# Presentation: 082783

## Optimal Use of Information for Measuring Mt in lepton+jets tt Events.

- Gaston Gutierrez
- for the DØ Collaboration
- PASCOS’03

** ****Introduction**
** ****Event topology and selection**
** ****Explanation of the method used in the new M****t**** measurement **
** ****New preliminary measurement of ****M****t ****, and the ****M****W**** checks**
** ****MC tests with the new method**
** ****A few words on the systematic errors**
** ****Conclusions**

## Tevatron Top quark mass measurements

## Event topology and selections

***p***

***p***

**D****Ø ****Statistics RunI (125 pb****-1****)**
**Standard Selection**** :**
-  **Lepton:  E****t****>20 GeV     N=1     |********e****|<2   |************|<1.7**
** ****Jets:       E****T****>15 GeV    N********4     |********j****|<2**
** ****Missing E****T ****> 20 GeV**
** “****E****T****W ****’’> 60 GeV                      |********W ****|<2**
** ****gives 91 events**
*Ref.  PRD 58 (1998), 052001:*
- (After 2 cut gives 77 events)
**Additional cuts for this analysis**:
**4 Jets only (70% eff. for signal) :   71 events **
**Background Prob. (70% eff. for signal) :  22 events**** **

**12 jet permutations/event**

## The general method

**Most people would agree that if the probability of an event could be calculated accurately then the best estimate of a parameter will maximize a likelihood like:**

**The detector and reconstruction effects are always multiplicative and independent of the parameter to be estimated:**

**The probability P(x;****α****) can be calculated as:**

**Where x is the set of variables measured in the detector, y is the set of parton level variables, d****n****σ is the differential cross section and f(q) are the parton distribution functions. W(y,x) is the probability that a parton level set of variables y will show up in the detector as the set of variables x.  The integration reflects the fact that we want to sum over all the possible parton variables y leading to the observed set of variables x.**

## Transfer function W(x,y)

***W(x,y)*** probability of measuring** x **when** y **was produced ** (*****x*** measured 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 for the jet transfer function (*W**jet*), the parameters were extracted from MC simulation.

## Probability for tt events

-  2(in) + 18(final) = 20 degrees of freedom
-  3 (e) + 8 (1..4) + 3 (Pin=Pfinal) + 1 (Ein=Efinal) = 15 constraints
- 20 – 15 = 5 integrals
- Sum over 12 combinations of jets
- All values of the neutrino momentum are considered
*********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******      ******  ******   *****  **six particle phase space
***W(x,y)***      probability of measuring x when y was produced in the collision
- We chose these variables of integration because |M|2 is almost  negligible,  except near the four peaks of the Breit-Wigners within |M|2.

## Acceptance Corrections

- _Detector Acceptance_

- _Likelihood_

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

**Detector acceptance**

**Measured probability**

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

## Signal and Background

_**The background probability is defined only in terms of the main background**_ (W+jets, 80%)  which also proved to be an adequate representation for multijet background.
- 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 at each value of .

## Extra selection in Pbkg

**In order to increase the purity of signal another selection is applied on P****bkg****, with efficiencies:  ***********signal****** ******=0.70,  ************W+jets****** ******=0.30, ************multijets****** ******=0.23***

**ttbar@175GeV**

**W+jets**

**PRD 58, 52001 (1998)**

**D=P****sig****/(P****sig****+P****bkg****)**

## Two and three jet invariant masses

- Two (left plot) and three (right plot) jet invariant mass distributions.  The error bars correspond to t-tbar MC events for which the jets were matched to partons.  The curves correspond to our calculations for two different transfer functions Wjet(x,y).  The dashed-dotted line corresponds to the transfer function used in the final analysis.

**FWHM = 40 GeV**

## Signal and background probabilities: a MC vs. data comparison

- Background probability comparison between data (dots) and MC (histogram).  Background (signal) MC events are shown in blue (red).  The MC S/B ratio was set to the measured ratio S/B=12/10 for Pbkg<10-11 .

- Signal probability comparison between data (dots) and MC (histogram) in the form of a discriminant D=Psig/(Psig+Pbkg).  The signal probability was taken at it’s maximum value. The MC S/B ratio was set to the measured ratio S/B=12/10 for Pbkg<10-11 .

## Top probability for data events

**Left plot show  -ln(P****tt****) as a function of M****t**** for  10****-9****<P****bkg**** <10****-8****  (red arrows in lower figure).**

## Top probability for data events

**Left plots show  -ln(P****tt****) as a function of M****t**** for  9.7x10****-13 ****<P****bkg**** < 9.0x10****-12****   (red arrows in lower figure).**

## Changing the background probability cut

**The top plot shows M****top**** as a function of the cut in the background probability (P****bkg****).  The plot shows that M****top**** is very stable over a change in the number of events (N) of more that a factor of 2, and a change in P****bkg**** of more that a factor of 10****.**
**The plots on the right show –ln(L) as a function of M****top**** for each of the points in the plot above.  The plots show how the background enters mainly as a tail at low masses****.**

## New [preliminary] Result with DØ Run I data

**M****t****[preliminary]= 179.9 ******** 3.6 GeV ******** SYST**
**This new technique improves the statistical error on M****t**** from 5.6 GeV [****PRD 58 52001, (1998)****] to 3.6 GeV. **_**This is equivalent to a factor of  2.4 in the number of events.**_** **
**22 events pass our cuts out of which the analysis gives a total of 12.5 ± 3.0 t-tbar events.  This extrapolates to a total of 26 ± 6.0 t-tbar events in the Run I sample.**

**D****Ø Preliminary**

**D****Ø Preliminary**

## Check of Mw with DØ Run I data

**This can be very **_**helpful for reducing the uncertainty in the jet energy scale (JES**_**)**** , D****Ø has already been studying this option, for reference see the Proceedings of DPF2002 (Top quark physics) **_[http://dpf2002.velopers.net/talks_pdf/120talk.pdf](http://dpf2002.velopers.net/talks_pdf/120talk.pdf)__.  _
_**M**__**w**__** can be measured in the same events where M**__**t**__** is measured!**_

**D****Ø Preliminary**

**D****Ø Preliminary**

## Crosschecks on Ensemble tests (12s+10b)

**From the ensemble tests we estimate a 0.5 GeV bias in the peak with respect to the generated value**

## Crosschecks on Ensemble tests (12s+10b)

**The most probable result of these experiments is M****t****=174.7 GeV (top generated at M****t****=175.0 GeV).**

## Crosscheck of linearity of response

**Test of linearity of response is with MC samples containing large numbers of events.**

## Total Uncertainty

- I. Determined from MC studies with large  event samples:

| Signal model | 1.5 GeV |
| --- | --- |
| Background model | 1.0 GeV |
| Noise and multiple interactions PRD 58 52001, (1998) | 1.3 GeV |

- II. Determined from data:

**Total systematic:****	****6.0 GeV**
**Total:****	****	****	****7.0 GeV**

**D****Ø Preliminary**

| Jet Energy Scale | 5.6 GeV |
| --- | --- |
| Parton Distribution Function | 0.2 GeV |
| Acceptance Correction | 0.5 GeV |

**We will reduce this error in our final result (M****w****)**

## Conclusions 

**       **
**M****t****[preliminary] 179.9 ******** 3.6 (stat) ******** 6.0 (syst.) GeV **
**	**_**Significant improvement to our previous measurement**_** with ****M****t****= 173.3 ******** 5.6 (stat) ******** 5.5 (syst.) GeV (LB analysis in PRD) ****is equivalent to **_**2.4 times more data**_**:**
- Correct permutation is always considered (with the other 11)
- 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.

## Systematic error due to tt model

**Herwig MC with official D****Ø simulation**

**Herwig MC with official D****Ø simulation**

**u****: fraction of events in the experiment where all the jets can be matched with partons from top quark decays.   Increasing the fraction u, effectively turns on radiation and hadronization effects.  The systematic uncertainty is:  ********=1.5 GeV**

## Systematic error due to background model

**Results for different VECBOS flavors: Q****2**** scale of either <p****t****jet****>****2**** or M****2****W**** ,and with either HERWIG or ISAJET fragmentation.**
**From left to right: 1) M****2****W**** and IS, 2) M****2****W**** and HW, and 3) <p****t****jet****>****2**** and HW.**
**The points with large error bars were calculated with 250s+500b events, and the ones with small error bars with 400s+800b events.  The number of events is specified before the cut in P****bkg**** .**
**The assigned systematic uncertainty is:  ********=1.0 GeV **

## 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