Introduction

l An alternative framework for probing physics beyond SM is effective field theories(EFT)

the SM Lagrangian is supplemented by additional dimension-D operators

ℒ"#$ = ℒ'( +∑+,(.)

0.12 Ο4(5)

4,5

l 𝑐4(5) specify the strength of new interaction, are known as Wilson coefficients

l In this analysis, limits are set in Wilson coefficients of dimension-6 operators

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Effective field theories

l There are two bases for a dimension-6 EFT Lagrangian

l SILH: the basis of Strongly-Interacting-Light-Higgs Lagrangian

l SMEFT: the “Warsaw” basis of SM Effective Field Theory Lagrangian

l For different bases, different Wilson coefficients take effect

l Parameter ranges for each EFT parameter

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EFT analysis workflow

l Generate samples with MadGraph5, and output EVNT.root

l Change parameters in the param_card, generate a variety of samples

l Use Rivet to select over those EVNT.root and generate histograms into .yoda files

l Calculate Reweight scale factors, and applying reweight factors to all of the yoda files

l Use Professor software to make 2nd order polynomial interpolation over reweighted .yoda

files

l Scan over parameters in EFT through gamma-combo to obtain confidence intervals of these

parameters.2019/12/15 3

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6Powheg ggH

SILH c=0

γγpT

0 0.5 1 1.5 2 2.5 3 3.5 4~

5

10

15

20

25

30

~

Powheg ggH

SILH c=0

From Amed

30 GeVjetexcl N

N_j_30

MadGraph generation with SILH modell Try to reproduce SM expectation with SILH model

generate ggH samples with commands below

l Import model HEL_UFO(set all Wilson coefficients to 0)

l Generate p p > h NP=1 QED=1 QCD=99, h > aa NP=1 QED=2 @0

l Add process p p > hj NP =1 QED=1 QCD=99, h > aa NP=1 QED=2 @1

l Add process pp > hjj NP=1 QED=1 QCD=99, h > aa NP=1 QED=2 @2

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l ggH125 Powheg+Pythia(H+j) as comparisonl There is still deviation on N_j_30 and pT_yyl More jet numbers in SILH(coefficients = 0)

than Powheg ggH

pT_yy

EFT parameters tested in ggH samples

l Choose two EFT parameters as tested( 𝑐89 & 𝑐8: : 5 points for per parameter, 25 points

totally), while keeping other Wilson coefficients to 0:

𝑐89 : [-0.001 , -0.0005 , 0.0 , 0.0005 ,0.001]

𝑐8: : [-0.001 , -0.0005 , 0.0 , 0.0005 ,0.001]

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Event Selection with HGamRivetl Perform event selection on EVNT.root from samples generated by MadGraph5 to generate

histogram(.yoda files)

l Selection Criteria for Photons(same as H->yy fiducial region):

l pT > 25GeV

l |eta| <1.37 or 1.52 < |eta| < 2.37

l Photons.size > 2 & relative pT cut 0.35(0.25)

for leading(sub-leading)photon

l 105GeV < m_yy < 160GeV

l HGamRivet can save distributions of a set of variables, and they will work in the period of limit-

setting.

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Rivet results of N_j_30 and pT_yyl HGamRivet can get N_j_30 and pT_yy distributions in the events passing event selection

l For different Wilson coefficient sets, the histograms would be quite different, even with one or two order of magnitude

difference

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0 0.5 1 1.5 2 2.5 3 3.5 490

210

210×2

210×3

210×4

210×5

210×6

210×7

210×8 cg= 0.001cg= 0.0005cg= 0.0cg= -0.0005cg= -0.001

scan over cg in N_j_30

0 0.5 1 1.5 2 2.5 3 3.5 4

60708090

210

210×2

210×3

210×4

210×5

210×6 tcg= 0.001tcg= 0.0005cg= 0.0tcg= -0.0005tcg= -0.001

scan over tcg in N_j_30

0 2 4 6 8 10 12 14 16 185−10×84−104−10×2

3−10

3−10×2

2−10

2−10×2

1−10

1−10×2

12

1020

HistoEntries 18Mean 5.862Std Dev 3.246

cg= 0.001cg= 0.0005cg= 0.0cg= -0.0005cg= -0.001

scan over cg in pT_yy

0 2 4 6 8 10 12 14 16 185−10×64−104−10×2

3−10

3−10×2

2−10

2−10×2

1−101−10×2

12

1020 Histo

Entries 18Mean 5.815Std Dev 3.238

tcg= 0.001tcg= 0.0005cg= 0.0tcg= -0.0005tcg= -0.001

scan over tcg in pT_yy

Re-weightl Get distribution shapes of kinematic variables(like N_j_30 and pT_yy) from MC Powheg ggH samples. Mimic it with our

histograms with all of Wilson coefficients set to zero through multiplying by scale factors.

l Those scale factor are then applied to all of the other histograms with some coefficients changed, which is the process of

re-weighting.

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BinContent of N_j_30 l Apply reweight factors to all ofthe N_j_30 histograms

l The factors in N_j_30 are[1.84556, 1.14742 , 0.545151,0.272658]

l Replace old histograms with reweighted ones beforeinterpolation

Interpolation with Professor

l Interpolation with 2nd polynomial functions

there are 3 parameters for the model function in 1D interpolation.

Since two SILH coefficients(cG and tcG) get involved in the interpolation, there are 6 parameters for the model.

l Interpolation parameters in 4 bins of N_j_30 varying cg and tcg in SILH

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Parameters of the model function

Interpolation over one parameter l 1D interpolation results for cG

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l 1D interpolation results for tcG

cG tcG

Njets=1 Njets=1

l The interpolated values of the cross-sections are in excellent agreement with those predicted by theevent generator

Limit setting with gamma-combol Limits on Wilson coefficients are set by means of a likelihood function

l Input distribution of data(.HepData file) and interpolation results from professor

l 1D Scan over cg/tcg to observe limits of 95% and 68% CI

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Limit setting with gamma-combo

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gc0.001− 0.0005− 0 0.0005 0.001

1-C

L

0

0.2

0.4

0.6

0.8

1

1.2 EFT Run 2 Scan of cg (Prob)

68.3%

95.5%

GammaCombo

Reweighted results (cg) publication results (cg)

gc~0.001− 0.0005− 0 0.0005 0.001

1-C

L

0

0.2

0.4

0.6

0.8

1

1.2 EFT Run 2 Scan of ~cg (Prob)

68.3%

95.5%

GammaCombo

Reweighted results (tcg)

publication results(tcg)

Next to do

l Increase the number of MadGraph events from 1 thousand to 10 thousand to follow the

workflow again. (Have submitted condor jobs.)

l Store more variables(like pT_yy, excl_N_j_30) into histograms in the event selection

l Replace old distribution of data with Summer_2019_nofJVT.HepData in gamma-combo,

since there are new pT_yy binning and data update in 2019 HepData

l Change other coefficients in SILH model to compare CI limits with publication

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Backup

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