Cargese Summer School July 2010Tim Stelzer MadGraph/MadEvent 5

Cargese Summer School July 2010Tim Stelzer 5

Cargese Summer School July 2010Tim Stelzer A Great Time In Physics 9

Cargese Summer School July 2010Tim Stelzer A Great Time In Physics 11

Cargese Summer School July 2010Tim Stelzer The Challenge 1 / 1,000,000,000 14

Cargese Summer School July 2010Tim Stelzer

Cargese Summer School July 2010Tim Stelzer Discoveries at hadron colliders (adapted from MLM) Peak (easy)Shape (medium)Rate (hard) 22

Cargese Summer School July 2010Tim Stelzer SuperSymmetry at LHC 23

Cargese Summer School July 2010Tim Stelzer New MC shows much harder! 24

Cargese Summer School July 2010Tim Stelzer Discovery LHC Rediscover Standard Model Identify excess Identify nature of excess Repeat 26

Cargese Summer School July 2010Tim Stelzer Standard Model u d d Matter Leptons Quarks Force Carriers e-e- d u d u 30

Cargese Summer School July 2010Tim Stelzer Details 32

Cargese Summer School July 2010Tim Stelzer Perturbation Theory 34

Cargese Summer School July 2010Tim Stelzer Example: e + e - →  +  - Scattering cross section Feynman Diagrams 37

Cargese Summer School July 2010Tim Stelzer  QED Z W +- QED gQCD h QED (m) Feynman Rules! Partial list from SM 38

Cargese Summer School July 2010Tim Stelzer These are basic building blocks, combine to form “allowed” diagrams – e.g. u u~ -> t t~ Draw Feynman diagrams: – gg -> tt~ (gg -> bb~ e+ ve j j ) – gg -> tt~h Determine “order” for each diagram Feynman Rules! Order is QCD

Cargese Summer School July 2010Tim Stelzer Draw Feynman diagrams + determine order (QED, QCD): – gg -> tt~ – gg -> tt~h – gg -> tt~bb~ (QCD only) Feynman Rules! Partial list from SM

Cargese Summer School July 2010Tim Stelzer 50

Cargese Summer School July 2010Tim Stelzer Register 60

Cargese Summer School July 2010Tim Stelzer MadGraph User Requests: –gg -> tt~bb~ –QCD Order = 4 –QED Order =0 MadGraph Returns: –Feynman diagrams –Self-Contained Fortran Code for |M|^2 SUBROUTINE SMATRIX(P1,ANS) C C Generated by MadGraph II Version Updated 06/13/05 C RETURNS AMPLITUDE SQUARED SUMMED/AVG OVER COLORS C AND HELICITIES C FOR THE POINT IN PHASE SPACE P(0:3,NEXTERNAL) C C FOR PROCESS : g g -> t t~ b b~ C C Crossing 1 is g g -> t t~ b b~ IMPLICIT NONE C C CONSTANTS C Include "genps.inc" INTEGER NCOMB, NCROSS PARAMETER ( NCOMB= 64, NCROSS= 1) INTEGER THEL PARAMETER (THEL=NCOMB*NCROSS) C C ARGUMENTS C REAL*8 P1(0:3,NEXTERNAL),ANS(NCROSS) C 40 1:05

Cargese Summer School July 2010Tim Stelzer Hadron Colliders 1:10

Cargese Summer School July 2010Tim Stelzer Exercise List processes for signal pp > h > tt~bb~ – e.g. uu~ > h > tt~ bb~ List processes for background pp > tt~bb~ – e.g. uu~ > tt~bb~ List processes for reducible background pp>ttjj – e.g. uu~ > tt~gg 1:20

Cargese Summer School July 2010Tim Stelzer Homework Play w/ MadGraph site – Try pp > h > tt~bb~ – Go to wiki page Watch John Ellis on Daily show View event animation 1:30

Cargese Summer School July 2010Tim Stelzer End---Day 1

Cargese Summer School July 2010Tim Stelzer

Cargese Summer School July 2010Tim Stelzer Parton Distribution Functions (Measured) Evolution +Splitting Hard Scattering Showering Fragmentation Hadronization e-e+

Cargese Summer School July 2010Tim Stelzer Hadron Collider Master Formula Probability of finding parton a having momentum fraction x in proton 1. Leading order Next-to-leading order Next-to-next-to-leading order Long distance (measured + th) Short distance (expansion)

Cargese Summer School July 2010Tim Stelzer LO: Technical Challenges (3 LHC) 1.Identify all subprocesses (gg->ggg, qg->qgg…) 2.For each one, calculate amplitude: 3.Square amplitude, sum over spins & color, integrate over phase

Cargese Summer School July 2010Tim Stelzer Exercises 1.tt~ production pp>tt~> bb~m+e- ve~ vm 2.tt~+Higgs: pp>h>tt~bb~ (QCD=2,QED=2) 3.tt~h background: pp>tt~bb~ QCD=99, QED=0 4.tH: pp>tHj (QCD=0, QED=3) 1.Try using proc_card method.

Cargese Summer School July 2010Tim Stelzer MadGraph User Requests: –gg -> tt~bb~ –QCD Order = 4 –QED Order =0 MadGraph Returns: –Feynman diagrams –Self-Contained Fortran Code for |M|^2 SUBROUTINE SMATRIX(P1,ANS) C C Generated by MadGraph II Version Updated 06/13/05 C RETURNS AMPLITUDE SQUARED SUMMED/AVG OVER COLORS C AND HELICITIES C FOR THE POINT IN PHASE SPACE P(0:3,NEXTERNAL) C C FOR PROCESS : g g -> t t~ b b~ C C Crossing 1 is g g -> t t~ b b~ IMPLICIT NONE C C CONSTANTS C Include "genps.inc" INTEGER NCOMB, NCROSS PARAMETER ( NCOMB= 64, NCROSS= 1) INTEGER THEL PARAMETER (THEL=NCOMB*NCROSS) C C ARGUMENTS C REAL*8 P1(0:3,NEXTERNAL),ANS(NCROSS) C 40 8

Cargese Summer School July 2010Tim Stelzer Web Process Specification Initial state u u~> b b~ t t~ Final state / AZc Excluded particles > h Required particles > b b~ t (t~ >W- b~) Decay Chain 10

Cargese Summer School July 2010Tim Stelzer Examine the following processes a.uu~ > tt~bb~ QED=99, QCD=99 b.uu~ > tt~bb~ QED=2, QCD=2 c.uu~ > tt~ bb~ /AZ QED=2, QCD=2 d.uu~ > h > tt~bb~ QED=2, QCD=99 e.uu~ > tt~ (h > bb~) QED=2, QCD=99 What would you use to generate – Pure QCD background (dominant) – Full background SM w/o Higgs – What would you use for Signal? U: Angels P: _ _ _ _ _ _ 20 D

Cargese Summer School July 2010Tim Stelzer Integrating to get cross sections (and events too)! Large number of dimensions (3N-4)+2 Sharply peaked

Cargese Summer School July 2010Tim Stelzer Integrals as averages Only works for f(x) = 1 50 Cuts OK Independent of N Event Generation Only Option

Cargese Summer School July 2010Tim Stelzer Importance Sampling 52

Cargese Summer School July 2010Tim Stelzer Importance Sampling (a la VEGAS) 53

Cargese Summer School July 2010Tim Stelzer Too Good To Be True? Works in multiple dimensions P(x,y,z) = p(x)*p(y)*p(z) But, peaks must be aligned w/ axis of integration variables! 54

Cargese Summer School July 2010Tim Stelzer Multi-channel Can’t map these peaks Solution “Multi-channel”, each channel solves one peak

Cargese Summer School July 2010Tim Stelzer Multi-channel = + 55

Cargese Summer School July 2010Tim Stelzer Single Diagram Enhanced Key Idea – Any individual diagram is “easy” to integrate – Divide based on diagrams N Independent Integrals – Errors add in Quadrature – Parallel in Nature What about Interference terms?

Cargese Summer School July 2010Tim Stelzer pp > tt~ (h > bb~) Let’s Play!

Cargese Summer School July 2010Tim Stelzer Break

Cargese Summer School July 2010Tim Stelzer Exercise Look at run results for signal pp > tt~ (h>bb~) – Which channels contribute – Which diagrams contribute – 3 “sanity” checks Look at plots Compare w/ plots for QCD background (ttbb) PSDSDEPC PtM 55

Cargese Summer School July 2010Tim Stelzer Check 1 (process symmetry)

Cargese Summer School July 2010Tim Stelzer Check 2 (Diagram Symmetry)

Cargese Summer School July 2010Tim Stelzer Check 3 (Enhancements)

Cargese Summer School July 2010Tim Stelzer Check 4 (process contributions) 160 7

Cargese Summer School July 2010Tim Stelzer PT Distributions

Cargese Summer School July 2010Tim Stelzer Mbb Distributions

Cargese Summer School July 2010Tim Stelzer Warm up! Madgraph -- wiki -- Lectures&Tutorials -- Cargese 21

Cargese Summer School July 2010Tim Stelzer Competition! 5:37