Changes between Version 22 and Version 23 of SMEFTatNLO


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Timestamp:
Dec 16, 2020, 3:29:44 PM (4 years ago)
Author:
gdurieux
Comment:

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  • SMEFTatNLO

    v22 v23  
    33 ''Céline Degrande, Gauthier Durieux, Fabio Maltoni, Ken Mimasu, Eleni Vryonidou & Cen Zhang'', [https://arxiv.org/abs/2008.11743 arXiv:2008.11743]
    44
    5 The implementation is based on the Warsaw basis of dimension-six SMEFT operators, after canonical normalization.
     5The implementation is based on the Warsaw basis of dimension-six SMEFT operators, after canonical normalisation.
    66Electroweak input parameters are taken to be G,,F,,, M,,Z,,, M,,W,,.
    7 The 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.
    8 It forbids all fermion masses and Yukawa couplings except that only of the top quark.
    9 The model therefore implements the five-flavor scheme for PDFs.
    10 
    11 
    12 A new coupling order, {{{NP=2}}}, is assigned to SMEFT interactions.
     7The CKM matrix is approximated as a unit matrix, and an exact U(2),,q,, x U(2),,u,, x U(3),,d,, x (U(1),,l,, x U(1),,e,,)^3^ flavour symmetry is enforced.
     8It notably forbids all fermion masses and Yukawa couplings except that only of the top quark.
     9The model therefore implements the five-flavour scheme for PDFs.
     10
     11
     12A new coupling order {{{NP=2}}} is assigned to SMEFT interactions.
    1313The cutoff scale {{{Lambda}}} takes a default value of 1 TeV^-2^ and can be modified along with the Wilson coefficients in the {{{param_card}}}.
    1414Operators definitions, normalisations and coefficient names in the UFO model are specified in [attachment:definitions.pdf].
    15 The notations and normalizations of top-quark operator coefficients comply with the LHC TOP WG standards of [https://arxiv.org/abs/1802.07237 1802.07237].
    16 Note 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).
     15The notations and normalisations of top-quark operator coefficients mostly comply with the LHC TOP WG standards of [https://arxiv.org/abs/1802.07237 1802.07237].
     16Note however that the flavour symmetry enforced here is slightly more restrictive than the baseline assumption there (see the [wiki:dim6top dim6top page] for more information about differences).
    1717This 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]).
    1818
    … …  
    2121=== Current implementation ===
    2222
    23 UFO model: [attachment:SMEFTatNLO_v1.0.tar.gz]
     23UFO model: [attachment:SMEFTatNLO_v1.0.1.tar.gz]
    2424
    2525The current implementation imposes CP conservation.
    … …  
    2727The light-quark current operator, qqHDH, uuHDH, ddHDH, with coefficients {{{cpq3i}}}, {{{cpqMi}}}, {{{cpu}}}, {{{cpd}}} are however included.
    2828The triple-gluon operator, with coefficient {{{cG}}}, is currently not available (see the loop-capable [wiki:GGG] implementation).
    29 Vertices including more than four scalars or four leptons are not included.
    30 Scalar and tensor {{{QQll}}} operators, with coefficients {{{ctlS3}}}, {{{ctlT3}}}, and {{{cblS3}}}, break our flavor symmetry assumption and are not available for one-loop computations.
    31 Top-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 
    33 Unlike 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,,.
    34 This normalization factor temporarily ensures compatibility with the 2.X.X series of MadGraph5_aMC@NLO but may be dropped in the future.
    35 As 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).
     29Vertices including four leptons or more than four scalars are not included.
     30Scalar and tensor {{{QQll}}} operators, with coefficients {{{ctlS3}}}, {{{ctlT3}}}, and {{{cblS3}}}, break our flavour symmetry assumption and are not available for one-loop computations.
     31Top-quark flavour-changing interactions, not compatible with the imposed flavour 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 normalised with a factor of the strong coupling, g,,S,,.
     34This normalisation 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 renormalisation scale (set in the run_card).
    3636
    3737
    3838Counterterms required for one-loop computations are currently included up to five points.
    39 The unitary gauge (default) is recommended when computing anomalous quark-loop amplitudes like {{{ggZ}}}, {{{gggZ}}}, {{{ggZH}}} and {{{ggff}}}.
    40 
    41 
    42 MadGraph5_aMC@NLO does not evolve operator coefficients which are therefore kept at fixed scale {{{mueft}}} distinguished from the QCD renormalization scale {{{MUR}}}.
    43 We 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 
    46 The {{{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,,.
     39The unitary gauge (default) is required 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 renormalisation scale {{{MUR}}}.
     43We recommend to use fixed renormalisation and factorisation scales (in the {{{run_card}}}), and to set {{{mueft}}} equal to those (in the {{{param_card}}}).
     44
     45
     46The {{{3.0.3-neworders}}} or {{{3.0.4}}} development branches of MG ([https://bazaar.launchpad.net/~maddevelopers/mg5amcnlo/3.0.3-neworders/tarball here] and [https://bazaar.launchpad.net/~maddevelopers/mg5amcnlo/3.0.4/tarball here]) are required for one-loop predictions involving four-quark operators and (in general) H^2^G^2^ with coefficient {{{cpG}}} not normalised with any power of g,,S,,.
    4747It also allows for a better control over coupling orders and, in particular, for the separate computation of linear and quadratic EFT contributions at NLO.
    48 It is however only available for fixed order computations (i.e. not for event generation).
     48It is however only available for fixed order computations (i.e. not for event generation, with {{{fixed_order = ON}}}).
    4949Sufficiently coarse differential distributions can be obtained by implementing a !FixedOrderAnalysis in Fortran (see examples in the corresponding subdirectory).
    50 A branch allowing for the separate computation of different orders in event-generation mode (with matching to parton shower) is being validated.
     50A branch allowing for the separate computation of different orders in event-generation mode (with matching to parton shower) is currently being validated.
    5151
    5252The 2.X.X series of MadGraph5_aMC@NLO should be used for event generation (i.e. beyond fixed-order computations).
    53 It can handle bosonic and two-fermion operators at one-loop.
    54 The model should in that case be loaded with a restriction card where other coefficients are set to zero.
     53It can however not handle four-quark operators at one-loop.
     54The model should in that case be loaded with the {{{no4q}}} restriction card (doing {{{import model SMEFTatNLO-no4q}}}) which excludes four-quark operator coefficients.
     55An exception is single top-quark production in which the colour singlet {{{cQq13}}} and and octet {{{cQq83}}} are available in 2.X.X.
     56For the latter, see however the specific instructions below about "loop filtering".
    5557
    5658
    … …  
    6163* 2019/08/12  - v0.1: Uploaded a new version matching {{{dim6top}}} operator conventions, also some bugfixes and gs normalisation for {{{OtG}}}
    6264* 2020/08/24  - v1.0: Official release including notably four-quark operators at NLO.
     65* 2020/12/16  - v1.0.1: Compatible with python3; BR for t,W,Z (SM and LO) in restriction cards to ease Madspin use; {{{no4q}}} restriction card without four-quark operators for use with MG v2.
    6366
    6467=== Support  ===
    … …  
    100103We recommend avoiding setting values of Wilson coefficients to 0 when computing at NLO using MadGraph5_aMC@NLO.
    101104
    102 Operators should either be removed explicitly with restriction cards or set to a very small non-zero value, e.g., 1e-5.
     105Operators should either be removed explicitly with restriction cards or set to a very small non-zero value in parameter cards, e.g., 1e-5.
    103106
    104107==== Plugin for b-quark Yukawa coupling and operator ({{{ymb}}} and {{{cbp}}}) ====
    … …  
    109112Setting it to {{{True}}} restores the SM & SMEFT bottom Yukawa parameters ({{{ymb}}} and {{{cbp}}}), the bbh(h)(h) vertices, and corresponding couplings.
    110113The bottom mass parameters, {{{MB}}}, is not restored which has a percent effect on the {{{h > b b~}}} partial width.
    111 The corresponding Goldstone boson interactions are not included, such that the extended model can only be used in unitary gauge (default).
     114The corresponding Goldstone-boson interactions are not included, such that the extended model can only be used in unitary gauge (default).
    112115
    113116==== !MadSpin
    114 [https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/MadSpin MadSpin] can be used to perform tree-level decays (accounting for leading-order spin correlations).
    115 Information about the branching fractions of the decayed particles should then be included in the restriction (and/or param) card used.
    116 E.g. for the top quark, Z and W bosons:
    117 {{{
    118 DECAY  6   1.470800e+00
    119    1.000000e+00   2    5  24 # 1.4708
    120 DECAY  23   2.416039e+00
    121    1.517939e-01   2    -1  1
    122    1.517939e-01   2    -3  3
    123    1.517939e-01   2    -5  5
    124    1.176099e-01   2    -2  2
    125    1.176099e-01   2    -4  4
    126    6.865783e-02   2    -12  12
    127    6.865783e-02   2    -14  14
    128    6.865783e-02   2    -16  16
    129    3.447502e-02   2    -11  11
    130    3.447502e-02   2    -13  13
    131    3.447502e-02   2    -15  15
    132 DECAY  24   2.002950e+00
    133    3.333333e-01   2    -1  2
    134    3.333333e-01   2    -3  4
    135    1.111111e-01   2    -11  12
    136    1.111111e-01   2    -13  14
    137    1.111111e-01   2    -15  16
    138 }}}
    139 These values can be recomputed for a given param_card by running {{{compute_widths <particle-name> --path=<input-param-card> --output=<updated-param-card>}}} after having loaded the model.
    140 To ensure gauge invariance, MadGraph_aMC@NLO would still set the widths of external particles to zero (saying, e.g., "For gauge cancellation, the width of 'Z' has been set to zero") but pass the required information to !MadSpin.
    141 If the operator coefficients varied affect the widths of the decayed particles, extra care must be taken to properly account for that dependence.
     117[https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/MadSpin MadSpin] can be used to perform tree-level decays, accounting for leading-order spin correlations.
     118Information about the branching fractions of the decayed particles should then be included already in the restriction card used.
     119To ensure gauge invariance, MadGraph_aMC@NLO would still set the widths of external particles to zero (warning, e.g., that "For gauge cancellation, the width of 'Z' has been set to zero") but would pass the required information to !MadSpin.
     120From version 1.0.1 of the model, distributed {{{NLO}}} and {{{LO}}} restriction cards include the branching fraction information for top-quark, Z and W bosons.
     121These are computed in the SM, with default input parameters (Gf, MZ, MW, MT, etc.), and at tree level (consistently with the accuracy of !MadSpin).
     122If input parameters are modified from their default values, or to include SMEFT effects, these branching fractions need to be recomputed.
     123This can be done for a given {{{<input-param-card>}}} by running {{{compute_widths <particle-names> --path=<input-param-card> --output=<updated-param-card>}}} after having loaded the model.
     124The {{{<updated-param-card>}}} produced should then include branching-fraction information for the specified {{{<particle-names>}}} that is consistent with the other parameters it contains.
     125
    142126
    143127=== Generation recipes for validated processes ===
    144128Among many others, the following processes are supported at the one-loop level.
    145 Gauge invariance (see {{{help check}}} in MadGraph5_aMC@NLO) and pole cancellation have been checked explicitly for those.
    146 Widths should be set to zero to ensure gauge invariance.
     129Gauge invariance (see {{{help check}}} in MadGraph5_aMC@NLO) and pole cancellation have been checked explicitly for those (setting all widths set to zero is then required).
    147130For complicated processes and in case of doubts, please contact the authors.
    148131
    … …  
    163146==== Multi-boson production ====
    164147''quark-initiated''
    165 
    166148{{{
    167149 > p p > W+ W-    QED=2 QCD=0 NP=2 [QCD]
    … …  
    171153   
    172154''loop-induced''
    173 
    174155{{{
    175156 > g g > W+ W-    QED=2 QCD=2 NP=2 [QCD]
    … …  
    205186
    206187When 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.
    207 This can be achieved with the following modification of MadGraph5_aMC@NLO:
     188This can be achieved through "loop filtering", with the following ad-hoc modification of MadGraph5_aMC@NLO:
    208189{{{
    209190=== modified file 'madgraph/loop/loop_diagram_generation.py'
    … …  
    240221 #        self['loop_diagrams'] = base_objects.DiagramList(
    241222}}}
     223The width of the W may also need to be set to zero, to ensure precise gauge invariance and pole cancellation.
    242224
    243225==== Analytic validation ====