Optimal use of Information for Extracting Parameters in Single-lepton tt Events.

May, 2002 J.Estrada -University of Rochester & Fermilab

Optimal use of Information for Extracting Parameters in Single-lepton tt Events.

T. Ferbel

University of Rochester

Planck 2002, Kazimierz

•Event selection

•Published solutions to this problem

•The new approach under study at DØ

•Statistical uncertainty with the new approach

•Energy scale for jets (JES) in the new approach

•Conclusions


Event topology and selections

The lepton + jets channels offer a good handle for selecting events with less background than tt->all-jets, and better statistics than dilepton decays

p

pt

b

W

qq

W b

t

l

Criteria:

• Leptons: Et>20 GeV,|e|<2 |,||<1.7

• Jets: 4, ET>15 GeV, ||<2

• Missing-ET > 20 GeV

DØ Statistics (125 pb-1):

29 signal + 48 backg. (0.8 W+ jets and 0.2 from all-jet production)

12 permutations


Published measurements of Mt

(DØ and CDF)

Template(xi;mt=B)

Data => mt~B

Template(xi;mt=A)

A multidimensional (xi) template is obtained for each value of the mass, and the data are then compared with those templates to find the most likely value for mt:

•The best permutation is selected on basis of a kinematic fit.

•A few variables, containing most of the information, are selected for the templates.

•A likelihood is built to select the template closest to the data.

• The background is also taken into account via its own template.


DØ top mass analysis (lepton+jets)

From: PRD 58 52001, (1998)

Mt (GeV) Mt (GeV)


DØ Studying a Different Approach

The probability for each event being signal is calculated as a function of the top mass. The probability for each event being background is also calculated. The results are combined in one likelihood for the sample. [This similar to the methods of Dalitz, Goldstein and Kondo, and the dilepton mass analysis by DØ - PRD 60, 52001 (1999)]

One background Three signal events

For each event, signal and background probabilities are added. The probabilities for individual events are then multiplied together.

Psignal Pbackground


Difference

Template Method New Method1. All the events are presented to

the same template.

2. The template corresponds to a probability distribution for the entire sample, based on several variables calculated from MC.

3. The features of individual events are integrated (averaged) over the variables that are not considered in the template.

4. Requires clever selection of variables for the template.

1. Each event has its own probability distribution.

2. The probability depends on all measured quantities (except for unclustered energy).

3. Each event contributes with its own specific features to the probability, which depends on how well it was measured...

4. All variables, except for missing ET , contribute. Essentially no information is discarded.


Probability for t t Signal

Sum over 12 combinations of jets and neutrino solutions

1 momentum of one of the jets

m1,m

2 top mass in the event

M1,M

2 W mass in the event

f(q1),f(q

2) parton distribution functions (CTEQ4) for qq incident channel

q1,q

2 initial parton momenta

6 phase space

W(x,y) probability of measuring x when y was produced in the collision

We choose these variables of integration because |M|2 is almost negligible, except near the four peaks of the Breit-Wigners within |M|2.

,

62|1

21222

22

21

211 ),(

||||

)()(||

combtt

yxWqq

qfqfMdMdmdMdmdP


Matrix Element

no ttbar spin correlation included s

qt sine of angle between q and t in the q q CM

top quark's velocity in the q q CM g

s strong coupling constant

Leptonic decay

Hadronic decay

Mt, MW pole mass of top and W mt top mass in any eventme ,mdu invariant mass of the e and du (or cs) systemt ,W width of top and W gW weak coupling constant(cos eb,db) angular distribution in W decay

)2(9

|| 224

2qt

s sFFg

M

22222222

224

)()(

)(cos

)()(4 WWWe

be

tttt

etw

MMmMMm

mmgF

22222222

224

)()(

)(cos

)()(4 WWWud

bd

tttt

udtw

MMmMMm

mmgF


Acceptance Corrections

Detector Acceptance

Likelihood

Production probability

Detector acceptance

N

ii dxxPNxPL

1

);();(ln)(ln

);()();( 0 xPxAccxPMeasured probability

N

ii dxxPxAccNxPL

100 );()();(ln)(ln

N

accepjj

gen

xPN

VdxxPxAcc

.00 );(

12);()(

)()()( 2121 qfqfdqdqydV MCMCMCn , Ngen(N) = generated (observed) events


Signal and Background

• The background probability is defined in terms of only the main backgound from W+jets (80%)

• The background probability for each event is calculated using VECBOS subroutines for W+jets.

• The values of c1 and c2 are optimized, and the likelihood is normalized automatically after this is done.

N

iiVECitt

VECtt

xPcxPc

dxxPcxPcxANL

121

21

)();(ln

)();()()(ln


Transfer Function W(x,y)

W(x,y) is the probability of measuring x when y is produced

(x jet variables, y parton variables):

where Ey energy of the produced quarks Ex measured and corrected jet energy py

e produced electron momenta px

e measured electron momenta y j x

j produced and measured jet angles

)(),()(),(4

1

24

1

3

i

xi

yi

j

xj

yjjet

xe

ye EEWppdxyxW

Energy of electrons is considered well measured. And, due to the excellent granularity of the D calorimeter, angles are also considered as well measured. A sum of two Gaussians is used to parameterize the Wjet transfer function.


Testing Procedure in Run-1 DØ MC

Examples of product likelihood functions. Each example corresponds to one experiment with statistics that DØ collected during Run-1. The signal (HERWIG) and background (VECBOS) events were run through the full DØ Run-1 simulation.


Testing the New Approach via Linearity of the Response

24 (tt)24 (tt) + 40 (W+jets)

From this fit :

GeV 4.299.0 inout mm


MC

En

sem

ble

Tes

t (24

s +

40 b

)

For Mt:

Peak: 174.8 GeVMean:173.1 GeVWidth: 4.1 GeV(symmetric 68%)

<>=4.2 GeV

pull = 1.02

<Ns/N>=0.31


MC

En

sem

ble

test

(20

s +

44 b

)

For Mt:

Peak: 172.3 GeVMean: 170.0 GeVWidth:4.7 GeV(symmetric 68%)

<>=4.8 GeV

pull = 1.08

<Ns/Ntot>=0.29


Re No. of Events for Signal and Backgnd.

Because of radiation, ~20% of the signal events look more like background. When only events with good jet-parton matching are used, this is resolved (not a problem).


The Likelihood in the (mW,mt) Plane

The likelihood is also a function of mW, and can therefore be examined in two dimensions

This provides a new handle on systematic uncertainty from the Jet Energy Scale (JES) via use of known MW.

*****

Shown at left are contours of constant likelihood, calculated for a MC sample of 30 signal events.


Issue of Scale for Jet Energies (JES)

• A Monte Carlo simulation of the detector is used to build the transfer function (or the templates used in previous analyses)

• It is essential to check that the energy scale in the MC simulation is representative of that in the detector. This can be done easily for the case of electromagnetic showers by using Ze+e- decays. It is not so easy to do for hadronic showers.

• In our previous analysis, the JES introduced an uncertainty of 2.5% in Mt . Now we want to reduce this uncertainty by using the mW peak observed in the top decays.


Handle on JES from MW

We assume that there is an unknown multiplicative factor FJES for all jet energies. The likelihood can be regarded as a 3D function that can be integrated on the two variables (FJES,,MW) that we do not want to measure.

Because DØ has information on FJES (from independent checks), with an uncertainty of 2.5%, this we can be used in our prior. The width in the prior for MW will be the systematic error on the evaluation of MW from our likelihood (this is still to be determined).

After performing the measurement, our knowledge of Mt is contained in:


FJES=1.06

Likelihood for a Different FJES

Scaling of the masses with FJES


Conclusion

At DØ, we are studying a new way to do analyses with low statistics. Comparing with our previous measurement of Mt , we note significant improvement in performance

• Statistical uncertainty improves because:

1. The correct permutation contributes for every event (not only 40% of the time) giving effectively better statistics.

2. All features of individual events are included, thereby well measured events contribute more information than poorly measured events.

3. Discrimination of signal to background improves dramatically.

• The possibility of checking the value of the W mass in the hadronic branch on the same events provides a new handle on controlling the largest systematic error, namely, the jet energy scale.


DØ published top mass analysis (lepton+jets)

• Four variables are used to parameterize signal and background probabilities (missing Et, A, HT2/Hz, x4). These variables are chosen to minimize the correlation with mt . A discriminant is defined as

• A kinematic fit is performed to each event, and the permutation with best 2 selected (correct in 40% of the cases) and mfit obtained for each event (the longitudinal momentum of the neutrino is also obtained from this constrained fit). Events with bad fit (2>10) are rejected.

• P is parameterized in 2 dimensions (mfit, ). Templates are obtained for different values of the MC input top mass, and then compared with data via a likelihood function.

bs

s

PP

P


DØ top mass analysis (lepton+jets), plots

Jet energy smearing is the dominant factor in the mass resolution (not limited by the DØ calorimeter!)

Hatched: correct permutation

Open: all permutation.


Energy Corrections in DØ-Run-1


Our Published Analysis

1. MC events are generated according to production probability (modeled via HERWIG for signal and VECBOS for W+jets) and run through the detector simulation to get

: parameter to be measured (i.e., mt)

x =(x1,…,x15): all measured variables for the event

2. The variables containing most information on mass are selected and used in the analysis, and the rest are integrated/averaged over.

3. In general, a maximum likelihood is used to obtain the most probable value of .

)()();( productionacceptxP

Optimal use of Information for Extracting Parameters in Single-lepton tt Events.

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