A program for Matrix Element

Transcription

1 A program for Matrix Element Olivier Mattelaer University of Illinois at Urbana Champaign May Olivier Mattelaer 1

2 Aims of this seminar Motivate Monte-Carlo Physics Describe the methods Advertise MadGraph Advertise the MEM 2

3 LHC DATA 3

4 LHC DATA Random search: model independent 3

5 LHC DATA Random search: model independent Use specific tools: model dependent 3

6 What do We need? 2#$3&)4((&)5&%55,&6".&3#5&789:!"# $2-()'+4-6&3/ '-44:5)'1()-5 ;&.8+&2-()'+ 4-6&3/ $%%&'()*&+(,&-.)&/ C&'18+',1)5/ 01(.)2+ $3&4&5(/ E&13+'-..&'()-5/ 0&.<)5<+0$=>? F3:/(&.=G.)6+ '-4B:()5< Testing/robustness 76*15'& /)/ (&',5)9:&/ C&'18+>1'D1<&/ J/&.+%.)&563)5&// 4

7 From Theory to Detector Lagrangian Detector events 5

8 From Theory to Detector Lagrangian FeynmanRules Detector events 5

9 From Theory to Detector Lagrangian FeynmanRules matrix-element Detector events 5

10 From Theory to Detector Lagrangian FeynmanRules matrix-element parton events Detector events 5

11 From Theory to Detector Lagrangian FeynmanRules matrix-element parton events shower/hadronize events Detector events 5

12 From Theory to Detector Lagrangian FeynmanRules matrix-element Fully Automated parton events shower/hadronize events Detector events 5

13 From Theory to Detector Lagrangian FeynRules FeynmanRules MadGraph Fully Automated matrix-element MadEvent parton events Pythia shower/hadronize events Delphes Detector events 5

14 From Theory to Detector Lagrangian FeynRules FeynmanRules MadGraph Fully Automated matrix-element MadEvent Hard parton events Pythia shower/hadronize events Delphes Detector events 5

15 From Theory to Detector Lagrangian FeynRules FeynmanRules MadGraph Fully Automated matrix-element MadEvent Hard MadWeight parton events Pythia shower/hadronize events Delphes Detector events 5

16 The Matrix Element 6

17 Evaluate a square Matrix Element 2 1 e+ e- a mu- mu+ 4 3 M = e 2 (ū µ v) g µ q 2 (ū v) 1 X M 2 = 1 X M M 4 4 pol pol X ūu = 6p + m e 4 pol 4q 4 Tr[6p 1 µ 6p 2 ]Tr[6p 3 µ 6p 4 ] 7

18 Evaluate a square Matrix Element 2 1 e+ e- a mu- mu+ 4 3 M = e 2 (ū µ v) g µ q 2 (ū v) 1 X M 2 = 1 X M M 4 4 pol pol X ūu = 6p + m e 4 pol 4q 4 Tr[6p 1 µ 6p 2 ]Tr[6p 3 µ 6p 4 ] Very Efficient!!! 7

19 Evaluate a square Matrix Element 2 1 e+ e- a mu- mu+ 4 3 M = e 2 (ū µ v) g µ q 2 (ū v) 1 X M 2 = 1 X M M 4 4 pol pol X ūu = 6p + m e 4 pol 4q 4 Tr[6p 1 µ 6p 2 ]Tr[6p 3 µ 6p 4 ] Very Efficient!!! But The number of term raises as N 2 7

20 Evaluate a square Matrix Element 2 1 e+ e- a mu- mu+ 4 3 M = e 2 (ū µ v) g µ q 2 (ū v) 1 X M 2 = 1 X M M 4 4 pol pol X ūu = 6p + m e 4 pol 4q 4 Tr[6p 1 µ 6p 2 ]Tr[6p 3 µ 6p 4 ] Very Efficient!!! But The number of term raises as N 2 Only for 2>2 and 2>3 7

21 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v a e+ e

22 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v a Numbers for given helicity and momenta e+ e

23 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v a Numbers for given helicity and momenta e+ e+ 1 3 CALL OXXXXX(P(0,1),ZERO,NHEL(1),-1*IC(1),W(1,1)) CALL IXXXXX(P(0,2),ZERO,NHEL(2),+1*IC(2),W(1,2)) CALL IXXXXX(P(0,3),ZERO,NHEL(3),-1*IC(3),W(1,3)) CALL OXXXXX(P(0,4),ZERO,NHEL(4),+1*IC(4),W(1,4)) 8

24 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v e+ a e+ Numbers for given helicity and momenta Calculate propagator wavefunctions 1 3 CALL OXXXXX(P(0,1),ZERO,NHEL(1),-1*IC(1),W(1,1)) CALL IXXXXX(P(0,2),ZERO,NHEL(2),+1*IC(2),W(1,2)) CALL IXXXXX(P(0,3),ZERO,NHEL(3),-1*IC(3),W(1,3)) CALL OXXXXX(P(0,4),ZERO,NHEL(4),+1*IC(4),W(1,4)) CALL JIOXXX(W(1,2),W(1,1),GAL,ZERO,ZERO,W(1,5)) 8

25 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v 1 e+ a e+ 3 Numbers for given helicity and momenta Calculate propagator wavefunctions Finally evaluate amplitude (c-number) CALL OXXXXX(P(0,1),ZERO,NHEL(1),-1*IC(1),W(1,1)) CALL IXXXXX(P(0,2),ZERO,NHEL(2),+1*IC(2),W(1,2)) CALL IXXXXX(P(0,3),ZERO,NHEL(3),-1*IC(3),W(1,3)) CALL OXXXXX(P(0,4),ZERO,NHEL(4),+1*IC(4),W(1,4)) CALL JIOXXX(W(1,2),W(1,1),GAL,ZERO,ZERO,W(1,5)) CALL IOVXXX(W(1,3),W(1,4),W(1,5),GAL,AMP(1)) 8

26 Basics: Helicity amplitudes Idea: Evaluate M for fixed helicity of external particles 2 4 e- e- M =ū µ vp µ ū v 1 e+ a e+ 3 Numbers for given helicity and momenta Calculate propagator wavefunctions Finally evaluate amplitude (c-number) Helicity amplitude calls written by MadGraph{ CALL OXXXXX(P(0,1),ZERO,NHEL(1),-1*IC(1),W(1,1)) CALL IXXXXX(P(0,2),ZERO,NHEL(2),+1*IC(2),W(1,2)) CALL IXXXXX(P(0,3),ZERO,NHEL(3),-1*IC(3),W(1,3)) CALL OXXXXX(P(0,4),ZERO,NHEL(4),+1*IC(4),W(1,4)) CALL JIOXXX(W(1,2),W(1,1),GAL,ZERO,ZERO,W(1,5)) CALL IOVXXX(W(1,3),W(1,4),W(1,5),GAL,AMP(1)) 8

27 HELAS Original HELicity Amplitude Subroutine library All helicity amplitude routines needed for the Standard Model, MSSM and certain other applications in hand-written library Any new Lorentz structures or other refinements need addition by hand Murayama, Watanabe, Hagiwara (1991) Introduced a severe restriction on types of models that could be implemented in MadGraph 9

28 ALOHA ALOHA UFO Helicity Brussels October 2010 Tim Stelzer 30 10

29 ALOHA ALOHA UFO Helicity FeynRules output New Model Format Gosam/ Herwig++/ MG5 Fully generic color/lorentz/... [Degrande, Duhr, Fuks, Grellscheid, OM, Reiter: ] Brussels October 2010 Tim Stelzer 30 10

30 ALOHA ALOHA UFO Helicity Brussels October 2010 Tim Stelzer 30 10

31 ALOHA ALOHA UFO Helicity Options: Standard (HELAS) Feynman gauge Complex-mass scheme Loop Open Loop Resolved Loop Brussels October 2010 Tim Stelzer 30 10

32 ALOHA ALOHA UFO Helicity in progress with V. Hirschi/Huassheng Options: Standard (HELAS) Feynman gauge Complex-mass scheme Loop Open Loop Resolved Loop Brussels October 2010 Tim Stelzer 30 10

33 MATRIX ELEMENT UFO+ALOHA+MG5: ALL BSM are available in a Fully automatic and fast way. Color representation (1/3/6/8) --support epsilon-- No restriction on the Lorentz structure. Possibility to define the propagator. No restriction on the number Leg. Should be local CPT invariant 11

34 MADGRAPH 5 12

35 MadGraph Original MadGraph by Tim Stelzer was written in Fortran, first version from 1994 hep-ph/ Event generation by MadEvent using the single diagram enhanced multichannel integration technique in 2002 (Stelzer, Maltoni) hep-ph/ Support for BSM (and many other improvements) in MG/ME 4 (2006) arxiv: , arxiv: Rewritten in Python in 2011: MG5 First version of amc@nlo in (late) 2012 arxiv: In preparation 13

36 MadGraph MAD stands for Madison Original MadGraph by Tim Stelzer was written in Fortran, first version from 1994 hep-ph/ Event generation by MadEvent using the single diagram enhanced multichannel integration technique in 2002 (Stelzer, Maltoni) hep-ph/ Support for BSM (and many other improvements) in MG/ME 4 (2006) arxiv: , arxiv: Rewritten in Python in 2011: MG5 First version of amc@nlo in (late) 2012 arxiv: In preparation 13

37 MadGraph Original MadGraph by Tim Stelzer was written in Fortran, first version from 1994 hep-ph/ Event generation by MadEvent using the single diagram enhanced multichannel integration technique in 2002 (Stelzer, Maltoni) hep-ph/ Support for BSM (and many other improvements) in MG/ME 4 (2006) arxiv: , arxiv: Rewritten in Python in 2011: MG5 First version of amc@nlo in (late) 2012 arxiv: In preparation 13

38 Decay chains Thanks to developments in MadEvent, also (very) long decay chains possible to simulate directly in MadGraph! 14

39 Command Interface Nice Interactive session Auto-completion Tutorial interactive help If You test it, you are going to like it! Simple command set import model sm generate p p > e+ e- output FORMAT MY_DIR launch 15

40 Comparing MC with experiment 16

41 From Theory to Detector Lagrangian FeynRules FeynmanRules MadGraph Fully Automated matrix-element MadGraph Hard MadWeight parton events Pythia shower/hadronize events Delphes Detector events 17

42 Shower ME are enhanced when particles are closed in the Phase Space 1 (p q + p g ) 2 1 2E q E g (1 cos θ) Collinear approximation: M p+1 2 dφ p+1 M p 2 dφ p dt Allow recursive relations Parton shower t Mp α S 2π P (z)dzdφ 1-z z Q 2 x 0 t 0 x 1 t 1 x n 1 t n 1 x n t n p 18

43 (pb/bin) d!/dp T 10 t t P T (a (Pythia la Pythia) only) of the 2-nd extra jet Q 2 Q (wimpy) (power) P T (wimpy) P T (power) GeV 19

44 (te ME Shower MC 1. Fixed order calculation 2. Computationally expensive 3. Limited number of particles 4. Valid when partons are hard and well separated 5. Quantum interference correct 6. Needed for multi-jet description 1. Resums large logs to all orders 2. Computationally cheap 3. No limit on particle multiplicity 4. Valid when partons are collinear and/or soft 5. Only partial interference (through angular ordering) 6. Needed for hadronization 20

45 (te ME Shower MC 1. Fixed order calculation 2. Computationally expensive 3. Limited number of particles 4. Valid when partons are hard and well separated 5. Quantum interference correct 6. Needed for multi-jet description 1. Resums large logs to all orders 2. Computationally cheap 3. No limit on particle multiplicity 4. Valid when partons are collinear and/or soft 5. Only partial interference (through angular ordering) 6. Needed for hadronization Approach are complementary!! 20

46 Matching 0 jet sample: 1 jet sample: 21

47 Matching Parton shower 0 jet sample:... 1 jet sample:... 21

48 Matching Parton shower 0 jet sample:... 1 jet sample:... There is double counting between the +n jets matrix elements samples and the parton shower 21

49 Matching Parton shower 0 jet sample:... 1 jet sample:... There is double counting between the +n jets matrix elements samples and the parton shower Needs to merge the sample (Qcut) 21

50 Matching Parton shower 0 jet sample:... 1 jet sample:... There is double counting between the +n jets matrix elements samples and the parton shower Needs to merge the sample (Qcut) Needs to match the ME to the shower. 21

51 MLM algorithm in a nutshell 1. Generate ME events (with different parton multiplicities) using parton-level cuts (pt ME /ΔR or kt ME ) 2. Cluster each event and reweight αs and PDFs based on the scales in the corresponding clustering vertices 3. Run the parton shower with starting scale t0 = mt. 4. Check that the number of jets after parton shower is the same as ME partons, and that all jets after parton shower are matched to the ME partons at a scale Q match. If yes, keep the event. If no, reject the event. Q match is called the matching scale. 5. For highest multiplicity, allow radiation < lowest ME scale 22

52 d!/dp T (pb/bin) 10 tt+0,1,2,3 partons + Pythia (MMLM) P T of the 2-nd extra jet Q 2 Q (wimpy) (power) P T (wimpy) P T (power) [MadGraph] GeV 23

53 Matching with b-quarks Shower ME Gives smooth matching to Pythia PS 24

54 Need for NLO!! 25

55 Going NLO At NLO the dependence on the renormalization and factorization scales is reduced First order where scale dependence in the running coupling and the PDFs is compensated for via the loop corrections: first reliable estimate of the total cross section Better description of final state: impact of extra radiation included (e.g. jets can have substructure) Opening of additional initial state partonic channels 26

56 NLO Basics NLO Virtual Real Born NLO = Z m d (d) V + Z m+1 d (d) R + Z m d (4) B 27

57 NLO Basics NLO Virtual Real Born NLO = Z m d (d) V + Z m+1 d (d) R + Z m d (4) B Need to deal with singularities NLO = Z m d (d) ( V + Z 1 d 1 C)+ Z m+1 d (d) ( R C)+ Z m d (4) B 27

58 NLO Basics NLO Virtual Real Born NLO = Z m d (d) V + Z m+1 d (d) R + Z m d (4) B Need to deal with singularities NLO = Z m d (d) ( V + Z 1 d 1 C)+ Z m+1 d (d) ( R C)+ Z m d (4) B MadLoop MadFKS MadGraph 27

59 A Joint Venture MadGraph FKS FKS CutTools MC@NLO 28

60 Why automation? Time: Less tools, means more time for physics Robust: Easier to test, to trust Easy: One framework/tool to learn 29

61 Why automation? Time: Less tools, means more time for physics Robust: Easier to test, to trust Easy: One framework/tool to learn Why matched to the PS? Parton are not an detector observables Matching cure some fix-order ill behaved observables 29

62 Why automation? Time: Less tools, means more time for physics Robust: Easier to test, to trust Easy: One framework/tool to learn Why matched to the PS? Parton are not an detector observables Matching cure some fix-order ill behaved observables Why NOT merging? works in progress 29

63 MADLOOP Disclaimer: I will not describe MADFKS / The matching to the shower 30

64 Basis of scalar integrals M 1-loop = i 0 <i 1 <i 2 <i 3 d i0 i 1 i 2 i 3 Box i0 i 1 i 2 i 3 i 0 <i 1 <i 2 c i0 i 1 i 2 Triangle i0 i 1 i 2 i 0 <i 1 b i0 i 1 Bubble i0 i 1 i 0 +R + O( ) a i0 Tadpole i0 The a, b, c, d and R coefficients depend only on external parameters and momenta D i =(l + p i ) 2 Tadpole i0 = d d l 1 D i0 Bubble i0 i 1 = d d 1 l D i0 D i1 Triangle i0 i 1 i 2 = d d 1 l D i0 D i1 D i2 Box i0 i 1 i 2 i 3 = d d 1 l D i0 D i1 D i2 D i3 All these scalar integrals are known and available in computer libraries (FF [v. Oldenborgh], QCDLoop [Ellis, Zanderighi], OneLOop [v. Hameren]) m 2 i 31

65 Divergences M 1-loop = i 0 <i 1 <i 2 <i 3 d i0 i 1 i 2 i 3 Box i0 i 1 i 2 i 3 i 0 <i 1 <i 2 c i0 i 1 i 2 Triangle i0 i 1 i 2 i 0 <i 1 b i0 i 1 Bubble i0 i 1 i 0 +R + O( ) a i0 Tadpole i0 The coefficients d, c, b and a are finite and do not contain poles in 1/є The 1/є dependence is in the scalar integrals (and the UV renormalization) When we have solved this system (and included the UV renormalization) we have the full dependence on the soft/collinear divergences in terms of coefficients in front of the poles. These divergences should cancel against divergences in the real emission corrections (according to KLN theorem) D i =(l + p i ) 2 Tadpole i0 = d d l Virtual v 0 + v 1 + v D i0 m 2 i Bubble i0 i 1 = d d 1 l D i0 D i1 Triangle i0 i 1 i 2 = d d 1 l D i0 D i1 D i2 Box i0 i 1 i 2 i 3 = d d 1 l D i0 D i1 D i2 D i3 32

66 The OPP Method Reduce the Amplitudes at the Integrand level. N(l) = m 1 i 0 <i 1 <i 2 <i 3 m 1 i 0 <i 1 <i 2 m 1 i 0 <i 1 m 1 i 0 + P (l) d i0 i 1 i 2 i 3 + d m 1 i0 i 1 i 2 i 3 (l) D i i =i 0,i 1,i 2,i 3 m 1 c i0 i 1 i 2 + c i0 i 1 i 2 (l) D i i =i 0,i 1,i 2 b i0 i 1 + b m 1 i0 i 1 (l) D i i =i 0,i 1 m 1 a i0 +ã i0 (l) m 1 i D i i =i 0 D i Feed CutTools with loop numerator and obtain the coefficients (including R1 Term) Add R2 counter-terms. 33 [Ossola, Papadopoulos, Pittau 2006]

67 MADLOOP 2 g g 3 d~ d~ d~ 1 g d 2>2 g 4 34

68 MADLOOP 2 g g 3 d~ d~ d~ 1 g d 2>2 g 4 34

69 MADLOOP 2 g g 3 d~ d~ d~ d~ d d 1 g 2>4 g 4 34

70 MADLOOP 2 3 g g d~ d~ Diagram Generation d~ d d~ d g g 1 2>4 4 34

71 MADLOOP 2 3 g g d~ d~ Diagram Generation Generate diagrams with 2 extra particles 1 g d~ d 2>4 d~ d g 4 34

72 MADLOOP 2 3 g g d~ d~ Diagram Generation Generate diagrams with 2 extra particles 1 g d~ d 2>4 d~ d g 4 Need to filter result 34

73 MADLOOP 2 3 g g d~ d~ Diagram Generation Generate diagrams with 2 extra particles 1 g d~ d 2>4 d~ d g 4 Need to filter result Evaluation of the Numerator: 34

74 MADLOOP 2 3 g g d~ d~ Diagram Generation Generate diagrams with 2 extra particles 1 g d~ d 2>4 d~ d g 4 Need to filter result Evaluation of the Numerator: OpenLoops techniques [S. Pozzorini & al.(2011)] N (l µ )= rx max r=0 C (r) µ 0 µ 1 µ r l µ 0 l µ1 l µ r 34

75 DEMO Is it really automatic? 35

76 DEMO 1) Download the code 36

77 launch the code [./bin/mg5] Exactly like MG5!!! DEMO 37

78 You can enter ANY process! add [QCD] for NLO functionalities generate p p > t t~ [QCD] generate p p > e+ e- mu+ mu- [QCD] generate p p > w+ j j [QCD] 38

79 Create your code Run it: output PATH launch [PATH] 39

80 Create your code Run it: output PATH launch [PATH] 39

81 Create your code Run it: output PATH launch [PATH] First Question: 39

82 Create your code Run it: output PATH launch [PATH] Second Question: 39

83 The code runs: Compilation `` Check Poles cancelation 40

84 The code runs: Compilation `` Check Poles cancelation 40

85 The code runs: Compilation Check Poles cancelation 40

86 Integration Events Generation 41

87 Unweight Events Main Results The Shower 42

88 DEMO Is it really automatic? 43

89 DEMO Is it really automatic? As much as LO! 43

90 The Matrix Element Method The reverse problem Can we help the experimentalit? 44

91 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption 45

92 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption 45

93 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption P(p vis )= M (p vis ) 2 M (p) 2 is the squared matrix element 45

94 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption P(p vis )= M (p) 2 W (p, p vis ) M (p) 2 W (p, p vis ) is the squared matrix element is the transfer function 45

95 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption P(p vis )= d dx 1 dx 2 M (p) 2 W (p, p vis ) M (p) 2 W (p, p vis ) d dx 1 dx 2 is the squared matrix element is the transfer function is the phase-space integral 45

96 Matrix Element Re-weighting Associate to each experimental event characterised by p vis, the probability P(p vis ) to be produced and observed following a theoretical assumption P(p vis )= 1 vis d dx 1 dx 2 M (p) 2 W (p, p vis ) M (p) 2 W (p, p vis ) d dx 1 dx 2 vis is the squared matrix element is the transfer function is the phase-space integral is the cross-section (after cuts) 45

97 Matrix Element Method Most common and Important use is to combine those in a Likelihood L( )= N i=1 P(p vis i ) 46

98 Matrix Element Method Most common and Important use is to combine those in a Likelihood L( )= N i=1 P(p vis i ) The best possible estimation of maximizing the likelihood is the one 46

99 Matrix Element Method Most common and Important use is to combine those in a Likelihood L( )= N i=1 P(p vis i ) The best possible estimation of maximizing the likelihood is the one Semi-leptonic decay m top = ± 1.2GeV 46

100 Matrix Element Method Most common and Important use is to combine those in a Likelihood L( )= N i=1 P(p vis i ) The best possible estimation of maximizing the likelihood Semi-leptonic decay m top = ± 1.2GeV Also use for Higgs Exclusion is the one single top cross observation 46

101 Critics of the method The Likelihood methods builds the BEST discriminating variable Fully Model dependent Pure LO approximation Transfer Function approximation Factorize for each parton Not valid for hard radiation Strong sensitivity in analysis cut Computing time ( integrals) N event N th 47

102 Matrix Element Re-weighting How to evaluate those weights? P(p vis )= 1 d dx 1 dx 2 M (p) 2 W (p, p vis ) 48

103 Matrix Element Re-weighting How to evaluate those weights? P(p vis )= 1 d dx 1 dx 2 M (p) 2 W (p, p vis ) Fit from MC tuned to the detector resolution 48

104 Matrix Element Re-weighting How to evaluate those weights? P(p vis )= 1 d dx 1 dx 2 M (p) 2 W (p, p vis ) Fit from MC tuned to the detector resolution Use of matrix-element generator: MadGraph 48

105 Matrix Element Re-weighting How to evaluate those weights? P(p vis )= 1 d dx 1 dx 2 M (p) 2 W (p, p vis ) Fit from MC tuned to the detector resolution Use of matrix-element generator: MadGraph Need a specific integrator: MadWeight 48

106 TTH measurement [Artoisenet, Aquino, Maltoni, OM: ] 49

107 TTH measurement [Artoisenet, Aquino, Maltoni, OM: ] Especially difficult since the huge number of permutations. 49

108 TTH measurement [Artoisenet, Aquino, Maltoni, OM: ] Especially difficult since the huge number of permutations. Need to correct for the presence of additional jets [Alwall, Freytas, OM: ] 49

109 TTH measurement [Artoisenet, Aquino, Maltoni, OM: ] Especially difficult since the huge number of permutations. Need to correct for the presence of additional jets D i = P (x i S) P (x i S)+P (x i B) [Alwall, Freytas, OM: ] signal events (D S ) bg. events (D B ) di lepton channel single lepton channel D 49

110 TTH measurement [Artoisenet, Aquino, Maltoni, OM: ] L R = = N i N i r 0 P (x i S)+(1 r 0 )P (x i B) P (x i B) r 0 D i +(1 r 0 )(1 D i ) (1 D i ), di lepton, S+B di lepton, B only 100 di lepton channel single lepton channel ln L R 1 SM Exclusion luminosity (fb 1 ) 50

111 Conclusion 51

112 Conclusion Evaluation of Matrix Elements Numerical method beats analytical We have a framework for ALL BSM 51

113 Conclusion Evaluation of Matrix Elements MG5 Numerical method beats analytical We have a framework for ALL BSM fast, reliable and easy to learn/use 51

114 Conclusion Evaluation of Matrix Elements MG5 Numerical method beats analytical We have a framework for ALL BSM fast, reliable and easy to learn/use Matching/Merging MLM available in MG5/Pythia6 51

115 Conclusion Evaluation of Matrix Elements MG5 Numerical method beats analytical We have a framework for ALL BSM fast, reliable and easy to learn/use Matching/Merging MLM available in MG5/Pythia6 NLO available for SM 51

116 Conclusion Evaluation of Matrix Elements MG5 Numerical method beats analytical We have a framework for ALL BSM fast, reliable and easy to learn/use Matching/Merging MLM available in MG5/Pythia6 NLO available for SM Matrix Element Method allows to have precise measurement tth example 51

117 52