# Presentation: 886468

## Measurement of the Top Quark Mass Using Dilepton Events 

- Erich W. Varnes
- Lawrence Berkeley National Laboratory
- for
- the DØ Collaboration
- Wine & Cheese Seminar
- Fermilab
- May 30, 1997

## Outline

- Introduction
- Event Selection
- Extension to cross section analysis
- Jet corrections
- Event fitting
- How to handle an underconstrained system
- The Matrix-Element Weighting Method
- The Neutrino Weighting Method
- Maximum likelihood fit
- Systematic Uncertainties
- Combination of dilepton and single-lepton results
- Conclusion

## Introduction

- The familiar top quark decay chart:
- One expects only about 1/6 as many dilepton events as lepton + jets
- Why then, perform a mass measurement using dilepton events?

## Motivation

- There are three major motivations, listed in order of current relevance:
- Direct verification that the excess of dilepton events arises from the same source as the excess of lepton + jets events
- Combining  the dilepton result with the single lepton one is expected to reduce the uncertainty on *m**t *by ~10%
- The dilepton measurement might be expected to have smaller systematic uncertainties, and thus be the favored channel  in future high-statistics measurements.  Anything learned now can be applied then.

## The DØ Detector

## Event Selection

- Largely the same as used in the cross section analysis:
- Full Run I data sample used (~125 pb-1)
- Main Ring events are vetoed

## Particle Identification

- Again, nearly identical to the cross section analysis
- Jets: cone algorithm with *R *o                           0.5
- Muons:
- Required to penetrate iron toroid
- Good global fit in muon and central tracking chambers
- Ionization in calorimeter
- Electrons:
- Five parameter likelihood is used (EM fraction, dE/dx,  c2, track-match, and transition radiation detector response)
- Cut is placed at 0.5
- In addition, isolation               	       required to be < 0.10
- Electron ID is relaxed for m-tagged *ee *events

## Extension of the ee Analysis

- The extension of the *ee* analysis was motivated by the observation of a striking event (95653/10822):

## We relax the electron ID criteria for b-tagged ee events.  Require one tight electron and one EM cluster with c2 < 100 and isolation < 0.10

- Signal to background ratio for events accepted by this extension is 15/1  (0.15 signal events and 0.01 background events expected)
- Since we observe a single event, we increase the *ee* background by 0.06 events

## Additional evidence supports the dielectron hypothesis:

## Jet Energy Corrections

- Goal is to translate well-calibrated electromagnetic scale to jets
*Z* + jets and g + jets events are used
- Step 1: Standard DØ corrections.  These account for:
- Overall hadronic response
- Noise and underlying event
- Out-of-cone showering
- Step 2: h-dependent corrections are applied to improve the match between data and MC jet scales
- Step 3:  If a jet is *b*-tagged, add in the best estimate of the muon and neutrino energies (based on the measured muon momentum)

## Dilepton Mass Analysis

- Dilepton events:
- Final state contains 6 objects for a total of 18 kinematic variables
- One can directly measure the three-momenta of the jets and charged leptons, and missing *E**T* (14 observables)
- There are three equations of constraint:
*M*(*l*1n1) = *M*(*l*2n2) =*M**W*
*M*(*l*1n1jet1) = *M*(*l*2n2jet2)
- Therefore, kinematic reconstruction of the event is not possible

## Dilepton Mass Fitting

- To proceed, note that one* can* solve the event (up to a four-fold ambiguity) if the value of the top quark mass is assumed
- The idea then is to step through a range of assumed top quark masses, solve the system, and estimate the likelihood of the solution
- Based on the relative likelihood of each solution, information about the top quark mass can be gained
- K. Kondo, J. Phys. Soc. Jpn.** 57**, 4126 (1988) and** 60**, 836 (1991)** **

## Solution Likelihood

- The likelihood of a solution is given analytically by:
- 	where |*M*|2  is a matrix element, {o} is the set of observables, {v} is a convenient set of variables, the r’s represent detector resolution, and the *d*-function enforces the mass constraints.
- Evaluation of the above is too expensive to be performed on large samples of MC events
- DØ therefore uses two approximations to this likelihood
- As detector resolution and ambiguity in jet assignments dominate the resolution, using such an approximation negligibly reduces the sensitivity of the analysis

## Matrix-Element Weighting (MWT)

- Extension of ideas proposed by
- R.H. Dalitz and G.R. Goldstein, Phys. Rev. D **45**, 1531 (1992)
- Use the weight
*f *(*x*) : Structure function for valence quarks
*p *(*E**(l)| *m**t*) : Probability distribution for the energy of the charged lepton in the top rest frame
*A*(*m**t*) : Normalization factor
- Sum over both possible pairings of *b*-jets with leptons

## Neutrino Weighting (nWT)

- Assume a top mass (*m**t*) and a rapidity for each neutrino (h1,h2 )
- The event can then be solved without using the measured missing *E**T *
- Assign the weight based on the agreement between the calculated neutrino *p**T *(***p******T*** (*nn*)) and the measured missing *E**T *:
- 					    /						              /
- Integrate over the neutrino rapidity phase space:
- 	Approximate prior probabilities *p*(h1 | *m**t*) by gaussians with widths taken from top Monte Carlo

## Average Weight Curve nWT

- Average the weight curves from sample of unsmeared parton-level Monte Carlo, only considering the correct lepton-jet pairing

## Event Smearing

- Thus far, no account has been taken of detector resolution.  To remedy this, we:
- Fluctuate the lepton and jet energies,and the missing *E**T*
- Calculate the weight distribution
- Iterate 100 (5000) times for MC (data) events
- Sum the resultant weight distributions
- Energy resolutions used in fluctuation:
- Electrons:
- Muons:
- Jets: see next slide
- Missing *E**T*: adjusted to account for object fluctuations, and smeared by an additional        4 GeV

## Jet Resolutions

- Jet resolution may depend on final-state topology (e.g., fraction of “overlapping” jets)
- Therefore, jet resolutions are derived from signal MC
- Parameterized by double Gaussian, as a function of *E**T* and h:

## Dilepton Jet Combinatorics

- Gluon radiation may produce additional jets
- With three jets there are two possibilities:
- Ignore one jet (initial-state radiation (ISR))
- Merge two jets together
- Six permutations in all (in addition to twofold jet-lepton pairing ambiguity):
- Assign a weight to each such combination:
- ISR jet: μ exp (-0.04*p**T *sinq)
- Two jets merged: μ exp (-0.05*m**jj*)
- For each three jet event, multiply each of the six event likelihood curves by the weight and sum them to form a single likelihood curve.

## W (mt) Distributions  For em channel

- Apply fitting procedure to HERWIG v5.7 top events passing the selection cuts.
- Following is for nWT:

## Dilepton Event Sample

- From  ~125 pb-1, we select 6 dilepton candidates:

## Candidate Fits

- Results of applying the MWT (dashed) and nWT (solid) procedures to the candidate events:

## Maximum Likelihood Fit

- Once a sample of events has been fit for the top mass, a maximum likelihood fit is used to determine the top quark mass most consistent with the entire sample.
- In the past, this has been done by extracting a single feature of the* W*(*m**t*) distribution (usually the peak) as an estimator for the “fitted mass” of each event* *
- Intuitively, one suspects that the *W*(*m**t*) distribution carries more information than this

## Probability Density Estimation Method

- One may increase sensitivity by dividing the scanned mt region into N bins, and recording the fraction of W(mt) that falls in each bin
- This results in a vector **v **of N measurements (w1...wN) for each event
- Larger N increases sensitivity, but also complexity, of calculation.  N=5 is a reasonable compromise

## We perform an unbinned ML fit using the following likelihood function:

- The problem is to evaluate the four-dimensional probability densities *f**s* and *f**b**.*
- One solution is to use the technique of Probability Density Estimation
- L. Holmström *et al.*, Comp. Phys. Comm. **88**, 195 (1995)
- The idea is to insert a four-dimensional Gaussian kernel at the position of each MC point.  Summing over the contributions from each of the MC kernel functions at an arbitrary point** x** gives an estimate of* f*(**x**).  The width of the Gaussian kernel is the only free parameter.
- This method gives 25 - 30% better sensitivity than does using a single-valued mass estimator***      ***

## HERWIG v5.7 is used to model top events

- Backgrounds are modeled by ISAJET, PYTHIA, and DØ data (misidentified electron backgrounds)
*L* is maximized with respect to *n**s** *and *n**b* at every* m**t* where we have Monte Carlo
- The nine -ln*L* points nearest the minimum are then fit to a parabola.  The minimum and width of this parabola give *m**t* and s

## MWT Results

## nWT Results

## Ensemble Tests

- In order to test the self-consistency of the method,  likelihood fits are performed on ensembles of  Monte Carlo events
- Each ensemble is formed of three* e**m *, two *ee, *and one* **mm  *events
- Background events are included in proportion expected, with binomial fluctuations on an ensemble-by-ensemble basis
- Resultant ML mass distributions are generally non-Gaussian
- Narrowest region containing 68% of ensembles is taken as the width

## Ensemble Distributions

- Distribution of ML masses using the MWT method:

## nWT Analysis:

## Ensemble Results

- Table lists median ML masses and widths for MWT and nWT analyses:
- 			  MWT                       nWT
- We can expect about 10% statistical accuracy

## Distribution of Ensemble Widths

- MWT Analysis:

## nWT analysis:

## Pull Distributions

- To test whether the width of the likelihood curve is a reasonable estimator of the statistical uncertainty, look at the ensemble *pull distribution:*
- Shown for MWT analysis; nWT is similar

## Some Further Results

- Consider fits to subsamples of the data (statistical uncertainties only):

## Systematic I: Jet Scale

- After all corrections, data and MC jet scales agree, with an uncertainty of d(*E**T*) = 0.025*E**T** *+ 0.5 GeV
- Photon + jets events:
- Resultant systematic determined by scaling MC jets by ± d, and redoing the mass fit.  Ensemble tests are run using the modified events as input.

- Relative data-MC *E**T** *balance

## Jet Scale (cont.)

- For tests run using a Monte Carlo top mass of       170 GeV/c2, we find the following ensemble medians:

## Systematic II: Signal Generator

- Samples of ISAJET signal events are input to ensemble tests, and change in median with respect to HERWIG ensembles noted:

## Systematic III: Background Shape

- For some background sources, MC statistics are very limited
- Model these backgrounds with Gaussian *W*(*m**t*) distributions
- Note change in ensemble results due to introduction of low-mass and high-mass Gaussian backgrounds

## Systematic IV: Multiple Interactions

- Use MC samples with 1 and 2 minimum bias events overlaid, in addition to standard samples
- These are combined in the ratio that occurs at the average Run I luminosity
- Shift in mean of *W*(*m**t*) distribution is noted
- MWT analysis finds 1.4 GeV/c2
- nWT analysis finds 1.2 GeV/c2

## Systematics V and VI: MC Statistics and Likelihood Fit

- To estimate the uncertainty on *m**t** *due to* *signal MC statistics, the samples are split into five subsets and the data fits redone.  Resultant systematics are     0.5 GeV/c2 (MWT ) and 0.3 GeV/c2 (nWT)
- It’s somewhat arbitrary to fit a parabola to nine       -ln *L* points.  Trying different fit regions, and also using cubic fits, in 170 GeV/c2 ensembles leads to a systematic of 1.2 GeV/c2 (MWT) and 1.3 GeV/c2 (nWT)

## Systematic Summary

## Combination of the Analyses

- To arrive at a final number, we combine the MWT and nWT analyses
- Using ensemble tests, we find that the analyses have a statistical correlation of 77%
- We assume that all systematics are 100% correlated
- This yields the DØ dilepton result:
*m**t*=168.4 ± 12.3 (stat.) ± 3.7 (syst.) GeV/c2

## Combination of the Dilepton and Lepton plus Jets Analyses

- We have recently submitted a lepton + jets mass measurement to PRL:
*m**t*=173.3 ± 5.6 (stat.) ± 6.2 (syst.) GeV/c2
- We combine this result with the dilepton result.  The jet scale, signal generator, and multiple interactions systematics are assumed to be 100% correlated.  All other uncertainties are uncorrelated.
- We obtain the DØ top quark mass:
*m**t*=172.0 ± 5.1 (stat.) ± 5.5 (syst.) GeV/c2

## Conclusions

- We have performed two analyses of the top quark mass using dilepton events, and find:
*m**t*=168.1 ± 12.4 (stat.) ± 3.7 (syst.) GeV/c2 (MWT)
*m**t*=169.3 ± 14.8 (stat.) ± 3.9 (syst.) GeV/c2 (nWT)
- Combination of these results gives
*m**t*=168.4 ± 12.3 (stat.) ± 3.7 (syst.) GeV/c2
- Finally, we combine the dilepton and lepton + jets results to give
*m**t*=172.0 ± 7.5 GeV/c2

## Top Mass vs. W Mass