Changes between Version 10 and Version 11 of SMEFTatNLO


Ignore:
Timestamp:
Aug 28, 2020, 9:30:37 AM (5 years ago)
Author:
Ken Mimasu
Comment:

Post paper submission

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  • SMEFTatNLO

    v10 v11  
    1 
    2 == Standard Model Effective Theory at Next-to-Leading-Order in QCD ==
     1== Standard Model Effective Theory at One-Loop in QCD ==
    32
    43 ''Céline Degrande, Gauthier Durieux, Fabio Maltoni, Ken Mimasu, Eleni Vryonidou & Cen Zhang''
    54
    6 A complete implementation of the SMEFT compatible with NLO QCD predictions.
    7 
    8 The implementation is based on the Warsaw basis of operators and includes all degrees of freedom consistent with the following symmetry assumptions:
    9 * CP-conservation.
    10 * U(2),,Q,, x U(2),,u,, x U(3),,d,, x U(3),,L,, x U(3),,e,, flavor symmetry.
    11 The CKM matrix is approximated as a unit matrix. The flavor symmetry imposes that only the top quark is massive. The model therefore implements the 5-flavor scheme for PDFs.
    12 The bosonic operators are implemented as in the Warsaw basis employing the M,,Z,,, M,,W,,, G,,F,, scheme of Electroweak input parameters.
    13 
    14 The Standard Model input parameters that need to be specified are:
    15 
    16    M,,Z,,, M,,W,,, G,,F,,, M,,H,,, M,,t,,, α,,S,,(M,,Z,,)
    17 
    18 The fermionic degrees of freedom (2 & 4 fermion operators) are defined according to the common standards and prescriptions established by the  LHC TOP WG for the EFT interpretation of top-quark measurements at the LHC (see the [https://feynrules.irmp.ucl.ac.be/wiki/dim6top dim6top page] for more information). This model has been validated at LO with the dim6top implementation.
    19 
    20 A new coupling order, {{{NP}}}, is added to the model for the SMEFT interactions. It is assigned through the universal cutoff parameter, {{{Lambda}}}, which takes a default value of 1 TeV^-2^ and can be modified along with the Wilson coefficients in the param card.
    21 
    22 The  [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SMEFTatNLO/definitions.pdf definitions.pdf] document specifies the operators definitions, normalisations and coefficient names in the UFO model
     5The implementation is based on the Warsaw basis of dimension-six SMEFT operators, after canonical normalization.
     6Electroweak input parameters are taken to be G,,F,,, M,,Z,,, M,,W,,.
     7The CKM matrix is approximated as a unit matrix, and a U(2),,q,, x U(2),,u,, x U(3),,d,, x (U(1),,l,, x U(1),,e,,)^3^ flavor symmetry is enforced.
     8It forbids all fermion masses and Yukawa couplings except that only of the top quark.
     9The model therefore implements the five-flavor scheme for PDFs.
     10
     11
     12A new coupling order, {{{NP=2}}}, is assigned to SMEFT interactions.
     13The cutoff scale {{{Lambda}}} takes a default value of 1 TeV^-2^ and can be modified along with the Wilson coefficients in the {{{param_card}}}.
     14Operators definitions, normalisations and coefficient names in the UFO model are specified in [attachment:definitions.pdf].
     15The notations and normalizations of top-quark operator coefficients comply with the LHC TOP WG standards of [https://arxiv.org/abs/1802.07237 1802.07237].
     16Note however that the flavor symmetry enforced here is slightly more restrictive than the baseline assumption there (see the [wiki:dim6top dim6top page] for more information).
     17This model has been validated at tree level against the {{{dim6top}}} implementation (see [https://arxiv.org/abs/1906.12310 1906.12310] and the [https://bazaar.launchpad.net/~rwgtdim6/mg5amcnlo/plugin_eft_contrib/files/head:/example/ comparison details]).
     18
     19
     20
     21=== Current implementation ===
     22
     23UFO model: [attachment:SMEFTatNLO_v1.0.tgz]
     24
     25The current implementation imposes CP conservation.
     26In the quark sector, it focuses primarily on top-quark interactions.
     27The light-quark current operator, qqHDH, uuHDH, ddHDH, with coefficients {{{cpq3i}}}, {{{cpqMi}}}, {{{cpu}}}, {{{cpd}}} are however included.
     28The triple-gluon operator, with coefficient {{{cG}}}, is currently not available (see the loop-capable [wiki:GGG] implementation).
     29Vertices including more than four scalars or four leptons are not included.
     30Scalar and tensor {{{QQll}}} operators, with coefficients {{{ctlS3}}}, {{{ctlT3}}}, and {{{cblS3}}}, break our flavor symmetry assumption and are not available for one-loop computations.
     31Top-quark flavor-changing interactions, not compatible with the imposed flavor symmetry, are not included (see the loop-capable [https://feynrules.irmp.ucl.ac.be/wiki/TopFCNC TopFCNC] implementation).
     32
     33Unlike prescribed by the LHC TOP WG, the top quark chromomagnetic-dipole operator coefficient {{{ctG}}} is normalized with a factor of the strong coupling, g,,S,,.
     34This normalization factor temporarily ensures compatibility with the 2.X.X series of MadGraph5_aMC@NLO but may be dropped in the future.
     35As with every other appearance of this coupling in MadGraph5_aMC@NLO, its value is renormalisation-group evolved to the QCD renormalization scale (set in the run_card).
     36
     37
     38Counterterms required for one-loop computations are currently included up to five points.
     39The unitary gauge (default) is recommended when computing anomalous quark-loop amplitudes like {{{ggZ}}}, {{{gggZ}}}, {{{ggZH}}} and {{{ggff}}}.
     40
     41
     42MadGraph5_aMC@NLO does not evolve operator coefficients which are therefore kept at fixed scale {{{mueft}}} distinguished from the QCD renormalization scale {{{MUR}}}.
     43We recommend to use fixed renormalization and factorization scales (in the {{{run_card}}}), and to set {{{mueft}}} equal to those (in the {{{param_card}}}).
     44
     45
     46The {{{3.0.3-neworders}}} development branch ([https://bazaar.launchpad.net/~maddevelopers/mg5amcnlo/3.0.3-neworders/tarball/ tarball]) of MG is required for NLO predictions involving four-fermion operators and (in general) H^2^G^2^ with coefficient {{{cpG}}} not normalized with any power of g,,S,,.
     47It also allows for a better control over coupling orders and, in particular, for the separate computation of linear and quadratic EFT contributions at NLO, in fixed order mode.
     48A branch allowing for the separate computation of different orders in event-generation mode (with matching to parton shower) is being validated.
     49The 2.X.X series of MadGraph5_aMC@NLO can handle bosonic and two-fermion operators at one-loop.
     50
     51
     52==== Version updates ====
     53* 2018/12/20  - v0.1: First version upload, 4F and c,,G,, operators at LO pending validation; a few minor convention tweaks required to match {{{dim6top}}} exactly. {{{decays.py}}} missing.
     54* 2019/04/03  - v0.1: Added definitions.pdf document and uploaded a new version with a fix for restrict_default.dat
     55* 2019/08/12  - v0.1: Uploaded a new version matching {{{dim6top}}} operator conventions, also some bugfixes and gs normalisation for {{{OtG}}}
     56* 2020/08/24  - v1.0: Official release including notably four-quark operators at NLO.
     57
     58
    2359=== Usage notes ===
     60
    2461==== Restriction cards ====
    2562Because of the mixture of LO/NLO compatible operators included in the model, restriction cards must be used to access the SMEFT interactions.
    … …  
    2764Default loading of the model
    2865{{{
    29  > import model SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO
     66 > import model SMEFTatNLO_vX.X
    3067}}}
    3168will load the pure SM without any effective operators.
    … …  
    3370The {{{LO}}} restriction card should be used when importing the model for LO generation:
    3471{{{
    35  > import model SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO-LO
     72 > import model SMEFTatNLO_vX.X-LO
    3673}}}
    3774
    3875For NLO QCD generation, the {{{NLO}}} restriction card should be used when importing the model:
    3976{{{
    40  > import model SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO-NLO
     77 > import model SMEFTatNLO_vX.X-NLO
    4178}}}
    4279This invokes a restricted set of operators for which the required counterterms are implemented.
    4380
    4481==== Coupling orders ====
    45 
    4682We recommend specifying the full {{{QCD}}}, {{{QED}}} and {{{NP}}} orders for process generation.
    4783
    … …  
    5187 > generate p p > t t~ QCD=2 QED=0 NP=2 [QCD]
    5288}}}
    53 Generates the NLO QCD top pair production process including the QCD-induced SM and the SMEFT contributions.
     89generates top-quark pair production at NLO QCD, including the QCD-induced SM and the SMEFT contributions.
    5490
    5591==== Excluding operators ====
    56 
    5792We recommend avoiding setting values of Wilson coefficients to 0 when computing at NLO using MadGraph5_aMC@NLO.
    5893
    5994Operators should either be removed explicitly with restriction cards or set to a very small non-zero value, e.g., 1e-5
    60 === Model Files ===
    61 * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/SMEFTatNLO/SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO.20190812.tgz SMEFTatNLO_U2_2_U3_3_cG_4F_LO_UFO.tgz] : archive of UFO model - 4 fermion and c,,G,, operators at LO, U(2)^2^ x U(3)^3^ flavor symmetry
    62 === Version updates ===
    63 * 2018/12/20  - v.0.1: First version upload, 4F and c,,G,, operators at LO pending validation; a few minor convention tweaks required to match dim6top exactly. {{{decays.py}}} missing.
    64 * 2019/04/03  - v.0.1: Added definitions.pdf document and uploaded a new version with a fix for restrict_default.dat
    65 * 2019/08/12  - v.0.1:  Uploaded a new version matching dim6top operator conventions, also some bugfixes and gs normalisation for otG
     95
     96==== Plugin for b-quark Yukawa coupling and operator ({{{ymb}}} and {{{cbp}}}) ====
     97
     98A plugin-like modification to the model including the bbh (SM+SMEFT), bbhh and bbhhh interactions has been implemented to account for the Higgs coupling to bottom quarks.
     99It can only be used at LO.
     100A {{{configuration.py}}} file is included in the UFO model with a {{{bottomYukawa}}} flag set to {{{False}}} by default.
     101Setting it to {{{True}}} restores the SM & SMEFT bottom Yukawa parameters ({{{ymb}}} and {{{cbp}}}), the bbh(h)(h) vertices, and corresponding couplings.
     102The bottom mass parameters, {{{MB}}}, is not restored which has a percent effect on the {{{h > b b~}}} partial width.
     103The corresponding Goldstone boson interactions are not included, such that the extended model can only be used in unitary gauge (default).
     104
     105=== Generation recipes for validated processes ===
     106Among many others, the following processes are supported at the one-loop level.
     107Gauge invariance (see {{{help check}}} in MadGraph5_aMC@NLO) and pole cancellation have been checked explicitly for those.
     108For complicated processes and in case of doubts, please contact the authors.
     109Widths should be set to zero to ensure gauge invariance.
     110
     111==== QCD ====
     112{{{
     113 > p p > j j          QED=0 QCD=2 NP=2 [QCD]
     114}}}
     115
     116==== Drell Yan ====
     117{{{
     118 > p p > mu+ mu-      QCD=0 QED=2 NP=2 [QCD]
     119 > p p > mu+ vm       QCD=0 QED=2 NP=2 [QCD]
     120 > p p > W+  j  $$ t  QCD=1 QED=1 NP=2 [QCD]
     121 > p p > W-  j  $$ t~ QCD=1 QED=1 NP=2 [QCD]
     122 > p p > Z   j        QCD=1 QED=1 NP=2 [QCD]
     123}}}
     124
     125==== Multi-boson production ====
     126''quark-initiated''
     127
     128{{{
     129 > p p > W+ W-    QED=2 QCD=0 NP=2 [QCD]
     130 > p p > W+ Z     QED=2 QCD=0 NP=2 [QCD]
     131 > p p > Z  Z     QED=2 QCD=0 NP=2 [QCD]
     132}}}
     133   
     134''loop-induced''
     135
     136{{{
     137 > g g > W+ W-    QED=2 QCD=2 NP=2 [QCD]
     138 > g g > Z  Z     QED=2 QCD=2 NP=2 [QCD]
     139 > g g > W+ W- Z  QED=3 QCD=2 NP=2 [QCD]
     140 > g g > Z  Z  Z  QED=3 QCD=2 NP=2 [QCD]
     141}}}
     142
     143==== Higgs production ====
     144
     145''loop-induced''
     146{{{
     147 > g g > H        QED=1 QCD=2 NP=2 [QCD]
     148 > g g > H H      QED=2 QCD=2 NP=2 [QCD]
     149 > g g > H H H    QED=3 QCD=2 NP=2 [QCD]
     150 > g g > H j      QED=1 QCD=3 NP=2 [QCD]
     151}}}
     152
     153==== Top quark production ====
     154{{{
     155 > e+ e- > t t~        QED=2 QCD=0 NP=2 [QCD]
     156 > p p > t t~          QED=0 QCD=2 NP=2 [QCD]
     157 > p p > t t~ h        QED=1 QCD=2 NP=2 [QCD]
     158 > p p > t t~ Z        QED=1 QCD=2 NP=2 [QCD]
     159 > p p > t t~ W+       QED=1 QCD=2 NP=2 [QCD]
     160 > p p > t W-    $$ t~ QED=1 QCD=1 NP=2 [QCD]
     161 > p p > t W- j  $$ t~ QED=1 QCD=2 NP=2 [QCD]
     162 > p p > t j     $$ W- QED=2 QCD=0 NP=2 [QCD]
     163 > p p > t h j   $$ W- QED=3 QCD=0 NP=2 [QCD]
     164 > p p > t Z j   $$ W- QED=3 QCD=0 NP=2 [QCD]
     165 > p p > t a j   $$ W- QED=3 QCD=0 NP=2 [QCD]
     166}}}
     167
     168When generating one of the last four processes ({{{tj}}},{{{thj}}},{{{tZj}}},{{{taj}}}) with the {{{cQq83}}} operator coefficient, all loops including a gluon have to be allowed.
     169This can be achieved with the following modification of MadGraph5_aMC@NLO:
     170{{{
     171=== modified file 'madgraph/loop/loop_diagram_generation.py'
     172--- madgraph/loop/loop_diagram_generation.py    2020-03-11 09:28:14 +0000
     173+++ madgraph/loop/loop_diagram_generation.py    2020-04-03 21:08:18 +0000
     174@@ -384,7 +384,7 @@
     175         # By default the user filter does nothing if filter is not set,
     176         # if you want to turn it on and edit it by hand, then set the
     177         # variable edit_filter_manually to True
     178-        edit_filter_manually = False
     179+        edit_filter_manually = True
     180         if not edit_filter_manually and filter in [None,'None']:
     181             return
     182         if isinstance(filter,str) and  filter.lower() == 'true':
     183@@ -415,6 +415,10 @@
     184                     raise InvalidCmd("The user-defined filter '%s' did not"%filter+
     185                                  " returned the following error:\n       > %s"%str(e))
     186 
     187+            # requires a gluon to run in all loops
     188+            if 21 not in diag.get_loop_lines_pdgs():
     189+                valid_diag = False
     190+
     191 #            if any([abs(pdg) not in range(1,7) for pdg in diag.get_loop_lines_pdgs()]):
     192 #                valid_diag = False
     193 
     194@@ -538,7 +542,7 @@
     195             
     196             if valid_diag:
     197                 newloopselection.append(diag)
     198-        self['loop_diagrams']=newloopselection
     199+        #self['loop_diagrams']=newloopselection
     200         # To monitor what are the diagrams filtered, simply comment the line
     201         # directly above and uncomment the two directly below.
     202 #        self['loop_diagrams'] = base_objects.DiagramList(
     203}}}
     204
     205==== Analytic validation ====
     206The following loop computations of amplitudes relevant for several processes have been cross-checked analytically:
     207    * ttbar: tt, gg, ggg, gtt, ggtt
     208    * single top/decay: tbW, 4f
     209    * ttV: ttV, ggV, gggV, gttV
     210    * ttH: ggh, gggh, htt, ghtt