1. T. Ferbel University of Rochester Planck 2002, Kazimierz
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
May, 2002
J.Estrada -University of Rochester & Fermilab

2. 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 t b W q
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) p W b t l n p
12 permutations
May, 2002
J.Estrada -University of Rochester & Fermilab

3. Published measurements of Mt (DØ and CDF)
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:
Template(xi;mt=A)
Template(xi;mt=B)
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.
Data => mt~B
May, 2002
J.Estrada -University of Rochester & Fermilab

4. DØ top mass analysis (lepton+jets)
From: PRD , (1998)
Mt (GeV)
Mt (GeV)
May, 2002
J.Estrada -University of Rochester & Fermilab

5. 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, (1999)]
One background
Three signal events   
Psignal
Pbackground
For each event, signal and background probabilities are added. The probabilities for individual events are then multiplied together.
May, 2002
J.Estrada -University of Rochester & Fermilab

6. J.Estrada -University of Rochester & Fermilab
Difference
Template Method
New Method
All the events are presented to the same template.
The template corresponds to a probability distribution for the entire sample, based on several variables calculated from MC.
The features of individual events are integrated (averaged) over the variables that are not considered in the template.
Requires clever selection of variables for the template.
Each event has its own probability distribution.
The probability depends on all measured quantities (except for unclustered energy).
Each event contributes with its own specific features to the probability, which depends on how well it was measured...
All variables, except for missing ET , contribute. Essentially no information is discarded.
May, 2002
J.Estrada -University of Rochester & Fermilab

7. Probability for t t Signal
Sum over 12 combinations of jets and neutrino solutions
 momentum of one of the jets
m1,m top mass in the event
M1,M2 W mass in the event
f(q1),f(q2) parton distribution functions (CTEQ4) for qq incident channel
q1,q initial parton momenta
 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.
May, 2002
J.Estrada -University of Rochester & Fermilab

8. J.Estrada -University of Rochester & Fermilab
Matrix Element
no ttbar spin correlation included
sqt sine of angle between q and t in the q q CM
b top quark's velocity in the q q CM
gs strong coupling constant
Leptonic decay
Hadronic decay
Mt, MW pole mass of top and W
mt top mass in any event
men ,mdu invariant mass of the en and du (or cs) system
Gt ,GW width of top and W
gW weak coupling constant
(cos jeb,db) angular distribution in W decay
May, 2002
J.Estrada -University of Rochester & Fermilab

9. Acceptance Corrections
Likelihood
Detector Acceptance
Measured probability
Detector acceptance
Production probability
, Ngen(N) = generated (observed) events
May, 2002
J.Estrada -University of Rochester & Fermilab

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

11. 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
pye produced electron momenta
pxe measured electron momenta
y j xj produced and measured jet angles
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.
May, 2002
J.Estrada -University of Rochester & Fermilab

12. 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.
May, 2002
J.Estrada -University of Rochester & Fermilab

13. Testing the New Approach via Linearity of the Response
24 (tt)
24 (tt) + 40 (W+jets)
From this fit :
May, 2002
J.Estrada -University of Rochester & Fermilab

14. J.Estrada -University of Rochester & Fermilab
For Mt:
Peak: GeV
Mean:173.1 GeV
Width: 4.1 GeV
(symmetric 68%)
<>=4.2 GeV
pull = 1.02
<Ns/N>=0.31
MC Ensemble Test (24 s +40 b)
May, 2002
J.Estrada -University of Rochester & Fermilab

15. J.Estrada -University of Rochester & Fermilab
For Mt:
Peak: GeV
Mean: GeV
Width:4.7 GeV
(symmetric 68%)
<>=4.8 GeV
pull = 1.08
<Ns/Ntot>=0.29
MC Ensemble test (20s +44 b)
May, 2002
J.Estrada -University of Rochester & Fermilab

16. 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).
May, 2002
J.Estrada -University of Rochester & Fermilab

17. 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.
May, 2002
J.Estrada -University of Rochester & Fermilab

18. 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 Ze+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.
May, 2002
J.Estrada -University of Rochester & Fermilab

19. J.Estrada -University of Rochester & Fermilab
Handle on JES from MW
After performing the measurement, our knowledge of Mt is contained in:
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).
May, 2002
J.Estrada -University of Rochester & Fermilab

20. Likelihood for a Different FJES
Scaling of the masses with FJES
May, 2002
J.Estrada -University of Rochester & Fermilab

21. J.Estrada -University of Rochester & Fermilab
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:
The correct permutation contributes for every event (not only 40% of the time) giving effectively better statistics.
All features of individual events are included, thereby well measured events contribute more information than poorly measured events.
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.
May, 2002
J.Estrada -University of Rochester & Fermilab

22. 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.
May, 2002
J.Estrada -University of Rochester & Fermilab

23. 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.
May, 2002
J.Estrada -University of Rochester & Fermilab

24. Energy Corrections in DØ-Run-1
May, 2002
J.Estrada -University of Rochester & Fermilab

25. Our Published Analysis
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
The variables containing most information on mass are selected and used in the analysis, and the rest are integrated/averaged over.
In general, a maximum likelihood is used to obtain the most probable value of .
May, 2002
J.Estrada -University of Rochester & Fermilab