattelaer and Manimala Mitra [ [#Mattelaer 1] ], and
     10Manimala Mitra, Darren Scott, and Michael Spannowsky [ [#Mitra 2] ].
     11
     12
     13== Model Description ==
     14This effective model extends the Standard Model (SM) field content by introducing heavy Left-Right symmetric gauge bosons W,,R,,^+/-^, Z,,R,, with masses M,,WR,, and M,,ZR,,, as well as three heavy Majorana neutrinos N,,i,, with mass m,,Ni,,. The Lagrangian is given by,
     15
     16{{{
     17#!latex
     18\begin{equation}
     19\mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{\rm LRSM~Kin.} + \mathcal{L}_{\rm LRSM~Int.}
     20\nonumber
     21\end{equation}
     22}}}
     23The W,,R,,, Z,,R,,, couplings to fermions are separated into three pieces:
     24{{{
     25#!latex
     26\begin{equation}
     27\mathcal{L}_{\rm LRSM~Int.} = \mathcal{L}_{W_R-q-q'} + \mathcal{L}_{W_R-\ell-\nu/N} +
     28\mathcal{L}_{Z_R-f-f}
     29\nonumber
     30\end{equation}
     31}}}
     32The W,,R,, chiral coupling to quarks are
     33{{{
     34#!latex
     35\begin{equation}
     36 \mathcal{L}_{W_R-q-q'} = \frac{-\kappa_R^q g}{\sqrt{2}}\sum_{i,j=u,d,\dots}\overline{u}_i V_{ij}^{\rm CKM'}~W_{R \mu}^+ \gamma^\mu P_R~ d_j + \text{H.c.}
     37\nonumber
     38\end{equation}
     39}}}
     40V,,ij,,^CKM'^ is the right-handed (RH) Cabbibo-Kobayashi-Masakawa (CKM) matrix and is related to the SM CKM matrix. g=\sqrt{4\pi\alpha_{\rm EM}(M_Z)}/\sin\theta_W is the SM Weak coupling constant and
     41k,,R,,^q^ is an overall normalization for the W,,R,, interaction strength.
     42For leptons, the W,,R,, coupling and leptonic mixing is parametrized by
     43[ [#Atre 3], [#Han 4] ],
     44{{{
     45#!latex
     46\begin{equation}
     47 \mathcal{L}_{W_R-\ell-N} = \frac{-\kappa_R^\ell g}{\sqrt{2}}
     48 \sum_{\ell=e,\mu,\tau}
     49 \sum_{m'=1}^3  \overline{N_{m'}} Y_{\ell m'}
     50~W_{R \mu}^+ \gamma^\mu P_R~ \ell^-+\text{H.c.}
     51\nonumber
     52\end{equation}
     53}}}
     54For chiral fermion f, the Z,,R,, neutral currents are parameterized by
     55{{{
     56#!latex
     57\begin{equation}
     58 \mathcal{L}_{Z_R-f-f} = \frac{-\kappa_{R}^f g}{\sqrt{1 - \left(1/\kappa_{R}^f\right)^2 \tan^2\theta_W}}\sum_{f=u,e,\dots}
     59 \overline{f} Z_{R \mu} \gamma^\mu \left(g_{L}^{Z_R,f}P_L + g_{R}^{Z_R,f}P_R\right)f.
     60\nonumber
     61\end{equation}
     62}}}
     63k,,R,,^f^ are the same k,,R,,^q,l^ as for W,,R,,. The chiral couplings g,,L,R,,^Z,,R,,,f^ are combinations of electric and isospin charges. For more details, see [ [#Mattelaer 1] ].
     64
     65
     66
     67
     68
     69
     70== QCD Corrections ==
     71The SM Lagrangian with Goldstone boson couplings in the Feynman Gauge
     72and the above Lagrangian in the Unitary 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.
     73In the UFO file, five massless quarks are assumed as are zero off-diagonal SM CKM and RH CKM' matrix entries. For additional details, see [ [#Mattelaer 1] ]. These additions permit tree-level calculations at LO and NLO in QCD and loop-induced calculations at LO in QCD using MadGraph_aMC@NLO, HERWIG, and SHERPA.
     74
     75
     76== Model Files ==
     77 * [http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/EffLRSM/EffLRSM_NLO.tgz EffLRSM_NLO.tgz]: Standalone NLO in QCD-accurate UFO folder.
     78
     79 * [http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/EffLRSM/effLRSM.fr effLRSM.fr]: Main model file. Relies on sm.fr (default FR model file) being declared elsewhere.
     80
     81 * [http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/EffLRSM/effLRSMnlo.nb effLRSMnlo.nb]: Mathematica notebook file that generates UFO file from FeynRules model files. Allows user to also run quick sanity checks (optional) on model.
     82
     83 * [http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/EffLRSM/EffLRSMnlo_Files.tgz EffLRSMnlo_Files.tgz]: Standalone package containing effLRSM.fr, effLRSMnlo.nb, diagonalMixing.rst, massless.rst (default FR file), and sm.fr (default FR file).
     84
     85 * [http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/EffLRSM/EffLRSMnlo_FilesWithUFO.tgz EffLRSMnlo_FilesWithUFO.tgz]: Combination of EffLRSMnlo_Files.tgz and EffLRSM_NLO.tgz.
     86
     87
     88To open any of the packages and unpack via the terminal, use the commands:
     89
     90'''~/Path $''' tar -zxvf EffLRSM_NLO.tgz
     91
     92'''~/Path $''' tar -zxvf EffLRSMnlo_FilesWithUFO.tgz
     93
     94== Notes ==
     95 * '''Important''': Default parameters are set so "out-of-the-box" checks can be made with [ [#Mattelaer 1] ] and [ [#Mitra 2] ].
     96
     97 * Aside from the SM inputs, this model contains 28 free parameters:
     98  * Five masses: MWR, MZR, mN1, mN2, mN3. Defaults are 3 TeV, 5.07 TeV, 173.3 GeV, 10^12^ GeV, and 10^14^ GeV, respectively.
     99  * Five widths: WWR, WZR, WN1, WN2, WN3. Defaults are 84.3 GeV, 114 GeV, 2.12^-8^ GeV, 100 GeV, and 100 GeV, respectively.
     100  * Nine real (no CP violation) mixing parameters for RH quark mixing: VCKMR[u,d] for ''u'' = ''up (1), charm (2), top (3)'' and ''d'' = ''down (1), strange (2), bottom (3)''. Default values are VCKMR = Identity(3x3), i.e., VCKMR[1,1] = VCKMR[2,2] = VCKMR[3,3] = 1 and all others zero.
     101  * Nine real (no CP violation) mixing parameters for RH leptonic mixing: YlN[l,N] for ''l'' = ''e (1), mu (2), tau (3)'' and ''N = N1 (1), N2 (2), N3 (3).'' Default values are YlN = Identity(3x3), i.e., YlN[1,1] = YlN[2,2] YlN[3,3] and all others zero.
     102 
     103 * Default model settings assumes five massless quarks, massless light neutrinos, and massless charged leptons. This is easily modifiable by regenerating UFO files.
     104
     105
     106
     107== Validation ==
     108* Partial and total widths for W,,R,,, Z,,R,,, and N,,1,, are checked against exact analytic calculations. See [ [# 1] ] for more information.
     109* The model file was checked against exact NLO W,,R,, predictions from [ [# 2] ] and references within [ [# 1] ].
     110
     111
     112
     113=== List of studies that have used the model file ===
     114* Please email to update this space.
     115
     116
     117== References ==
     118* Please cite [ 1 ] for the model file and [ 2 ] for neutrino jets.
     119
     120[=#Mattelaer] [1] O. Mattelaer, M. Mitra, R. Ruiz,
     121''Automated Neutrino Jet and Top Jet Predictions at NLO+PS Matching in Effective Left-Right Symmetric Models,'' arXiv:1610.08985 [hep-ph]
     122
     123[=#Mitra] [2] M. Mitra, D. Scott, and M. Spannowsky,
     124''Neutrino Jets from High-Mass W,,R,, Gauge Bosons in TeV-Scale Left-Right Symmetric Models'', arXiv:1607.03504 [hep-ph]
     125
     126
     127[=#Atre] [3] A. Atre, T. Han, S. Pascoli and B. Zhang, ''The Search for Heavy Majorana Neutrinos,'' JHEP '''0905''', 030 (2009),  arXiv:0901.3589 [hep-ph]
     128
     129[=#Han] [4] T. Han, I. Lewis, R. Ruiz, Z.-G. Si, ''Lepton Number Violation and W' Chiral Couplings at the LHC,'' PRD87, 035011 (2013)