Matrix Element Method and its Application for ILC Physics Analysis - - PowerPoint PPT Presentation

SLIDE 1

Matrix Element Method and its Application for ILC Physics Analysis

Junping Tian, Keisuke Fujii (KEK)

• Dec. 16-18 @ Tokusui Workshop 2014, KEK, Tsukuba

SLIDE 2

what is Matrix Element Method

reconstructing the likelihood of each event is alway one central task in any physics analysis: (i) best classifier to separate signal from background, LS/LB (Neyman-Pearson lemma); (ii) maximize likelihood to exact some parameters such as coupling, mass, etc. usual approach: (i) multivariate method such MLP, BDT — though very robust, due to correlation, non-linearity, hard to approach true likelihood; (ii) projected 1D or 2D likelihood, i.e. recoil mass fitting or template fitting in hadronic BRs — lose other information.

2

in fact, true likelihood of a event from one scattering process is given by its differential cross section —> Matrix Element Method = approach the true likelihood of every event

L

SLIDE 3

Application of MEM

used in discovery of top quark (precision top mass measurement) at Tevatron (D0,

• Phys. Rev. D 87,055006)

used in discovery of Higgs (H—>ZZ*—>4l) at LHC, as well as in Higgs JCP measurement (CMS, Phys. Rev. D 89, 092007; A. Caudron @ LCWS14) though not a new method, generally not widely used comparing to other multivariate method; at LHC often only Higgs decay part of matrix element is used, due to not precisely known initial state (need integrate pdf for production part) best application would be at lepton collider + imaging detector = well defined initial state + precisely measured final states even though, it’s not that simple: ISR + Beam-strahlung; detector transfer function; missing neutrino and particle spin not directly measured

3

L(pvis

i |a) = 1

σa [ Y

j∈inv.

Z d3pj (2π)32Ej ][ Y

k∈vis.

Z d3pk (2π)32Ek Wi(pvis

i |pk, a)]|M(pj, pk; a)|2

SLIDE 4

status of developing MEM for ILC Physics Analysis

just started in this year; first goal was to develop the tool to calculate matrix element for various e+e- processes in full simulation analysis a working version has been released and available in latest ilcsoft- v01-17-06: Physsim-v00-01 including HELLib, c++ version of HELAS (KEK-91-11), and LCME, matrix element calculation for specific processes have been implemented: ZH, ννH and eeH (VBF), ZHH, ννHH (VBF); ZZ, WW, eeZ (VBF), ZZZ and ZZH following talk —> basic verification; look into MEM performance in analyses of eeH (via ZZ-fusion), recoil mass and Higgs self-coupling

4

svn co https://svnsrv.desy.de/basic/physsim/Physsim/trunk

SLIDE 5

M(Z) / GeV

85 90 95 100

(Z)

f

φ

• 3
• 2
• 1

1 2 3 100 200 300 400 500 600 700 800 900

M(Z) / GeV

85 90 95 100

(Z)

f

φ

• 3
• 2
• 1

1 2 3 2 4 6 8 10 12 14 16 18 20 22

15

10 ×

5

• riginal events

weighted by

1 |ME|2

φF: azimuthal angle defined in Z rest frame of fermion from Z—>ff test sample: ZHH @ 500 GeV, generated without ISR and BS

method to verify calculated matrix element

idea: re-weight each event by 1/|ME|2, all distribution should become uniform

SLIDE 6

)

1

/L ln(L

• 20
• 10

10

Normalized

0.02 0.04 0.06 0.08

H (ZZ-fusion)

• e

+

e H (ZH)

• e

+

e

application (I): e+e- —> e+e-H

6

H

e+ e−

Z Z

e+ e−

Z Z H

e+ e−

e+ e-

ratio of ME

Signal eff

0.95 0.96 0.97 0.98 0.99 1

Backgr rejection (1-eff)

0.9 0.92 0.94 0.96 0.98 1

MEM MLP BDT Likelihood

signal efficiency .vs. background rejection

simplest application, same final states, generator level testing principle: whether MEM can be better than other MVA or not? carefully tuned MVA (input variables cover complete information) versus just ratio of ME

SLIDE 7

application (II): recoil mass analysis

7

Z H

μ+ μ− e+ e−

Z X

M = M(µ+µ−H) 1 p2

H − m2 H + imHΓH

X

based on fully simulated and reconstructed samples momentum of Higgs are reconstructed by recoil technique don’t look at Higgs decay —> sum of matrix element for all decay modes —> equivalently multiply M(μμH) with Higgs propagator, similarly for μμΖ for purpose, first tried without ISR and BS

SLIDE 8

(ME_rec-ME_truth)/ME_truth

• 0.4
• 0.2

0.2 0.4

Entries

100 200 300 400 500

matrix element: reconstructed .vs. truth

8

ln(L)

• 18
• 16
• 14
• 12
• 10
• 8

Normalized

0.02 0.04 0.06

ME (truth) ME (reconstructed)

M = M(µ+µ−H)

(w/o ISR and beam strahlung)

ME can be reconstructed with a resolution ~5%

SLIDE 9

)

1

/L ln(L

• 5

5 10

Entries

20 40 60 80 100 120

H (ZH)

• µ

+

µ Z (ZZ)

• µ

+

µ

w/o ISR and BS

matrix element: signal .vs. background (ZZ)

9

M = M(µ+µ−H) 1 p2

H − m2 H + imHΓH

M = M(µ+µ−Z) 1 p2

Z − m2 Z + imZΓZ

(normalized to expected number of events w/ 250 fb-1)

without any other selection except recoil mass > 110 GeV, already very well separated

SLIDE 10

including everything: ISR + beam spectrum

10

Recoil Mass / GeV

60 80 100 120 140 160

Normalized

0.1 0.2 0.3

H (w/o ISR and BS)

• µ

+

µ H (w/ ISR and BS)

• µ

+

µ Z (w/o ISR and BS)

• µ

+

µ ZZ_sl (w/ ISR and BS)

)

1

/L ln(L

• 5

5 10

Entries

20 40 60 80 100 120

H (w/o ISR and BS)

• µ

+

µ H (w/ ISR and BS)

• µ

+

µ Z (w/o ISR and BS)

• µ

+

µ ZZ_sl (w/ ISR and BS)

normalized to 1 normalized to <E> @ 250 fb-1

ISR + BS significantly degraded the separation power against ZZ

any chance to recover ISR and BS?

SLIDE 11

proposal to recover ISR

11

ISR enters detector: identification (see T. Tomita’s study, eff ~ 90%) what if ISR goes to beam pipe? (dominant)

4C —> we can resolve it!

Pz(H) = −(Pz(Z) + Pz(γ) |Pz(γ)| = |P(γ)| E(Z) + q P 2

t (H) + P 2 z (H) + m2(H) + |P(γ)| = √s

Py(H) = −Py(Z); Px(H) = √s sin θ 2 − Px

P(γ) = s cos2 θ

2 − 2√s(E(Z) − Px(Z) sin θ 2) + m2(H) − m2(Z)

2[Pz(Z) ± (√s − E(Z))]

4 unknown: 3 PH + 1 Pγ

n.b.: there are two possible solutions! and Higgs mass has to be known

SLIDE 12

resolved ISR versus truth

12

(truth) / GeV

ISR

P

• 40
• 20

20 40

(resolved) / GeV

ISR

P

• 20

20 40

looks working well

(one of the two solutions are selected according to z-momentum of visible part )

SLIDE 13

matrix element after ISR recovery (signal μμH)

13

truth

) / L

truth

• L

rec

(L

• 0.4
• 0.2

0.2 0.4

Entries

100 200 300 400

w/ ISR recovery w/o ISR recovery

matrix element is significantly closer to truth (almost recover to the case with ISR and BS, as shown in previous slides )

SLIDE 14

role of ISR in case of background ZZ

14

) / GeV

2

γ E(

20 40 60 80 100 120

) / GeV

1

γ E(

20 40 60 80 100 120

ISR is the main reason to have recoil mass > 110 GeV M(recoil) > 110 GeV analysis including ISR recover for both ZH and ZZ is ongoing

SLIDE 15

application (III): Higgs self-coupling

15

)

1

/L ln(L

• 60
• 40
• 20

20

Normalized

0.02 0.04 0.06 0.08

ZHH ZZH

use ME to help jet pairing use ME ratio of ZHH and ZZH to improve background suppression use ME of different ZHH diagrams to improve significance

• f Higgs self-coupling

in any case, a major challenge is to handle missing neutrinos in b- jet (invariant mass of bb-bar is very asymmetric)

Z H Z H H

e+ e−

Z H Z H

e+ e−

Z H Z H

e+ e−

Z H Z H

e+ e−

• ngoing…

SLIDE 16

summary and next step

16

MEM = approach true likelihood of every event, maximal use of well defined initial states, precisely measured final states and precise theoretical calculation at ILC; has potential to be applied for all physics analysis ILC; now in its initial stage, tools are being developed and improved; calculated ME are verified by first look; better performance than other MVA are seen in idea case; several applications are looked into, representing various aspects of challenges to use MEM for real analyses. a new idea to resolve ISR is proposed and looks promising a main step next is to include detector transfer function

SLIDE 17

back up

17

SLIDE 18

what Physsim package provides

hellib: C++ version of HELAS (by K. Fujii), subroutines to calculate generic parts of one Feynman diagram, i.e. wave function, vertex, propagator, amplitude, etc.); LCME: implementation of matrix element calculation for specific e+e- processes, i.e. e+e- —> ZH, ννH, ZZ, etc. example processors to calculate ME in marlin framework

18

what Physsim does not provide

radiative correction automatically generate all possible Feynman diagrams for given final states integrate ME with detector transfer function or unmeasured kinematics (yet-to-be supported)

L(pvis

i |a) = 1

σa [ Y

j∈inv.

Z d3pj (2π)32Ej ][ Y

k∈vis.

Z d3pk (2π)32Ek Wi(pvis

i |pk, a)]|M(pj, pk; a)|2

SLIDE 19

update of package

more processes implemented previous: ZH, ννH (VBF), eeH (VBF), ZHH, ννHH (VBF) new: ZZ, WW, eeZ, ZZZ, ZZH

• n the way: ννZ (VBF), ttH, WWH

19

new features switch to allow Z not decay, i.e. for ZZ as background in recoil mass analysis switch to allow Higgs decay, i.e. add Breit-Wigner structure only or full ME be able to select Feynman diagrams, i.e. in ZHH case, four diagrams. switch to return differential cross (default) or amplitude squared only support for anomalous couplings (gHZZ, gHWW)

SLIDE 20

reminder: two solutions to resolve ISR

20

(truth) / GeV

γ

P

• 40
• 20

20 40

(resolved) / GeV

γ

P

10 20 30 40

(truth) / GeV

γ

P

• 40
• 20

20 40

(resolved) / GeV

γ

P

• 40
• 30
• 20
• 10

solution 1 solution 2

)

• /L

+

ln(L

• 0.4
• 0.2

0.2 0.4

Entries

20 40 60 80

)

• /L

+

ln(L

• 0.4
• 0.2

0.2 0.4

Entries

20 40 60 80

P(γ) > 0 P(γ) < 0

both solutions seem allowed

ME

SLIDE 21

correlation between visible and ISR momentum (Pz)

21

z-momentum of ISR and visible part turn to have

• pposite sign —> to help select the solution

pzvis

• 50

50

pzisr1+pzisr2

• 40
• 20

20 40

pzisr1+pzisr2:pzvis {(eisr2<1.E-3 && eisr1>3 && abs(costhetaisr1)>0.999) || (eisr1<1.E-3 && eisr2>3 && abs(costhetaisr2)>0.999)}

SLIDE 22

(truth) / GeV

BS

P

• 20
• 10

10 20 30

(resolved) / GeV

BS

P

• 25
• 20
• 15
• 10
• 5

(truth) / GeV

BS

P

• 20
• 10

10 20 30

(resolved) / GeV

BS

P

10 20 30

is also possible to resolve beamstrahlung?

22

solution 1 solution 2

events without hard ISR (< 1 MeV), but with reduced Ecm (> 5 GeV)

SLIDE 23

angular distribution of ISR (by whizard 2 ISR kept)

ISR1

θ cos

• 1
• 0.5

0.5 1

ISR2

θ cos

• 1
• 0.5

0.5 1 |cosθ1| > 0.999 or |cosθ2| > 0.999 |cosθ1| < 0.999 and|cosθ2| < 0.999

~93% ~7%

SLIDE 24

cos2

• 0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1

0.0339 / (1/N) dN

2 4 6 8 10

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: cos2

e1

20 40 60 80 100120 140160 180200220

3.91 / (1/N) dN

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: e1

e2

20 40 60 80 100120 140160180 200220

3.91 / (1/N) dN

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: e2

input to MVA (eeH)

24

mz

50 100 150 200 250 300 350

6.15 / (1/N) dN

0.02 0.04 0.06 0.08 0.1 0.12

Signal Background

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: mz

cosz

• 1 -0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1

0.0339 / (1/N) dN

0.1 0.2 0.3 0.4 0.5 0.6 0.7

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: cosz

coszf

• 0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1

0.0339 / (1/N) dN

0.2 0.4 0.6 0.8 1 1.2

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: coszf

phizf

• 3
• 2
• 1

1 2 3

0.106 / (1/N) dN

0.2 0.4 0.6 0.8 1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: phizf

cosh

• 0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1

0.0339 / (1/N) dN

0.2 0.4 0.6 0.8 1 1.2

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: cosh

cos1

• 0.8 -0.6 -0.4 -0.2

0.2 0.4 0.6 0.8 1

0.0339 / (1/N) dN

2 4 6 8 10

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

Input variable: cos1