Software Tools in High Energy Physics

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Software Tools in High Energy Physics

Matthew Low

Institute for Advanced Study

Collider Physics in Mexico

September 19, 2015

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Lecture 1 Review

I Introduced Monte Carlo method of computing cross-sections

I Monte Carlo generatesevents(lists of four-vectors)

I Allows arbitrary phase space cuts

I Introduced Madgraph

I Downloaded and installed

I Made process (Feynman diagrams)

I Computed cross-sections

I Played withrun card settings

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Lecture 2 Review

I Moved fromparton-level todetector-level

I Interfaced Pythia and Delphes with Madgraph

I Looked at differential distributions using ROOT

I Performed simple analysis using ROOT

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Lecture 3 Overview

1 Beyond the Standard Model

I Exploring other models in Madgraph

2 Implementing your own model

I Introduction to FeynRules

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Beyond the Standard Model

I Madgraph has a number of common BSM models implemented

I They are stored in themodelsdirectory

> ls models/

sm mssm nmssm heft 2HDM 4Gen RS ...

I Standard model

I Minimal supersymmetric standard model

I Next-to-Minimal supersymmetric standard model

I IncludeshGG and hγγ effective vertices

I Two Higgs doublet model

I Adds 4^th generation of fermions

I Adds RS gravitons

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Beyond the Standard Model

I Models are all stored inUFO format

I UFO = Universal FeynRules Output

I Paper: http://arxiv.org/abs/1108.2040

I Written in Python, relevant files are human readable

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Beyond the Standard Model

I What defines a UFO?

I particles.pydefines fields

I parameters.pydefines parameters (by values or by formula)

I vertices.pylists the interaction vertices and their Lorentz structure

I couplings.pylists the coupling formulas at each vertex

I lorentz.pylists the Lorentz structures used in the vertices

I couplings orders.pylists the orderof each interaction

(to save time, Madgraph only generates leading order diagrams unless specified)

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Beyond the Standard Model

I The order is specified viaQED=Nand QCD=Mcommands whereN,M counts vertices of that type

I Example: p p > t t∼only generatestt¯from QCD production corresponds toQCD=2 QED=0

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I Example: p p > t t∼

I There are also (subleading) diagrams withs-channelγ’s andZ’s

I To get these, specifyQCD=0 QED=2

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Beyond the Standard Model

I There are also (subleading) diagrams withs-channelγ’s andZ’s

I To get these, specifyQCD=0 QED=2

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I Can get both sets of diagrams withQCD=2 QED=2

I Can read these asless than or equal to

I Can modify orders to select only certain classes of diagrams(to speed up calculations)

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Beyond the Standard Model

I Returning to BSM models

I Can check particles in a given model

MG5 aMC> import model mssm ...

MG5 aMC> display particles

Current model contains 48 particles:

w+/w- x1+/x1- x2+/x2- h+/h- ve/ve∼ vm/vm∼ vt/vt∼

e-/e+ mu-/mu+ ta-/ta+ u/u∼ c/c∼ t/t∼ d/d∼ s/s∼ b/b∼

sve/sve∼ svm/svm∼ svt/svt∼ el-/el+ mul-/mul+ ta1-/ta1+ er-/er+

mur-/mur+ ta2-/ta2+

ul/ul∼ cl/cl∼ t1/t1∼ ur/ur∼ cr/cr∼ t2/t2∼

dl/dl∼ sl/sl∼ b1/b1∼ dr/dr∼ sr/sr∼ b2/b2∼

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Supersymmetry

I Adds new symmetry that exchanges bosons and fermions Q|fermioni=|bosoni

Q|bosoni=|fermioni

I Every particle has a “s”-partner

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Supersymmetry

I Broad phenomenology

I Colored partnerssquarks andgluinos are strongly produced

I Decay to SM particles and the LSP(lightest supersymmetry particle) I Signal is many SM particles andE/_T

I Also can have various resonances

I No observations so far (mg˜ &1.3 TeV)

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Supersymmetry

I “Natural” realization

I Only sparticles requires for Hierarchy problem are light

I The others are heavy and not seen in colliders

H˜

˜tL

˜bL

˜tR

˜ g

natural SUSY decoupled SUSY

W˜ B˜

L˜i,˜ei

˜bR Q˜1,2,˜u1,2,d˜1,2

I Discussed inhttp://arxiv.org/abs/1110.6926

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Beyond the Standard Model

I e.g. MSSM particles

particle name

χ⁰_1,2,3,4 n1,n2,n3,n4 χ^±_1,2 x1+/x1-,x2+/x2-

˜

g go

ν˜ sve/sve∼, . . .

`˜ el+/el-,er+/er-, . . .

˜

q ul/ul∼,ur/ur∼, . . . t˜ t1/t1∼,t2/t2∼, . . . H,H^±,A h2,h+/h-,h3

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I Can check interactions in a model

MG5 aMC> display interactions

Current model contains 812 interactions 1:h1 h1 h2 QED=1

2:h2 h2 h2 QED=1 3:h1 h1 h1 QED=1 4:h1 h2 h2 QED=1 5:a a h- h+ QED=2 ...

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I Example: Generatepp→g˜g˜

MG5 aMC> import model mssm MG5 aMC> generate p p > go go MG5 aMC> output MyGluinoProcess MG5 aMC> launch

MG5 aMC> generate events

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Beyond the Standard Model

I How does this depend on the model parameters?

I e.g. mg˜,mq˜, tanβ, etc.

I Stored inparam card.dat

I There are masses, widths, mixing angles, etc.

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> cat param card.dat BLOCK MASS #

5 4.889917e+00 # mb 6 1.750000e+02 # mt 15 1.777000e+00 # mta 1000021 6.077137e+02 # mgo 1000022 9.668807e+01 # mneu1

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SUSY Parameters

I Note in older supersymmetry studies, often one chooses a model with fewer parameters

I e.g. mSUGRA has only: M₀,M_1/2,A₀, tanβ, and sign(µ)

I Means all parameters in supersymmetry card are not independent

I Specify high energy parameters, usespectrum generators to RG evolve down to the weak scale

I Options for how many loops to include in the running

2 4 6 8 10 12 14 16 18

Log₁₀(Q/1 GeV) 0

500 1000 1500

Mass [GeV]

m₀ m_1/2 (µ²+m₀²)^1/2

squarks sleptons M₁ M₂ M₃ H_d H_u

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SUSY Parameters

I At the LHC, supersymmetry searches are based onsimplified models

I Described in this writeuphttp://arxiv.org/abs/1105.2838

I Not tied to adhoc assumptions in the high-scale models

I e.g. consider looking for stop squarks

I ˜t→tχ1 →t+E/_T

I ˜t→bχ^±→b+W +E/_T

I ˜t→tχ₂ →t+Z +E/_T

I Can apply to your specific SUSY model

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SUSY Parameters

I Spectrum generators are still useful to make MSSM parameter cards

I Two common programs are:

I SUSPECT2

(http://www.coulomb.univ-montp2.fr/perso/jean-loic.kneur/Suspect/) I SoftSUSY

(http://softsusy.hepforge.org/)

I For low energy spectra, can disable all RG running

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MSSM

I In the spirit of simplied models, studies often use simplified spectra

I Keep a few particles at low energies, decouple the rest

I Event generation is faster if you exclude irrelevant diagrams

I e.g. studying electroweakino pair production

I Relevant in split SUSY models

I Electroweakino production has lower rates, weaker limits

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MSSM

I The process is: generate p p > x1+ n1 I Mediated by SM gauge bosons

I Also mediated by squarks

I But whenmq˜ is large, we know this diagram will go to zero

I Can speed up generation using special Madgraph syntax

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MSSM

I The process is: generate p p > x1+ n1

I Recall theslashcommand to exclude particles

I And themultiparticlecommand to group particles

define squark = ul ul∼ dl dl∼ ur ur∼ dr dr∼

generate p p > x1+ n1 / squark

I Now only gauge boson mediated diagrams are computed

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FeynRules

I What if we want to study something other than the MSSM?

I Use FeynRules(other default models also made in FeynRules) I Homepage is http://feynrules.irmp.ucl.ac.be/

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FeynRules

I Below are thecategories

I Within each category are a number of implemented models

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FeynRules

I e.g. the strongly interacting light Higgs

I Paper: http://arxiv.org/abs/hep-ph/0703164

I Basis of dimension-6 operators that parameterize strong dynamics

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FeynRules

I If model is not already implemented, can implement it yourself

I FeynRules is a Mathematica package that allows the calculation of Feynman rules in momentum space for any QFT physics model

I The Feynman rules calculated by the code can then be used to implement the new physics model into other existing tools, such as MC generators

I Download fromhttp://feynrules.irmp.ucl.ac.be/

I Unzip into a directory

FeynRules.m

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FeynRules

I Models are stored inModels

I Default include the standard model

I Models specified by 3 main types of information

I Fields

I Parameters

I Lagrangian

I Can also specify symmetries and can rotate fields

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FeynRules

I We will look at some examples of how to input information

I e.g. photon field

V[1] = {

ClassName -> A, SelfConjugate -> True, Mass -> 0,

Width -> 0,

ParticleName -> ‘‘a’’, PDG -> 22,

PropagatorLabel -> ‘‘a’’, PropagatorType -> W,

Manual on the arxiv http://arxiv.org/abs/1310.1921 Table 6, Page 23-25

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FeynRules

I The photon is a vector so it fills the arrayV[]

I Fermions fill the arrayF[]

I Scalars fill the arrayS[]

I Ghosts fill the arrayU[]

I Can also defined “unphysical” fields that are not mass eigenstates

V[11] = {

ClassName -> B, Unphysical -> True, SelfConjugate -> True,

Definitions -> { B[mu ] -> -sw Z[mu]+cw A[mu]}

}

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FeynRules

I We can input parameters

I asexternalor internal

I with formulas or numbers

I e.g. the top mass(external, number) ymt = {

ParameterType -> External, BlockName -> YUKAWA, OrderBlock -> 6, Value -> 172,

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FeynRules

I We can input parameters

I asexternalor internal

I with formulas or numbers

I e.g. sin²θ_w (internal, formula) sw2 = {

ParameterType -> Internal, Value -> 1-(MW/MZ)^2,

Description -> ‘‘Squared Sin of the Weinberg angle’’

}

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FeynRules

I Note that standard model parameters are specified by 3 numbers

I The other parameters are computed in terms of these

I Common choices areα⁻¹_em,G_F,α_s.

Block sminputs

1 1.325070e+02 # aEWM1 2 1.166390e-05 # Gf 3 1.180000e-01 # aS

I Can write parameters in a new model in terms of a few inputs

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FeynRules

I Once we havefieldsand parameters, we use them to write a Lagrangian

I The Lagrangian is written in Mathematica notation

I e.g. gauge kinetic terms

lag := -1/4 FS[B,mu,nu] FS[B,mu,nu]

- 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii]

I lagis the Lagrangian

I FSis a function to represent the field strength

I B, Wiare the field variables

I mu, nu, iiare indices to be summed

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FeynRules

I All of these are stored in text fileSM.fr

I Will use this file inside Mathematica

I In Mathematica, load FeynRules

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FeynRules

I All of these are stored in text fileSM.fr

I Will use this file inside Mathematica

I In Mathematica, load FeynRules

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FeynRules

I Now FeynRules has been loaded

I Next we need to load our model into Mathematica

I LoadModeluploads our fields, parameters, and Lagrangian

I LoadRestrictionremoves interactions considered irrelevant

I DiagonalCKM.rstremoves off-diagonal CKM interactions

I Massless.rstremoves Yukawa interactions for light quarks (huu¯,hdd¯,hss¯,hcc)¯

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FeynRules

I Now the model has been uploaded

I FeynRules provides a number of functions to check your Lagrangian

I See Table 16, page 46

CheckMassSpectrum[Lag];

CheckHermiticity[Lag];

I Can construct vertices using

vertices = FeynmanRules[lag]

decays = ComputeWidths[vertices];

I Will warn when conserved currents are violated at vertices

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FeynRules

I FeynRules does 2→1 computations already

I Sufficient to compute decay widths and branching ratios

PartialWidth[{φ1, φ2, φ3}, decays];

TotWidth[φ1, decays];

BranchingRatio[{φ1, φ2, φ3}, decays];

I Can be used for studies (without having to run Madgraph)

I Also returns closed form formulas for the width

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FeynRules

I We have seen once we load a Lagrangian into FeynRules, we can

I perform simple checks (mass diagonal, Hermitian, etc.)

I compute widths and branching ratios

I Our main use is to write a UFO model to be used in Madgraph

WriteUFO[lag];

I Writes a new folder containing our model

I Take the folder, copy it intomodelsin Madgraph directory, now can run the new model!

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FeynRules

I Let’s do an example

I ψ colored fermion (top partner) I φ neutral scalar(dark matter) I with the interaction

L=L_kin+λφψtR + h.c.

I The parameters areλ,m_Ψ,m_φ

I (Simplified model of top partners in composite models)

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FeynRules

I In FeynRules, we open a new file MyModel.fr

I We start with the parameters

M$Parameters = { lam = {

ParameterType -> External, Value -> 1.0,

InteractionOrder -> {NP, 1}, ComplexParameter -> False }

}

I NPnames the vertex, rather than QEDor QCD

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FeynRules

I Next we specify the fields

I First, we start with ψ

M$ClassesDescription = { F[100] = {

ClassName -> tp, SelfConjugate -> False, Indices -> {Index[Colour]},

QuantumNumbers -> {Y -> 2/3, Q -> 2/3}, Mass -> {Mtp, 1000},

Width -> {Wtp, 1}

},

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FeynRules

I Next, the fieldφ

S[100] = {

ClassName -> phi, SelfConjugate -> True, Indices -> { }, Mass -> {Mphi, 200}, Width -> {Wphi, 1}

} }

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FeynRules

I Finally we write the Lagrangian

LKin := I tpbar.Ga[mu].DC[tp,mu] - Mtp tpbar.tp

+ 1/2 del[phi,mu] del[phi,mu] - 1/2 Mphi^2 phi^2;

LInt := lam1 phi tpbar.ProjP.t;

LNew := LKin + LInt + HC[LInt];

I Load the model into FeynRules

LoadModel[‘‘SM.fr’’, ‘‘MyModel.fr’’]

LoadRestriction[‘‘DiagonalCKM.rst’’, ‘‘Massless.rst’’]

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FeynRules

I Can perform cross-checks (mass spectrum)

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FeynRules

I Can perform cross-checks (Hermiticity)

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FeynRules

I Can compute total widths

I Then write the UFO model

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FeynRules

I Can compute total widths

I Then write the UFO model

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FeynRules

I Directory made: MyModel UFO

I Copy this intomodelsin Madgraph directory

I Run Madgraph, but import this model

MG5 aMC> import model MyModel UFO MG5 aMC> generate p p > tp tp MG5 aMC> output MyOwnProcess

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FeynRules

I Can include the new interaction

I Notice the coupling orderNP=2

I Now can compute cross-sections and generate events

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FeynRules

I Production rate forpp→ψψ¯

[TeV]

MT

2 4 6 8 10 12 14 16

TT) [pb]→(pp σ

10-6 10-5 10-4 10-3 10-2 10-1 1 10 102

)-1(3 abnumber of events

10 102 103 104 105 106 107 108 109

Fermionic Top Partner 100 TeV 14 TeV

I (Aside: as mentioned, stop searches can be recast for this channel, very useful for future collider studies)

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Lecture 3 Summary

I Looked at the new physics models included in Madgraph

I Learned how to load a model and check particle content

I Noted that additional models are available on FeynRules website

I Downloaded and load FeynRules program

I Learned manipulations/checks that can be done with FeynRules

I Implemented our own model into FeynRules