# Presentation: 177387

## Optimal use of information for extracting parameters in single-lepton tt events.

- Juan Estrada for the
- DØ Collaboration
- DPF 2002

**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 channel  **

***p***

***p***

- Cuts:
-  Lepton: Et>20 GeV,|e|<2,||<2
-  Jets: 4, ET>15 GeV, ||<2
-  Missing ET > 20 GeV
- DØ Statistics (125 pb-1):
- 29 signal + 48 backg. (.8 *W+jets* and .2 QCD)

**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 accounted for using its own template.

## DØ top mass analysis (lepton+jets) From: PRD 58 52001, (1998)

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

******M****t ****(GeV)**

## DØ is now studying a different approach to this measurement  

- 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. Similar to the methods of Dalitz, Goldstein and Kondo, and mt measurement in the dilepton channel by DØ - PRD **60** 52001 (1999).

- one background event

- signal events

****

****

****

*For each event, signal and background probabilities are added. The probabilities ofor 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, using several variables calculated from MC simulations.
- The features of individual events are integrated (averaged) over the variables 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 (not on unclustered energy).
- Each event contributes with its own  specific features to the probability, which depends how well it was measured.
- All variables except missing Et components (unclustered energy) are used.

##  Probability for tt events

- 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 chann.
***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 of the W decay

## Acceptance Corrections

- _Detector Acceptance_

- _Likelihood_

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

**Detector acceptance**

**Measured probability**

- where

- , Ngen(N) is the number of generated(observed) events

## Signal and Background

- The background probability is defined in terms of the main backgound (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.

## Transfer functions W(x,y)

***W(x,y)*** probability of measuring** x **when** y **was 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. The sum of two gaussians
- is used for Wjet transfer function.

## Testing this in Run 1 DØ MC

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

## S/B discrimination

- One can define a discriminator, in the same way as was done for the published analysis:
***D=P******s******/(P******s******+P******b******)***
- In the new approach, we do not select on this variable, but present it to show how well we can distinguish our signal from background.

**PRD 58 52001, (1998)**

## Testing new approach via linearity of response

**24 (tt)**
**24 (tt) + 40 (W+jets)**
**From this fit :**

## MC ensemble test (24s +40 b)

**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)

**M****t****:**
**peak:174.9 GeV**
**mean:172.6 GeV**
**width:4.7 GeV**
**(symmetric 68%)**
**<********>=4.8 GeV**
******pull**** = 1.08**
**<Ns/Ntot>=0.29**

## Number of events for signal and backg.

***Number of events for signal and backg.***

**Because of radiation ~20% of the signal events look more like background than signal. 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 one could look at it in two dimensions.**
**This can provide a new handle on the systematic uncertainty coming from the Jet Energy Scale (JES). using M****W.**
**These are contours of constante likelihood calculated for a MC sample of 30 signal events. **

## JES issue

- We use a Monte Carlo simulation of the detector to build the transfer function (or the templates in previous analyses)
- It is essential to check that the energy scale in this MC simulation is representative of that in the detector. This can be done easily for the electromagnetic showers 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 using the mW peak 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±0.5%, this 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:

## Results for Different Priors

**Each line corresponds to a different width of the prior for M****W****. The x-axis is the width for the F****JES ****prior.**
**As the prior information on F****JES ****weakens (to the right), the value of M****t **** is pegged purely to M****W****.**

******top ****(linear scale)**

## 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 improvements 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.

## Results

- mass

- stat.err.

- uncertainty from JES

- PRD** 58 52001, (1998)**

- (new)

- [GeV]

| 173.3 | 5.6 | (NN)      (LB)
8.0      8.7  | 4.0
 |
| --- | --- | --- | --- |
|  |  | (24s+40b)    (20s+44b) 
4.1     4.7 | W mass in the hadronic branch |

- data

-   expected

## 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 is selected (correct in 40% of the cases) and ***m******fit**** *is 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 in a likelihood function.

## DØ top mass analysis (lepton+jets), plots

- Jet energy smearing is the dominant factor in the mass resolution.
- Hatched: correct permutation
- Open: all permutation.

## Energy corrections DØ-RunI

***Energy corrections D******Ø-RunI***

## Our published analysis

- MC events are generated according to production probability (models in Herwig for signal and Vecbos for *W+jets*) and ran 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 on mass are selected and used in the analysis, and the rest are integrated/averaged over generated events.
- In general, a maximum likelihood is in general used to obtain the most probable value of .

## Transfer function Wjet(x,y)

- Models the smearing in jet energies
- from effects of ***radiation, hadronization******, measurement ******resolution****** and ******jet****** reconstruction ******algorithm***

**These effects produce asymmetry**

- Correcting on average, and considering these distributions to be single Gaussians, can underestimate jet energies

- Use 2 Gaussians, one to account for the peak and the other to fit the asymmetric tails,

## Test of the Transfer Function in tt events

**Angular decay of the W**

**Histogram:** HERWIG events after full DO reconstruction, using the  standard criteria
**Solid Line:** Calculated by using the transfer function on partons
**Dashed: **Same as solid, but with
- a variant transfer function

**In black:** HERWIG events passed through full DO reconstruction, with standard  Run-1 criteria
**In red:** PYTHIA events (partons) after applying transfer function and standard Run-1 riteria

**Top Mass**

## Check of the Transfer Function in W+jets

**3 jets invariant mass**

- Invariant mass of three jets using W+4-jets events from VECBOS + ISAJET without requiring matching to initial partons*. (*Smooth curve, same as before.)

## Helicity of the W - MC  Studies

- Uses the full probability calculation
- Sums over all jet combination
- Sums over all neutrino solutions
-  Uses W(x,y)
-  Obtain F0=0.650.17

- Using 30 events