MadGraph MadEvent

1
MadGraph MadEvent

• Automated Tree-Level
• Feynman Diagram, Helicity Amplitude,
• and Event Generation

Tim Stelzer Fabio Maltoni
2
Reading Assignment
05
3
Timeline 200-545

• Introduction ----- 20
• Activity------ Generate Feynman Diagrams ---- 30
  minutes
• Hadron Colliders ---- 20
• Activity ----- Generate Sub Processes --- 30
• Monte Carlo --- 60
• Introduction --10
• Activity --- Write simple MC --- 30
• Adaptive MC --- 10
• Multi-channel MC --- 10
• Generate Events --- 10
• Activity ---- Generate Signal/Background events
  --- 15
• Download and run on local machine?

4
Goals

• Overview of Standard Model
• Monte Carlo Integration
• Signal/Background Calculations
• Build on and apply ideas from
• Introduction to Particle Physics --- Close
• The Standard Model --- Pich
• Introduction to Statistics --- Cowen

07
5
Standard Model

• Good News! SU(3)xSUL(2)xU(1)
• Most successful theory in physics!
• Tested over 30 orders of magnitude!
• (photon mass lt 10-18 eV , Tevatron gt 1012 eV)

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Standard Model

• Bad News!
• We cant solve it!

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7
Predictions from SM

• Cross Section
• Cant solve exactly because interactions change
  wave functions!
• Perturbation Theory
• Start w/ Free Particle wave function
• Assume interactions are small perturbation

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8
Example ee- ? mm-

• Scattering cross section
• Feynman Diagrams

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Feynman Rules!
Partial list from SM
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Feynman Rules!

• These are basic building blocks, combine to form
  allowed diagrams
• e.g. u u -gt t t
• Draw Feynman diagrams
• gg -gt tt
• gg -gt tth
• Determine order for each diagram

Order is QCD2
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Feynman Rules!

• Draw Feynman diagrams determine order (QED,
  QCD)
• gg -gt tt
• gg -gt tth
• gg -gt ttbb (QCD only)

Partial list from SM
Check at http//madgraph.hep.uiuc.edu/
Register w/ username madgraph password
guest
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MadGraph
SUBROUTINE SMATRIX(P1,ANS) C C Generated by
MadGraph II Version 3.83. Updated 06/13/05 C
RETURNS AMPLITUDE SQUARED SUMMED/AVG OVER
COLORS C AND HELICITIES C FOR THE POINT IN PHASE
SPACE P(03,NEXTERNAL) C C FOR PROCESS g g -gt t
t b b C C Crossing 1 is g g -gt t t b b
IMPLICIT NONE C C CONSTANTS C Include
"genps.inc" INTEGER NCOMB,
NCROSS PARAMETER ( NCOMB
64, NCROSS 1) INTEGER THEL
PARAMETER (THELNCOMBNCROSS) C C ARGUMENTS C
REAL8 P1(03,NEXTERNAL),ANS(NCROSS) C

• User Requests
• gg -gt ttbb
• QCD Order 4
• QED Order 0
• MadGraph Returns
• Feynman diagrams
• Self-Contained Fortran Code for M2

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Status

• Good News
• MadGraph generates all tree-level diagrams
• MadGraph generates fortran code to calculate
  SM2
• Bad News
• Madgraph generates fortran code.
• Hadron colliders are tough!
• Good News
• Theres a cool animation next!

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Hadron Colliders

• Initial State Protons
• Made of quarks/gluons in bound state
• Strongly interacting P.T. wont work
• Final State Hadrons
• Made of quarks/gluons in bound state
• Strongly interacting P.T. wont work
• Animation

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Parton Distribution Functions (Measured)
EvolutionSplitting
Hard Scattering
Showering Fragmentation
Hadronization
e-
e
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Protons

• Simple Model
• 3 Valence quarks u u d
• 2/3 chance of getting up quark
• 1/3 chance of getting down quark
• Guess each carries 1/3 of momentum
• Deep Inelastic Scattering Results
• Short time scales sea partons
• u and d. but also u d s, c and g with varying
  amounts of momentum
• Need to multiple matrix element by probability
  f(x) of finding parton i with fraction of
  momentum x

u
d
u
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Hadron Colliders

• Initial State Protons
• Made of quarks/gluons in bound state
• Approximately free at very short times
• Measure distributions in experiments and use
• Final State Hadrons
• Made of quarks/gluons in bound state
• Combine into jets and evolve back to partons
• Measure hadronization in experiments and use
• Many parton level sub processes contribute to
  same hadron level event (e.g. pp gt e n j j j)

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Exercise

• List processes for signal pp gt h gt ttbb
• e.g. uu gt h gt tt bb
• List process for background pp gt ttbb
• e.g. uu gt ttbb
• List process for reducible background ppgtttjj
• e.g. uu gt ttgg

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Exercise 2

• List processes for signal pp gt h gt ttbb
• e.g. uu gt h gt tt bb
• List process for background pp gt ttbb
• e.g. uu gt ttbb
• List process for reducible background ppgtttjj
• e.g. uu gt ttgg
• Check answers at http//madgraph.hep.uiuc.edu/

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MadGraph
DOUBLE PRECISION FUNCTION DSIG(PP,WGT) C

C Generated by MadGraph II Version 3.83.
Updated 06/13/05 C RETURNS DIFFERENTIAL CROSS
SECTION C Input C pp 4
momentum of external particles C wgt
weight from Monte Carlo C Output C
Amplitude squared and summed C

---------------------------
-------- IPROCIPROC1 ! u u -gt t
t b b PD(IPROC)PD(IPROC-1) u1
ub2 IPROCIPROC1 ! d d -gt t t b
b PD(IPROC)PD(IPROC-1) d1 db2
IPROCIPROC1 ! s s -gt t t b b
PD(IPROC)PD(IPROC-1) s1 sb2
IPROCIPROC1 ! c c -gt t t b b
PD(IPROC)PD(IPROC-1) c1 cb2 CALL
SMATRIX(PP,DSIGUU) dsig
pd(iproc)convdsiguu

• User Requests
• pp -gt bbtt
• QCD Order 4
• QED Order 0
• MadGraph Returns
• Feynman diagrams
• Fortran Code for M2
• Summed over all sub processes w/ pdf

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Hadronic Collision Cross Sections

• Good News
• Automatically determine sub processes and Feynman
  diagrams
• Automatically create function needed to integrate
• Bad News
• Hard to integrate!
• 3N-42 dimensions

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Monte Carlo Integration

• Advantages
• Large numbers of dimensions
• Complicated cuts
• ONLY OPTION
• Event generation
• Limitations
• Only works for function f(x) 1
• Error scales as 1/sqrt(N)

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Exercise 3

• Write MC integration for
• Estimate the error using variance
• Plot Error as function of w for w.4 to w.01
• Plot points needed for 1 accuracy for w.4 to
  w.01

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Exercise

• Write MC integration for
• Estimate the error using variance
• Plot Error as function of w for w10-1 to
  w10-5

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Adaptive M.C. (VEGAS)

• Advantages
• Grid adjusts to numerically flatten peaks
• Flexible
• Limitations
• Adjusting grid takes time
• Peaks must lie on integration variable

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Multi-Channel M.C.

• Advantages
• Allows for more complicated peaks
• NEXTCALIBUR, WHIZARD, AMEGIC
• Limitations
• Need to calculate all gi values for each point.
  (slow)
• Each phase space channel must be invertible
• N coupled equations for a so only works for small
  number of channels.

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Single Diagram EnhancedMadEvent

• Key Idea
• Any single diagram is easy to integrate
• Divide integration into pieces, based on diagrams
• Get N independent integrals
• Errors add in quadrature so no extra cost
• No need to calculate weight function from other
  channels.
• Can optimize of points for each one
  independently
• Parallel in nature

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MadEvent

• User Requests
• pp -gt bbtt
• QCD Order 4
• QED Order 0
• Cuts Parameters
• MadEvent Returns
• Feynman diagrams
• Complete package for event generation
• Events/Plots on line!

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MadEvent ExampleVector Bosons
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MadEvent Example Heavy Quarks
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Comparisons 1
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Comparisons 2
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Comparisons 3
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Advice

• A person who can efficiently calculate cross
  sections can be useful to a collaboration
• A person who can efficiently calculate the
  CORRECT cross section is ESSENTIAL to a
  collaboration

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Example

• Look at signal pp gt h gt ttbb
• Look at background pp gt ttbb
• Find cut to reduce background

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Final Project

• Chooose A Signal Process
• Pp gt h gtttbb
• Pp gt h gt ttww-
• Bb gt h gt mu mu- e e-
• Bb gt h gt eve mu vm
• Calculate Signal cross section (usernameAngels
  password_ _ _ _ _ _)
• Generate Backgrounds/ Calculate cross section
• Place cuts on background for invariant mass of
  higgs
• Check your results are reasonable!

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Conclusions

• Standard Model is Amazing (good news)
• S.M. is tough to Solve (good news!)
• Factorization allows use of Perturbation Theory
• Feynman Diagrams help
• MadGraph/MadEvent can help too
• Good Luck!