Top Mass in l+jets using Template Method

Result:
M_top = 173.4 +/- 2.5 (stat) +/- 1.3 (syst) GeV/c²
= 173.4 +/- 2.8 GeV/c²

We present a measurement of the top quark mass using 680 pb^-1 of data from ppbar collisions at a center-of-mass of 1.96 TeV collected by the CDF detector. We select ttbar events where one W boson from the top decays leptonically and the other W decays hadronically. The observed invariant mass distribution for the hadronic W boson decay is used to reduce the largest systematic uncertainty arising from the jet energy scale. The top quark mass and hadronic W boson mass distributions reconstructed in data are compared to Monte Carlo expectations to determine simultaneously the top quark mass and the jet energy scale. We measure M_top = 173.4 +/-2.5 (stat.+JES) +/- 1.3 (syst.) GeV/c^2, where the first uncertainty includes both the statistical and the jet energy scale (JES) uncertainty. This measurement is an update of an analysis published with 318 pb^-1 with the technique essentially unchanged, but using a data sample more than 2x as large.

Event selection:

Candidate events are selected for the lepton+jets channel of the ttbar system, ie where one W from the tops decays to a pair of hadrons, and the other W decays to a charged lepton (electron or muon) plus a neutrino. We require a well-identified electron or muon, at least 4 jets, and large missing transverse energy. We take advantage of different signal-to-background (S:B) and event shapes by splitting our sample into four non-overlapping subsamples, based primarily on the number of jets with a b-tag (using CDF's secondary vertex tagger, SECVTX). Events with 1-tag are further separated based on the Et threshold of the 4th jet - events passing only the loose 4th jet cut are fall into the 1-tag(L) category, and events with 4 jets that pass the tight cut fall into the 1-tag(T) category (L and T stand for loose and tight, respectively). The number of candidate events in each of the subsamples arising from this event selection are summarized in the following table:

	2-tag	1-tag(T)	1-tag(L)	0-tag
Number of b-tags	2	1	1	0
Jets 1-3 Et threshold (GeV)	15	15	15	21
4th jet Et threshold (GeV)	8	15	8	21

Top mass (m_t) reconstruction:

A chi-2 minimization is performed to reconstruct a top quark mass for each event. The fitter is based on the hypothesis that the event is ttbar: it contains W mass constraints on the hadronic and leptonic side and requires the two top masses in the event to be equal. Only the leading 4 jets are assigned to the four quark daughters from the top quark decay, though events with more than 4 jets are allowed. The jet-parton assignment that yields the lowest chi2 after minimization is kept for further analysis, and the corresponding top mass (m_t) is entered into a template (see below). To improve the S:B and remove poorly reconstructed events, we make a cut at minimum chi2 < 9. M_top templates for the 4 subsamples for an input top mass of 178 GeV/c2 are shown below.

Top mass templates:

The reconstructed top mass templates are built as a function of the true top quark mass (M_top) and the jet energy scale (JES) in the CDF detector. Analytical probability density functions (PDFs) of m_t (reconstructed mass) as a function of M_top (true top mass) and JES are extracted by fitting the multidimensional templates. The unit of JES chosen is 1 sigma_c as defined by the CDF Jet Energy and Resolution (JER) Group (see public page here). This unit is chosen to facilitate the combination of the JES from W->jj and the JER group. This uncertainty varies as a function of the jet eta and pt. Integrated over the ttbar jet pt and eta spectrum, it corresponds to an uncertainty of approximately 3%.

The PDFs for 4 value of M_top and JES = 0 in the 1-tag(T) sample, along with the histograms used to derive the PDFs, are shown here. Below them are the 0-tag histograms and the PDFs for JES = 0 as we vary across Mtop (on the left) and for Mtop = 180 as we vary across JES (on the right).

W_jj reconstruction:

To measure the JES, mass templates of the W boson decaying hadronically (m_jj) are also constructed in addition to the top mass templates. The chi2 fitter used for m_t reconstructio is not used, and no chi2 cut is made on the events. Instead, all invariant dijet masses consistent with b-tagging (ie not tagged as a b) from the first 4 highest Et jets are used. Therefore, the 2-, 1- and 0-tag templates contain 1, 3 and 6 m_jj entries per event, respectively. Default m_jj samples for the 4 subsamples for an input top mass of 178 GeV/c2 and JES = 0.0 are shown below.

W_jj templates

Similarly to the top mass templates, the W mass templates are constructed as a function of M_top and JES and then parameterized with analytic probability density functions.

Background

The background sources and their expected number of events are given in the table below (for the m_jj sample). The backgrounds are dominated by real W boson production in association with high-pt jets. This a priori information on the expected number of background events is used as a gaussian constraint in the likelihood fit for each subsample. No background estimate is used for the 0-tag events, so the number of background events is left unconstrained for that subsample.

	2-tag	1-tag(T)	1-tag(L)	0-tag
Non-w(QCD)	0.6 +/- 0.2	5.0 +/- 1.4	4.4 +/- 1.4	No background constraint Use <Nbackground> = 70.3 and <Nsignal> = 40.7 in pseudoexperiments
W+Heavy Flavor	2.4 +/- 1.0	8.4 +/- 3.0	14.6 +/- 4.7
W+light jets	0.9 +/- 0.2	6.9 +/- 1.4	8.9 +/- 1.9
WW/WZ	0.11 +/- 0.03	1.0 +/- 0.3	1.5 +/- 0.4
Single Top	0.02 +/- 0.01	1.1 +/- 0.3	1.3 +/- 0.3
Total Background	4.0 +/- 1.3	22.2 +/- 4.7	30.6 +/- 6.7
Expected ttbar (sigma = 6.1 pb)+Background	46.8	104.4	64.2

The background templates are independent of Mtop and JES (possible JES dependence will be taken as a systematic), and are shown here:

Validation of technique

We perform a variety of checks to ensure that our method is unbiased and performs as expected over an a priori determined range of top masses from 165-180 GeV/c2 and JES from -2 to 2 sigma_c. The legend for all the plots is the same:

We find an average pull width on the top quark mass of 1.019, larger than the expected 1.0 due to the non-Gaussian nature of our likelihood. The stat+JES error on our final result is scaled by this factor of 1.019 to reach 68% coverage with our error bars.

Top mass quantities	JES quantities

We also study the expected error as a function of input top quark mass and JES:

Systematic uncertainties

We have estimated the largest sources of systematic uncertainty and summarize these below. The jet energy scale is treated as a nuisance parameter in this analysis, and is constrained both by the a priori calorimeter calibration and the statistical information from the W mass. It is thus not considered a traditional source of systematic uncertainty, but included in the uncertainty arising from the likelihood fit.

Systematic Source	Delta Mtop (GeV/c2)
b-jet energy scale	0.6
Residual JES	0.7
Background JES	0.4
ISR	0.5
FSR	0.2
Parton Distribution Functions	0.3
Generators	0.2
Background Shape	0.5
b-tagging	0.1
Monte Carlo statistics	0.3
TOTAL	1.3

Fit and results

We perform a simultaneous unbinned likelihood fit of the data to the wjj and reconstructed top mass templates. The number of background events in each subsample is constrained to its expectation value with a gaussian prior, and the overall JES is constrained with a prior centered around 0.0 and a width of 1.0 (sigma_c). We find the following (the delta ln L contours can be thought of as roughly corresponding to 1, 2, 3 and 4 sigma):

Mtop = 173.4 +/- 2.5 (stat + JES) (GeV/c2)

dJES = -0.31 +0.59/-0.58 (stat + Mtop) (sigma_c)

Errors inflated by pull width scale factor

By fixing the JES to the measured value, the resulting reduction in the uncertainty from the likelihood fit gives a measure of the contribution of the JES nuisance parameter to the overall statistical uncertainty. By unfolding this in quadrature, we estimate the JES contribution to the statistical uncertainty to be 1.8 GeV/c2.

Category		2-tag	1-tag(T)	1-tag(L)	0-tag
Mtop	constraint	None

	fit	173.4 +/- 2.5 (stat + dJES) GeV/c2
		173.4 +/- 1.7 (stat) +/- 1.8 (dJES) GeV/c2
dJES	constraint	0.0 +/- 1.0 sigma_c
	fit	-0.3 +/- 0.6 sigma_c
nsignal	constraint	None
	fit	54.0 +/- 7.1	101.0 +/- 11.2	41.7 +/- 8.6	67.4 +/- 12.5
nbackground	constraint	4.0 +/- 1.3	22.2 +/- 4.7	30.6 +/- 6.7	None
	fit	3.7 +/- 1.2	20.3 +4.4/-4.3	32.2 +5.5/-5.4	40.6 +12.0/-11.1

We also fit the 4 subsamples separately:

	2-tag only Mtop = 175.7 +/- 3.4 (stat + JES) (GeV/c2) dJES = -0.30 +0.73/-0.72 (stat + Mtop) (sigma_c) Errors are raw and NOT inflated by pull width scale factor
	1-tag(T) only Mtop = 169.1 +3.5/-3.4 (stat + JES) (GeV/c2) dJES = 0.51 +/- 0.77 (stat + Mtop) (sigma_c) Errors are raw and NOT inflated by pull width scale factor
	1-tag(L) only Mtop = 173.7 +/- 6.3 (stat + JES) (GeV/c2) dJES = 0.05 +/- 0.92 (stat + Mtop) (sigma_c) Errors are raw and NOT inflated by pull width scale factor
	0-tag only Mtop = 174.1 +4.7/-5.5 (stat + JES) (GeV/c2) dJES = -0.95 +0.91/-0.88 (stat + Mtop) (sigma_c) Errors are raw and NOT inflated by pull width scale factor

We run pseudoexperiments with the observed number of events (input top mass = 172.5 GeV/c2) and our background expectations and find that 3.9% of psuedoexperiments give an average smaller error than the one observed in data. Below we show the expected positive and negative error distributions after applying the pull width scale factor. The arrows point to the errors returned by the likelihood fit.

Kinematic Plots

Below are plots for a wide variety of kinematic variables related to the ttbar system, along with KS probabilities for the observed data to fit come from the expected backgrounds (with the remaining events coming from ttbar events where the top quark mass is 172.5 GeV/c2). Keep in mind that we check these distributions only to see how well our background expectations and Monte Carlo samples model the observed data - though there is a relationship between true quantities and reconstructed quantities, we make no attempt to disentangle the true quantities from physics effects such as incorrect jet-parton assignments, mistags, ISR/FSR and parton distribution functions (which should all be modeled in our Monte Carlo).

Here we plot the mass and pT of the ttbar system for the separate subsamples: