Changes between Version 3 and Version 4 of WZPrimeAtNLO
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 01/19/17 16:54:27 (8 months ago)
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WZPrimeAtNLO
v3 v4 13 13 14 14 == Model Description == 15 This effective model extends the Standard Model (SM) field content by introducing the massive vector fields {{{$W^{'#pm}$}}} and {{{$Z'$}}} bosons, andare electrically charged and neutral, respectively. To remain model independence, couplings to SM gauge bosons and scalars are omitted.15 This effective model extends the Standard Model (SM) field content by introducing the massive vector fields W'^+/^ and Z' bosons, which are electrically charged and neutral, respectively. To remain model independence, couplings to SM gauge bosons and scalars are omitted. 16 16 17 Following Refs. [ [#Gopalakrishna X], [#Han Y] ], the Lagrangian parameterizing the new vector bosons' couplings to uptype and downtype quark fields {{{$u_i$}}} and {{{$d_j$}}}is given by17 Following Refs. [ [#Gopalakrishna 1], [#Han 2] ], the Lagrangian parameterizing the new vector bosons' couplings to uptype and downtype quark fields u,,i,, and d,,j,, is given by 18 18 {{{ 19 19 #!latex 20 20 \begin{eqnarray} 21 21 \mathcal{L}^q = 22 22  \frac{g}{\sqrt{2}} \sum_{i,j} \Big[ 23 23 \overline{u}_i V_{ij}^{\rm CKM}~W_\mu^{\prime+}~\gamma^\mu … … 30 30 \end{eqnarray} 31 31 }}} 32 Here, {{{$i$}}} and {{{$j$}}} denote flavor indices, {{{$P_{L/R}=(1/2)(1\mp\gamma_5)$}}} and33 are the usual left/righthanded chirality projectors, {{{$V^{\rm CKM}$}}}is the CKM matrix,32 Here, {{{$i$}}} and {{{$j$}}} denote flavor indices, P,,L/R,, 33 are the usual left/righthanded chirality projectors, V^CKM^ is the CKM matrix, 34 34 and {{{$g$}}} and {{{$\theta_W$}}} are the weak coupling constant and mixing angle respectively. 35 We choose coupling normalizations facilitating the mapping to the reference Sequential Standard Model 36 Lagrangian {{{${\cal L}_{\rm SSM}$}}} [ [#Altarelli X] ]. 35 We choose coupling normalizations facilitating the mapping to the reference Sequential Standard Model (SSM) Lagrangian {{{${\cal L}_{\rm SSM}$}}} [ [#Altarelli 3] ]. 37 36 The realvalued quantities {{{$\kappa_{L,R}^q$}}} and {{{$\zeta_{L,R}^q$}}} 37 serve as overall normalization of the new interactions relative to the strength of the weak coupling constant. 38 38 39 39 The interactions involving charged lepton $\ell$ and massless neutrino $\nu_\ell$ fields are parametrized by 40 40 {{{ 41 41 #!latex 42 42 \begin{eqnarray} 43 \mathcal{L}^\ell_{\rm NP}=43 \mathcal{L}^\ell = 44 44  \frac{g}{\sqrt{2}}\sum_i\Big[ 45 45 \overline{\nu}_{\ell_i} W_\mu^{\prime+}~\gamma^\mu … … 55 55 leptonic coupling strengths. As no righthanded neutrinos are present in the SM, the corresponding 56 56 righthanded leptonic new physics couplings are omitted ({{{$\zeta_R^\nu = \kappa_R^\ell = 0$}}}). 57 We assume that leptonic interactions are flavor diagonal.58 57 59 60 58 From our general Lagrangians, the SSM limit is obtained by imposing the coupling strengths to be equal to the SM weak couplings up to an overall normalization factor: 61 59 {{{ 62 60 #!latex … … 69 67 \end{eqnarray} 70 68 }}} 71 72 In 73 the canonical SSM, the overall normalizations are further trivially fixed as 69 In the canonical SSM, the overall normalizations are further trivially fixed as 74 70 {{{ 75 71 #!latex … … 84 80 85 81 86 == QCD Corrections ==82 == NLO in QCD Corrections == 87 83 The 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. 88 84 In the UFO file, five massless quarks are assumed as are zero offdiagonal CKM matrix entries. 89 For additional details, see [ [#Fuks 2] ] and references therein.85 For additional details, see [ [#Fuks 4] ] and references therein. 90 86 These additions permit treelevel calculations at LO and NLO in QCD, loopinduced calculations at LO in QCD, and NLO matched to NNLL(Veto) resummation using MadGraph_aMC@NLO. 91 87 … … 124 120 125 121 == Validation == 126 * 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.122 * The model file was validated at NLO in [ [#Fuks 4] ] by comparing against Standard Model predictions and W^'^ predictions from [ [#Sullivan 5 ] ], as well as private LO and NLO calculations. See Table III of [ [#Fuks 4] ] for representative total widths that have been checked against analytic computation. 127 123 128 124 … … 131 127 132 128 == References == 133 * Please cite [ ] for the model file, [] for NLO corrections, and [] for automated veto resummation.129 * Please cite [3,4] for the model file, [4,5] for NLO corrections, and [6] for automated veto resummation. 134 130 135 [=# Altarelli] [] G. Altarelli, B. Mele and M. RuizAltaba, ''Searching for New Heavy Vector Bosons in $p \bar{p}$ Colliders,'' Z. Phys. C'''45''', 109 (1989), doi:10.1007/BF01556677131 [=#Gopalakrishna] [1] 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 [hepph] 136 132 137 [=# 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[hepph]133 [=#Han] [2] 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 [hepph] 138 134 139 [=# Sullivan] [] Z. Sullivan, ''Fully differential {{{$W'$}}} production and decay at nexttoleading order in QCD,'' PRD'''66''', 075011 (2002), arXiv:hepph/0207290135 [=#Altarelli] [3] G. Altarelli, B. Mele and M. RuizAltaba, ''Searching for New Heavy Vector Bosons in $p \bar{p}$ Colliders,'' Z. Phys. C'''45''', 109 (1989), doi:10.1007/BF01556677 140 136 141 [=# Becher] [] T. Becher, R. Frederix, M. Neubert and L. Rothen, ''Automated NNLL $+$ NLO resummation for jetveto cross sections,'' EPJC'''75''', no. 4, 154 (2015) arXiv:1412.8408[hepph]137 [=#Fuks] [4] B. Fuks, R. Ruiz, ''A Comprehensive Framework for Studying {{{$W'$}}} and {{{$Z'$}}} Bosons at Hadron Colliders with Automated Jet Veto Resummation,'' arXiv:1701.xxxx [hepph] 142 138 143 [=# 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 [hepph]139 [=#Sullivan] [5] Z. Sullivan, ''Fully differential {{{$W'$}}} production and decay at nexttoleading order in QCD,'' PRD'''66''', 075011 (2002), arXiv:hepph/0207290 144 140 145 [=#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 [hepph] 141 [=#Becher] [6] T. Becher, R. Frederix, M. Neubert and L. Rothen, ''Automated NNLL $+$ NLO resummation for jetveto cross sections,'' EPJC'''75''', no. 4, 154 (2015) arXiv:1412.8408 [hepph] 142