b-Jet Energy Scale Determination Method

for Top Mass

Presentation forsummer student program

Mitsutoshi Ogino

Systematic uncertainties of Mtop measurementby top mass template group

This is excellent prescription, but we always want confirmation from data. 1

Many events come from All hadronic channel.

But, there are large background …(I did not consider the background at this study)

All-hadronic: ~45%No missing objects

Motivation

Method

22yxT PPP E

PPP

PPE

zyx

yx

T 222

22

2

)(bpT

perpendicular parallel

x

y

)(bpT

)( bbpT)( qpT

)(bfpT

)(bfpT)()1()( bbpfbbE TT

To estimate Jet Energy Scale

Sum of energy is 0 on x-y plane fron Energy momentum conservation.

fbbEbbp

bbEjT

jT

jT

1)()(

)(

To estimate Jet Energy Scale (JES),We watch response:

Method

3

Top Mass estimation

Estimation

Correction at All-hadronic (for check)

Likelihood (including product templates)

Identify b-quark with b-tagging and level 5 jet correction

Define as likelihood fitting function of b-jet energy scaling factor.

Estimate mean and sigma from fitting function of likelihood.

Check the effect of b-JES on parton, error bias and accuracy from plots.

Estimate top-quark mass and effect of error.

Match b-jet and 4 light quark jets. (dR < 0.4)

Event selectionLv:5_Correction (Pre-Selection)

A) Number of tight lepton = 0B) |Zjvert| < 60 cmC) |Zjvert - Zpvert| < 5 cmD) N(vert_class12) 1≧E) MET_significance < 3F) 6 Njet 8 (jets with Et 15, |η| 2.0)≦ ≦ ≧ ≦G) DeltaRmin (dRmin) 0.5 between jets≧

4

Matching 6 jets each other at dR < 0.4 after pre-selection.

[The method of least squares (LS)]

Likelihood

Nev

ii bJESxPbJesL

1

;)(

constbJesLbJES )(ln2)(2

bJES

truexxpull

[Likelihood function]

Estimate Mean, Mean’s Error, Sigma, and Sigma’s Error from χ2(bJES).

[pull]

Besides, to discuss accuracy …

5

)(ln2 bJESL

L(bJES) = “Gaussian”

bJES

χ2=-2lnL

bJES

L0

L0+1

1

1

σbJES

σbJES

If…

Signal template

fbbEbbp

bbEjT

jT

jT

1)()(

)(

[response]

Make signal templates and View the shift of response.

After, search all fitting function at f=0.90~1.10separating 21 variation.

6

pro

ba

bil

ity

)()(/)( bbpbbEbbE TTT

f : Jet Energy Scale

We fit the histograms above to get the P(xi,bJES).

Pseudo Experiment (practice)

7

Lln2 )()(/)( bbpbbEbbE TTT

1PE Example (f = 0.90)

fitting

Nev

t-2

ln(L

)

bJES

bJES = 0.917 +/- 0.016

To estimate statistical uncertainties,We performed pseudo experiments.

1. Get 191 events from template histogram

2. Performed likelihood fit to get the bJES and its error.

Repeat same procedure 10k times at each bJES

bJES

No

of

mea

n

Results (practice)

8

Problem (for practice result)

9

We didn’t consider acceptance effect due to bJES

Bad Fitting lead to slight bias & <1 pull width

We want to improve the uncertainties.

⊿(bJES) ~ 0.017 (Mtop) = 1.2GeV⊿

Try it again this analysis after introducing Top Specific Correction!!

Top Specific Correction (TSC)

10

Matching

Fitting

Correct Jet Energy

Change parameter form dR<0.4 to dR<0.1

Jet energy separate to 20~30, 30~40, 40~50, 50~60, 60~70, 70~100, and 100~ [Gev] each ranges. (to examine for Jet Energy dependence)

Product distribution plots of JetEt – PartonEt at each ranges.

Estimate mean and sigma around peak after fitting with Gaussian.

Recipe for TSC in this study

Make templates from estimated value of mean and sigma

Making template (TSC)

12

pro

ba

bil

ity

response

Example (f = 0.90)

original

corrected

Cannot improve top mass using this Top Specific Correction…

I abandoned to use this correcting method.

at f=0.90~1.10, corrected response approach 1-f,But no improve from original

Make template probability of response about f=0.90~1.10 cases.

To original response fit corrected…

summary

13

Hereafter …

Top Specific Correction

Estimate Jet Energy Scale

Result for practice

There is still scope for improvement.Try to improve using other correcting method?But, summer student program is last 2days only…

⊿(bJES) ~ 0.017 (Mtop) = 1.2GeV⊿But, there are some problem.

We do not have improvement from Top Specific Crrection.

To examine JES, We research response.

Back up

Template fitting（ practice）

15

Example (f = 0.90)

Error result (for practice)Example (f = 0.90)

Top specific correction（ b-Jet）

16

Number of event

jetEt - partonEt

Top specific correction (4 lq-Jet)

17

Number of event

jetEt - partonEt

Template（ TSC）

18

)()(/)(1 bbpbbEbbEf TTT

f = 1.00 f = 1.10

response

pro

bab

ilit

y

response:

Top invariant mass(for practice)

Mw constraint

response

Ne vt