# Presentation: 116619

## 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 D****Ø**
**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***

***p***

- 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;***m******t***=B)

- Data => ***m******t***~B

- Template(xi;***m******t***=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 ***m******t***:

- 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)**

**M****t ****(GeV)**

******M****t ****(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****.***

**P****signal**

**P****background**

## 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 *E**T* , 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
***m******1******,m******2***         top mass in the event
***M******1******,M******2***     *W* mass in the event
***f(q******1******),f(q******2******)*** parton distribution functions (CTEQ4) for qq incident channel
***q******1******,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.

## Matrix Element

-        no ttbar spin correlation included
-        sqt sine of angle between q and t in the q q CM
-          top quark's velocity in the q q CM
-        gs strong coupling constant

**Leptonic decay**

**Hadronic decay**

***M******t,**** ****M******W***  pole mass of  top and W
***m******t****** ***top mass in any event
***m******e************ ******,m******du*** invariant mass of the e and du (or cs) system
*********t****** ,************W***  width of top and W
***g******W***  weak coupling constant
*********(cos **********eb,db******)*** angular distribution in W decay

## Acceptance Corrections

- _Detector Acceptance_

- _Likelihood_

**Production probability***** ***

**Detector acceptance**

**Measured probability**

- ,  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 *c**1* and *c**2* are optimized, and the likelihood is normalized automatically after this is done.

## 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
-            ***E******y******  ****  *       energy of the produced quarks
-           * ****E******x  ****   *       measured and corrected jet energy
-           * ****p******y******e       *****         **produced electron momenta
-            ***p******x******e******   *****  ****      **measured electron momenta
-            *********y****** ******j****** ************x******j***   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 *W*jet 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 :**

## MC Ensemble Test (24 s +40 b)

**For M****t****:**
**Peak: 174.8 GeV**
**Mean:173.1 GeV**
**Width: 4.1 GeV**
**(symmetric 68%)**
**<********>=4.2 GeV**
******pull**** = 1.02**
**<Ns/N>=0.31**

## MC Ensemble test (20s +44 b)

**For M****t****:**
**Peak:  172.3 GeV**
**Mean: 170.0 GeV**
**Width:4.7 GeV**
**(symmetric 68%)**
**<********>=4.8 GeV**
******pull**** = 1.08**
**<Ns/Ntot>=0.29**

## Re No. of Events for Signal and Backgnd.

***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 m****W,**** 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 M****W.**
**               ***********
**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 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.

## Handle on JES from MW

- We assume that there is an unknown multiplicative factor *F**JES* for all jet energies. The likelihood can be regarded as a 3D function that can be integrated on the two variables (*F**JES,**,M**W*) that we do not want to measure.
- Because DØ has information on *F**JES* (from independent checks), with an uncertainty of 2.5%, this we can be used in our prior. The width in the prior for *M**W* will be the systematic error on the evaluation of *M**W* from our likelihood  (this is still to be determined).

- After performing the measurement, our knowledge of *M**t** *is contained in:

## Likelihood for a Different FJES

***Likelihood for a Different F******JES***

**Scaling of the masses with F****JES**

## Conclusion 

**       ****At D****Ø****, we are studying  a ****new way**** to do analyses ****with low statistics****.  Comparing with our previous measurement of M****t ****, 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.

## DØ published top mass analysis (lepton+jets)

- Four variables are used to parameterize signal and background probabilities (missing ***Et, A, H******T2******/H******z******, x******4***). These variables are chosen to minimize the correlation  with ***m******t**** **. *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 ***m******fit**** *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 (***m******fit***, ). Templates are obtained for different values of the MC input top mass, and then compared with data via     a likelihood function.

## 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

***Energy Corrections in D******Ø-Run-1***

## 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 =(x**1**,...,x**15**)*: 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 .