SMEFTsim - interactive Feynman Rules database
Author
Ilaria Brivio
Title
SMEFTsim - interactive Feynman Rules database
Description
An interactive tool to explore the Feynman Rules included in the SMEFTsim models set.
Category
Working Material
Keywords
particle physics, SMEFT, Feynman rules, Dynamic content
URL
http://www.notebookarchive.org/2022-01-5jz62qa/
DOI
https://notebookarchive.org/2022-01-5jz62qa
Date Added
2022-01-12
Date Last Modified
2022-01-12
File Size
59.04 kilobytes
Supplements
Rights
CC BY 4.0
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This notebook contains supplementary material to the SMEFTsim package, version 3.0 and higher. It provides an interactive interface to access the Feynman rules of the model.
The Feynrules and UFO models contained in SMEFTsim can be downloaded from the GitHub repository https://github.com/SMEFTsim/SMEFTsim.
More information about SMEFTsim can be found in the Manual and on the Website
Manual: arxiv.org/abs/2012.11343
Website: smeftsim.github.io
The Feynrules and UFO models contained in SMEFTsim can be downloaded from the GitHub repository https://github.com/SMEFTsim/SMEFTsim.
More information about SMEFTsim can be found in the Manual and on the Website
Manual: arxiv.org/abs/2012.11343
Website: smeftsim.github.io
SMEFTsim - interactive Feynman Rules database
SMEFTsim - interactive Feynman Rules database
Ilaria Brivio
Initialization
Initialization
In[]:=
SetDirectory[NotebookDirectory[]];<<SMEFTsimFR`
Instructions
Instructions
Main functionsFRbyOperator displays all the vertices affected by a chosen (list of) Wilson coefficient(s)FRbyVertex displays the complete SMEFT Feynman Rule for a chosen interaction vertex.A table summarizing the fields nomenclature can be visualized evaluating the function fieldsTable. A table indicating the SM parameters definitions can be visualized evaluating the function parameterDefinitions.How to read the Feynman RulesThe output is provided in FeynRules format.For each Feynman rule, the left box indicates the particles in each vertex, and assigns them a numerical label.◼ Lorentz indices are shown as μi with i the particle’s numerical label. η is the Minkowski metric contraction. pi is the four-momentum of the incoming particle i.◼ are the Dirac gamma matrices. The left and right chiral projectors are = and respectively. SlashedP[i] is the same as the contraction .◼ Color indices are shown as for quarks and for gluons. is the element ,) of the a-th generator of SU(3). is the SU(3) structure constant.◼ Internally contracted indices are numbered with $j.For further conventions and definitions see the FeynRules and SMEFTsim manuals.Output and simplification optionsThe option “display output in InputForm” is meant to help exporting the output to other notebooks.Three formatting options are provided, that display the Feynman rules expression in different ways: default SMEFT corrections rescaling the SM structure are collected in front of it, while the others are collected by operator by EFT param. each term in the sum shows the full contribution from one Wilson coefficient (or the SM one). simplify all: applies an automated Simplify to the whole expression In the “simplifications” menu: “CP conserving only” removes CP-violating SMEFT parameters CKM = 1 fixes the diagonal CKM entries to 1 and the off-diagonal ones to 0. = 0 sets to zero the Yukawa couplings of all fermions except the top and bottom quarks. =0 sets to zero the Yukawa coupling of the bottom quark. Notes◼ The Feynman Rules expressions for vertices with 5 and 6 gluons (from cG, cGtil) and for the SM loop-contribution to do not undergo algebraic manipulations, in order not to slow down the evaluation.◼ The SM loop-generated vertices , are not included in the model. ◼ In the case of four-fermion interactions containing a pair of identical particles, relative signs due to the exchange of identical fermions are not fully accounted for. This happens because in FeynRules-MonteCarlo interfaces the fermion-flow is conventionally assigned by the MonteCarlo generator.
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In[]:=
fieldsTable
Out[]=
Higgs boson | H | | | | | |
photon | A | | | | | |
Z boson | Z | | | | | |
W+ boson | W | | | | | |
W- boson | Wbar | | | | | |
gluon | G | | | | | |
up-type quarks | u | c | t | | | |
up-type antiquarks | ubar | cbar | tbar | | | |
down-type quarks | d | s | b | | | |
down-type antiquarks | dbar | sbar | bbar | | | |
charged leptons | e | mu | ta | | | |
charged antileptons | ebar | mubar | tabar | | | |
neutrinos | ve | vm | vt | | | |
antineutrinos | vebar | vmbar | vtbar | | | |
dummy particles (see Manual) | H1 | Z1 | W1 | W1bar | t1 | t1bar |
In[]:=
parameterDefinitions
Out[]=
ee | the electromagnetic coupling constant |
gs | the strong coupling constant |
sth | the sine of the Weinberg angle |
cth | the cosine of the Weinberg angle |
vevhat | the Higgs vacuum expectation value as determined from G F 1 2 2 vevhat |
LambdaSMEFT | the SMEFT cutoff scale Λ |
yup, yc, yt | the Yukawa couplings of the up-type quarks |
ydo, ys, yb | the Yukawa couplings of the down-type quarks |
ye, ym, ytau | the Yukawa couplings of the charged leptons |
gHaa | Coefficient encoding the SM Hγγ loop function in m t A μν μν A H vevhat |
gHza | Coefficient encoding the SM HZγ loop function in m t Z μν μν A H vevhat |
gHgg1 | Coefficient encoding the dim5 term of the SM Hgg loop function in m t a G μν aμν G H vevhat |
gHgg2 | Coefficient encoding a dim7 term of the SM Hgg loop function in m t D σ a G μν σ D aμν G H vevhat |
gHgg3 | Coefficient encoding a dim7 term of the SM Hgg loop function in m t f abc aν G μ bσ G ν cμ G σ H vevhat |
gHgg4 | Coefficient encoding a dim7 term of the SM Hgg loop function in m t μ D a G μν D σ aσν G H vevhat |
gHgg5 | Coefficient encoding a dim7 term of the SM Hgg loop function in m t aμν G D ν σ D a G σμ H vevhat |
Δ prop. | Flag parameter for interactions involving dummy fields, that carry propagator corrections |
Feynman Rules by Operator
Feynman Rules by Operator
Select one or more Wilson coefficients, using the same naming as in the UFO models.
Multiple coefficients must be separated by a comma, e.g. cHB, cHW . Wildcard characters can be used, e.g. cHu*
Some evaluations might take a few seconds.
Multiple coefficients must be separated by a comma, e.g. cHB, cHW . Wildcard characters can be used, e.g. cHu*
Some evaluations might take a few seconds.
In[]:=
FRbyOperator
Out[]=
Feynman Rules by Vertex
Feynman Rules by Vertex
Select one interaction vertex, specifying the incoming particles.
Different particles must be separated by a comma, e.g. H,Z,Z . The ordering is irrelevant.
All particles are understood to be incoming and only mass-eigenstate fields can be selected. Fermion fields are flavor-specific (e.g.. u is the 1st generation up quark)
Operator classes are defined in the SMEFTsim manual. The list of Wilson coefficients associated to class n (for all flavor setups) can be visualized evaluating the function WC6cl[n]
Different particles must be separated by a comma, e.g. H,Z,Z . The ordering is irrelevant.
All particles are understood to be incoming and only mass-eigenstate fields can be selected. Fermion fields are flavor-specific (e.g.. u is the 1st generation up quark)
Operator classes are defined in the SMEFTsim manual. The list of Wilson coefficients associated to class n (for all flavor setups) can be visualized evaluating the function WC6cl[n]
In[]:=
FRbyVertex
Out[]=
In[]:=
WC6cl1
Out[]=
{cG,cW,cGtil,cWtil}
In[]:=
WC6cl4
Out[]=
{cHG,cHW,cHB,cHWB,cHGtil,cHWtil,cHBtil,cHWBtil}
Cite this as: Ilaria Brivio, "SMEFTsim - interactive Feynman Rules database" from the Notebook Archive (2022), https://notebookarchive.org/2022-01-5jz62qa
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