1. Session 10 on Standard-Model Electroweak Physics
Combined Abstract 845 on Mass of Top:
Abstract 169: Measurement of Mass of Top Quark in Lepton+Jets
Abstract 170: Direct Measurement of Mass Difference of Top and Antitop Quarks
Abstract 174: Measurement of Mass of Top Quark in Dilepton Final States
And as special bonus: Combination of Mass Measurements from Dø
Tom Ferbel (on behalf of the Dø Collaboration)
Universities of Rochester and Maryland
Krakow EPS Meeting
July 17, 2009 /

2. Introduction – Overall
We report three analyses of the mass of the top quark (mt) using top-antitop candidate events collected by the DØ experiment at the Tevatron Collider. Both t quarks decay to W + b, with both b evolving into b jets, and W decaying to ln or q’q:
A 3.6 events/fb sample of data in lepton+jets channels (one Wln and other Wq’q) analyzed to extract a precision value of mt using the “matrix-element” method (ME), wherein each event probability is calculated from the differential production cross section for signal ( ) and background (W+jets), as a function of mt and an overall jet energy scale (JES), with the latter constrained by the two jets from Wq’q decays of one of the top quarks.
Measurement of the mass difference between top and antitop quarks (D), as a first direct check of CPT invariance in the quark sector. Utilizing the ME method in lepton+jets channels, but for a smaller 1event/fb data sample (Run 2a).
Measurements of mt in dilepton final states (both W decaying to ln, with the em sample updated to 3.6 events/fb). Based on “matrix” weighting, “neutrino” weighting and the ME method, relying, respectively, on: (i) a likelihood for observing events in data for a range of assumed mt values, (ii) distributions generated from event weights that compare the calculated and reconstructed missing transverse energies, and (iii) event probabilities for the em channel based on the leading-order differential cross section as a function of assumed mt, with Z(tt)+jets serving as background for the ME analysis.

3. Introduction - Selections
Selections for lepton+jets, where lepton (l ) refers to either electron (e) or muon (m) are by now relatively standard, and optimized to minimize background (from multijets and W+jets), without adversely affecting signal efficiency:
Backgrounds and kinematics set the requirements for the energy scale typically at > 20 GeV for jets and isolated leptons, as well as for the imbalance in transverse momentum (MET), the latter expected from the presence of undetected neutrinos.
Accepted l+jets events must have only four jets (exclusively), of which at least one must be a b-tagged jet.
A neural-network-based discriminant that provides a probability for tagging any observed jet as a b-jet is used to sharpen the analysis.
Selections for dilepton+jets are also straightforward, but since dilepton channels are cleaner than l+jets, there is more freedom to balance restrictions vs acceptance. Thus:
Require either two good leptons or one good lepton and just an isolated track (but only if there is a b-tagged jet), and at least two jets (not necessarily b-tagged).
The two leptons (or lepton and isolated track) must have opposite electric charge.
Lepton energy scale softer for all dileptons (> 15 GeV) than in l +jets.
Additional criteria on MET and mll to minimize background from Z+jets for ee and mm events, but for em require large transverse-energy sum for jets and leading l.

4. Introduction – Monte Carlo/Calibration
All analyses rely on calibrations of response based on sets of simulated signal and background events. Such events are generated for fixed values of input parameters (e.g., mass values, assumed helicities, etc.) and processed through the same DØ reconstruction and analysis packages as applied to data. Specifically, ensembles of sets of Monte Carlo (MC) events from signal and background contributions, each set corresponding to a “pseudo-experiment,” are studied to calibrate (and to correct) the extracted values of parameters and their uncertainties.
MC events are usually generated using leading-order (LO) ALPGEN or PYTHIA programs, with PYTHIA also used to evolve partons to jets.
All standard corrections are applied to data and to MC, before the MC events are analyzed to provide any final shifts in the parameters extracted from data.
Uncertainties on the parameters are also corrected from the observed pull widths in the MC relative to expectations for a purely Gaussian behavior.
In the ME approach, transfer functions, calculated through fits to separate samples of MC events, are used to correlate energies of reconstructed jets with those of their progenitor partons.
Since LO matrix elements are used in the ME analyses, exclusively 4 jets are required in the l+jets and 2 jets in dilepton+jets events, respectively, to minimize the impact of higher-order QCD corrections on these analyses. The ME for signal uses only , and ME for background uses LO VECBOS (for W+jets and Z+jets).

5. Basics of ME Analysis Technique
Event probability densities for different values of the mass for top and antitop quarks, for signal
fraction f , with A(x) signifying the acceptance, are:
This is identical to what is used for the assumption of equality of masses, except that the two
parameters (Mtop,JES) in that standard analysis are replaced here with (Mt,Mtbar). The signal
probability densities are calculated from the differential cross section for production and
decay, using a modified version of PYTHIA that provides different values for Mtbar and Mt :
x represents observed jet variables and y their nascent partonic values
PDF
Transfer Function
M is the LO matrix element for any process, with the background being independent of Mtop (e.g., from VECBOS)
where:

6. Extracting parameters using the ME method
To extract a mass from candidates, probabilities are calculated for each event as a function of :
Event 1
Event 2
Event 3
Event n-1
Event n
L can depend on as many
parameters as CPU $ permit:
f , mass, helicity, JES…
From these, form a
likelihood function
(xi are observed kinematic
variables: momenta, angles…)
The best estimate of the parameter is determined through minimizing:
Statistical uncertainty can be
estimated, e.g., from:
0.5

7. Precision Measurement of Top Mass (in l +jets)
Calibration of fitted signal fraction as a function of input signal fraction.

8. Precision Measurement of Top Mass (in l +jets)
(Following minimization wrt signal fraction)
Calibrated result of analysis as a function of top mass
and JES, with the JES prior constrained by the mass
of W in W  qq’ in l +jets and accepted value of mW.
Projection of L(Mtop,JES) onto Mtop axis.
With uncertainties already corrected for
small departures of pull widths from unity.
Uncertainties of the measurement are in agreement with expectations from ensemble
studies, and precision is limited mainly by systematics (theoretical and experimental)

9. Top-Antitop Mass Difference (D)
(The lepton in in l +jets events implies the charge of the top quark)
Analysis is performed as a
function of the two masses,
for a fixed JES derived from
a previous extraction of the
mass that assumes identical
values of mt for antitop as
for top . The observed small
correlation in the fit to data is
not significant, and results
from e+jets and m+jets agree.
To project L along the D axis:
integrate the 2-D likelihood fit
along the diagonal axes. One
yields D, and the other the
mean mass. Latter can be
compared to a single mass
obtained in a previous study.
MC ensembles for calibrating
unequal top/antitop masses
use a private PYTHIA version.

10. Mass in Dilepton+jets (Matrix and Neutrino Weighting Methods)
In the “neutrino weighting” method, the value of MET is not used to reconstruct event kinematics. Instead, pseudorapidities of the neutrinos are chosen from the expected distributions (as a function of mt ), which along with an assumed mt , specify the entire event. For each of the four solutions, a probability weight is defined on the basis of agreement between the measured MET and the sum of neutrino transverse momenta.
The “matrix weighting” method uses parton distribution functions, the observed particle momenta, MET, constraints from the W masses and from the assumption of equality of the two top masses. For some fixed value of mt , this fully resolves the event kinematics (up to a four-fold ambiguity). Thus, the distributions for variables in dilepton events can be used to define weights, which are used to choose the best mt value that describes all the data.
Per usual, results are calibrated via MC ensembles for all dilepton channels. Observed uncertainties are close to expectations based on such studies.
mt = ± 4.8 (stat) ± 2.1 (syst) GeV (neutrino weighting in Run 2a)
mt = ± 4.9 (stat) ± 2.0 (syst) GeV (matrix weighting in Run 2a)
mt = ± 4.4 (stat) ± 2.0 (sys) GeV (above combined)

11. Mass in Dilepton+Jets (ME Method)
Application of ME method to Run 2a (left) and Run 2b (right) for the em channel (before calibration).
mtop = (stat) (syst) GeV, or GeV (combined for all dilepton analyses)

12. Promised Bonus: mt from Production Cross Section
(See presentation of Sebastien Greder at this conference)
Mt=169.1± 5.6 GeV
(for the pole mass)
Experimental and theoretical s as function of mt. The point shows the DØ average, the black dashed line a fit to, and the gray band the experimental uncertainty in the fit to the theoretical dependence for the acceptance at DØ.

13. Summary of mass measurements from DØ 

14. Summary and Conclusions
Using Run 2a and Run 2b data combined, assuming the mass of top
and antitop is the same, we extract the mass using the ME method:
mt = (stat) (syst) = GeV
(in l+jets)
From Run 2a data for top quarks in l+jets top-pair events, we have the
first direct measurement of the mass difference between a t quark and
its antiquark and have found a result consistent with CPT invariance:
That is, no significant mass difference, with an uncertainty equal to about
2% of the currently accepted mass of the top quark of GeV.
(3.4 stat and 1.1 syst)
Using em dilepton channels from Run 2a and and Run 2b and the ME analysis,
we extract the following results for the top mass:
Run 2a (stat) (syst) GeV Run 2b (stat) (syst) GeV
em combined (stat) (syst) GeV
All dilepton channels and methods: (stat) (syst) GeV = GeV
All above DØ measurements yield combined: GeV

15. End

16. M.E. based analysis technique
The Matrix Element is given by (assuming only ):
Where the decay terms are given by:
The background probability is calculated in a similar fashion as that for signal, except that we take the ME from the Vecbos program.

17. | Estimated from Run IIa
Systematic Uncertainties in Mass Extraction in l + 4Jets (some cancel in measurement of D)
| Estimated from Run IIa

18. More on ME method
In the sum over different combinations in Psig, each permutation of jets carries a weight wi, which is the normalized product of probabilities for tagging any jet, assuming some given parton-flavor hypothesis
Thus the normalization corresponds to the observed cross section for the assumed ME