Top Quark Properties

Pekka Sinervo University of Toronto

Overview

• What We Learn From the Top Quark • Overview of Experiments

• Top quark mass and cross section • Single top production

• Top quark P_{T} distribution

• On to Run II

Work done in collaboration with Pierre Savard and Andrew Robinson

The Top Quark in the Standard Model

The SM “needs” a massive top quark

• b quark requires an SU(2) partner – suppression of FCNC decays

– e^{+} e^{−} → bb̄ scattering

• Many loop effects in SM driven by M_{top} – W/Z boson mass ratio

– b − b̄ mixing

– Rare K decays

Direct observation of top in 1995

• Confirmed all these predictions

• Gave us a “free quark” system to study ⇒ New frontier in particle physics

Recent History of Top

CDF and D0 / collected ∼ 100 pb^{−1} of data in 92-96 • 1.8 TeV pp̄ collisions

• Collected events with – High P_{T} leptons (P_{T} > ∼ 10 GeV/c)

– E̸_{T} > 25 GeV

– High P_{T} jets (P_{T} > ∼ 100 GeV/c)

• In 1995, presented evidence for tt̄ production

Subsequent studies have strengthened this

• Different techniques used to look at the same data – Kinematic distributions

– Neural network approaches

• Have verified consistency in all channels – See reasonable signals in τ lepton final states – All hadronic modes are also understood

SM Top Quark Phenomenology

Top quarks decay via the weak force

• Predict ∼ 100% t → W^{+} b

• Lifetime depends on mass

• For heavy top (M_{top} > ∼ 100 − 120 GeV/c^{2}), decays before it hadronises

Can be viewed as a “pure” charged current

Γ_{top} = \frac{G_{F} M_{t}^{3}}{8√2π} (1 − \frac{M_{W}^{2}}{M_{t}^{2}} )^{2} (1 + 2\frac{M_{W}^{2}}{M_{t}^{2}} )
∼ 175 MeV (\frac{M_{t}}{M_{W}} )^{3} ∼ 2 GeV

• Toponium doesn’t have time to form

• T mesons ∼ degenerate (if there was time...)

Decay dominated by “longitudinal W^{+} ”

• Means the W^{+} prefers helicity 0

• Result of large top and W^{+} mass

What Do Top Decays Tell Us?

SM predicts “pure” V − A decay

• clear test of polarisation at decay vertex

\frac{W_{long}}{W_{T}} ∼ \frac{1}{2} (\frac{M_{t}}{M_{W}} )^{2} ∼ 2.2

• V_{ts} CKM matrix elements

• Constraints on other SM parameters (eg. A_{LR})

• Effectively another consistency check of SM

Sensitive to some classes of “new physics”

• Higgs couples strongly to top

• Could decay into a SUSY H^{+}

t → H^{+} b
\underrightarrow{|}τ^{+} ν_{τ}

• Top quark might be “special” in unexpected way – New physics that couples to t t system

– Low Scale Gravity a good recent example

The Status of Top Today

CDF has now detected top in virtually all decay modes

• Lepton + Jets mode (for mass analysis) – lepton P_{T} > 20 GeV/c and E̸_{T} > 20 GeV

– ≥ 3 jets, E_{T} > 15 GeV and |η| < 2

– Require 1 b-tagged jet OR a 4th jet with E_{T} > 15 ⇒ 76 candidates (expect 31 ± 7 bkg)

• Dileptons – 2 leptons with P_{T} > 20 GeV/c

– Remove Drell-Yan and Z^{∘} background ⇒ 9 candidates (2.4 ± 0.5 events bkg)

• All hadronic decays – between 5 and 8 jets (E_{T} > 15 GeV and |η| < 2.0)

– ∑ E_{T} > 300 GeV + additional kinematic cuts ⇒ Observe 187 b-tagged jets (142 ± 11 expected bkg)

Used these samples for top quark measurements

What are the Interesting Top Properties?

• Top Quark Mass – SM constrains it to M_{W} /M_{Z}

– Important consistency check of theory

• Top Quark Production Cross Section – Predicted by QCD with less uncertainties than σ_{b} – Look for single top production

• Top Quark Decay Rates – Measured t → W^{+} b/t → W^{+} q

– Searched for FCNC such as t → Z^{∘}c

• Top Quark Decay Kinematics – SM expects decay to be polarized

– Have made first measurement of polarization

Top Quark Mass

Measurements now limited by systematic uncertainties

• Overall systematic uncertainty is ∼ 5 GeV/c^{2}

– Dominated by uncertainties in soft gluon contributions

and energy scale

• Statistical uncertainty limit our ability to constrain this

The final Run I values are

M_{top} = 176.0 ± 6.5 GeV c^{2} (CDF)
M_{top} = 172.1 ± 7.1 GeV c^{2} (D0 / )
M_{top} = 174.3 ± 5.1 GeV c^{2} (RunI)

HEP Seminar, 15 February 1999

Top Quark Production Cross Section

The cross section obtained by a fit to

• Lepton + jets rate

• Dileptons rate

• All hadronic event rate

Depends on M_{top} because of acceptance

σ_{t t} = 7.6_{−1.5}^{+1.8} pb

Rarest process ever measured in hadron collider!

• Theory predictions range from 4.7 to 5.5 pb HEP Seminar, 15 February 1999

Comparison with D0 /

Measurements by D0 / also quite consistent

Single Top Production

Single top production is a much lower rate process

• Sensitive to Γ_{t}

• Also could have contributions from non-SM sources

There are two primary SM production processes

1. t-channel W − g fusion ⇒ W^{+} bq final state

2. s-channel W^{∗} process ⇒ W^{+} bb̄ final state

• Predicted cross sections are 1.7 ± 0.3 and 0.7 ± 0.1 pb

Search Technique

Kinematics of processes somewhat different

• Use almost the same selection for both processes – Exactly 2 jets with E_{T} > 15 Gev and |η| < 2.0

– At least one b-tagged jet

– Require 145 ≤ M_{top} ≤ 205 GeV/c^{2}

• Differences are – For W -gluon fusion, require exactly one b-tag

– Have different acceptance

W^{∗}  W -gluon
σ_{theory} (pb)  0.73 ± 0.10  1.7 ± 0.3
Integrated luminosity (pb^{−1})  106 ± 4  106 ± 4
W + 2 jet acceptance (%)  3.4 ± 0.7  3.3 ± 0.6
SVX b-tag efficiency (%)  37.5 ± 3.1  24.8 ± 2.0
Number of expected events  1.0 ± 0.2  1.5 ± 0.3

Top Mass Reconstruction

HEP Seminar, 15 February 1999

Results of Search

Observed 42 events in this sample

• Largest single background are mis-tags

– tt̄ itself is a problem now

Process  Event Yield
W bb̄ + W cc̄  9.0 ± 2.5
Mistags  6.3 ± 2.6
W c  4.3 ± 1.5
Non-W  2.3 ± 1.0
Miscellaneous  2.1 ± 0.6
tt̄  5.7 ± 1.3
W -gluon  1.5 ± 0.3
W^{∗}  1.0 ± 0.3
Total expected  32 ± 5
Observed  42

Not yet sensitive to SM single top rate

• Can set limits separately on different processes

Single Top Production from W -gluon Fusion

Can exploit a rapidity correlation

• Top quark and light quark are in same hemisphere

• We fit the Q × η_{jet} distributions where Q = Q_{jet} × Q_{lepton}

Perform maximum likelihood fit to signal + backgrounds

• Constrains single top rate from this process

• Fit gives N_{W −gluon} = 1.4_{−3.4}^{+4.2} events

⇒ σ_{W −gluon} < 15.4 pb

HEP Seminar, 15 February 1999

Single Top Production from W^{∗} Production

Essentially all the information is in the observed yield

• Some discrimination in top mass distribution

• Set upper limit in similar manner to W -gluon fusion case

Perform maximum likelihood fit to signal + backgrounds

• Use likelihood function to constrain single top rate

• Fit gives N_{W^{∗}} = 7.3_{−6.7}^{+7.4}

σ_{W^{∗}} < 15.8 pb

So still well away from SM rate

• Can conclude that there is no huge anomaly

• It is a feasable measurement for Run II

Top Quark Transverse Momentum Distribution

• Goal is to produce model-independent constraints on the top quark P_{T} distribution

– Produce a set of confidence limits on \frac{dσ_{t}}{dP_{T}}

– Limited to large bins (ΔP_{T} = 75 GeV/c)

• Properly correct for resolution smearing and acceptance

• Can test models (such as ADD) in which the P_{T} spectrum is more sensitive to new physics then the total cross section

Event Selection

Use the “standard” lepton + jets event selection:

• Single isolated e(μ) having P_{T} > 20 GeV/c and |η| < 1.0 • E /_{T} > 20 GeV

• ≥ 4 jets, 3 with E_{T} > 15 GeV and |η| < 2.0 – fourth with E_{T} > 8 GeV, |η| < 2.4

To increase the signal significance, require that

N_{jet15} ≥ 4 or N_{tag} ≥ 1 .

Kinematically fit event, constraining M_{top} = 175 GeV/c^{2}

• Require χ^{2} < 10 ⇒ Left with 61 events

Measurement of P_{T}

Measurements on lepton-side and jet-side are strongly correlated!

• Make measurement using only jet-side top quarks

Output of the Fitter

Only ∼ 50% of top quarks in mass sample with true P_{T} in the range 150 ≤ P_{T} ≤ 225 GeV, have reconstructed P_{T} in the correct bin!

P_{T} Response Functions

Have measured P_{T} smearing using MC and detector simulation

• Use standard HERWIG MC calculations

• Most smearing arises from incorrect jet assignments HEP Seminar, 15 February 1999

Uncorrected P_{T} Distribution

• 61 events pass selection criteria

• Background distribution normalized to estimated rate

– We estimate N_{bgd} = 24.6 ± 5.8 events HEP Seminar, 15 February 1999

Resulting Fitted P_{T} Distribution

Perform unbinned likelihood fit to response functions and bkg shapes

• Fit tagged and untagged events with different templates • Use “bootstrap” technique to minimize assumptions about

shape of P_{T} spectrum within each true bin

• Define

R_{i} ≡ \frac{fraction in ith bin}{σ_{t t}}

Apply P_{T} -dependent acceptance correction

• Acceptance increases with P_{T}

Acceptance Corrected Results:

R_{1} = 0.29_{−0.18}^{+0.18}
R_{2} = 0.42_{−0.18}^{+0.18}
R_{3} = 0.29_{−0.10}^{+0.12}
R_{4} = 0.000_{−0.000}^{+0.035}

Combining R_{1} and R_{2}

R_{1} and R_{2} have strong negative correlation

• large uncertainties from fit

• Makes sense to combine these into single measurement

Resulting combined fraction of low P_{T} top quarks is

R_{1} + R_{2} = 0.68 ± 0.13

Verification of Methodology

Use MC technique to verify robustness of technique

Sample  N_{ev} N_{bgd} ± σ_{bgd}
No Tag  32 18.9 ± 5.6
Tagged  29  6.4 ± 1.3

Perform MC Carlo experiments on random samples of 32 untagged and 29 tagged events:

• Assume background in each tagging subsample distributed as N(N_{bgd}, σ_{bgd})

• Draw the appropriate numbers of background and signal events and run analysis

• Compare means of distributions to the expected SM P_{T} distribution So… Does all this work?

HEP Seminar, 15 February 1999 Problems in small fraction(4%) of the pseudo-experiments, flagged by a very small value of R_{3}.

Upper Limit in Highest P_{T} Bin

Examine the one-sided upper limit:

P = \frac{R_{4}^{true} − R_{4}^{meas}}{σ^{+}} ,  (1)

• Expect that P > 1 will occur 16% of the time • Observe 17.5%

HEP Seminar, 15 February 1999

Confidence Level Interval on R_{4}

Obtain R_{4}^{fit} = 0 (fraction of top with P_{T} > 225 GeV/c)

• Set a 95% CL limit using a MC technique – Analyze samples of MC events with varying R_{4}^{true} .

– Smear R_{4}^{true} in each with Gaussian distribution with a width equal to systematic uncertainty

– Determine value of R_{4}^{true} where only 5% of the pseudo experiments have R_{4}^{fit} = 0

CDF PRELIMINARY

Systematic Effect  δ(R_{4})
Background Model  ±0.0028
Jet Energy Scale {+0.0007 \atop −0.0042}
No Initial State Radiation  ±0.0045
Final State Radiation  ±0.0095
Flat P_{T} Spectrum  ±0.0157
m_{t} = 180 GeV  -0.0160

95% Confidence Level Upper Limit

In agreement with result obtained by integrating under the likelihood function. Without systematics, R_{4} < 0.109 at 95% CL

HEP Seminar, 15 February 1999

Magnitude of Various Systematics

CDF PRELIMINARY

Syst.  δR_{1}  δR_{2}  δR_{3}  δR_{4}  δ(R_{1} + R_{2})
m_{t}  {+0.026 \atop −0.000}  {+0.00 \atop −0.027}  {+0.023 \atop −0.000}  {+0.000 \atop −0.018}  {+0.006 \atop −0.012}
ISR  ±0.016 ±0.011 ±0.005 ±0.005  ±0.007
FSR  ±0.038 ±0.023 ±0.010 ±0.005  ±0.015
JES  {+0.020 \atop −0.028}  {+0.037 \atop −0.006}  {+0.000 \atop −0.008}  {+0.000 \atop −0.003}  {+0.014 \atop −0.000}
Q^{2}  ±0.025 ±0.008 ±0.008 ±0.010  ±0.016
P_{T}  ±0.032 ±0.045 ±0.055 ±0.016  ±0.036
Acceptance  {+0.010 \atop −0.023}  {+0.013 \atop −0.012}  {+0.016 \atop −0.014}  {+0.000 \atop −0.000}  {+0.025 \atop −0.011}

HEP Seminar, 15 February 1999

Top Quark Differential Cross Section

R_{1} + R_{2} = 0.72_{−0.13}^{+0.13} (stat) _{−0.06}^{+0.06} (syst)
R_{4} < 0.114 at 95% C.L.

P_{T} Bin  Measured Fraction of Top Quarks
0 < P_{T} < 75 GeV/c  R_{1} = 0.29_{−0.18}^{+0.18} (stat) _{−0.08}^{+0.08} (syst)
75 < P_{T} < 150 GeV/c  R_{2} = 0.42_{−0.18}^{+0.18} (stat) _{−0.07}^{+0.05} (syst)
150 < P_{T} < 225 GeV/c  R_{3} = 0.29_{−0.10}^{+0.12} (stat) _{−0.05}^{+0.06} (syst)
225 < P_{T} < 300 GeV/c  R_{4} = 0.000_{−0.000}^{+0.035} (stat) _{−0.000}^{+0.019} (syst)

Acceptance Calculations

Question: Are selection criteria/triggers biased in P_{T}?

• Generate large HERWIG+QFL′ samples, each constrained to have top quarks coming from one P_{T} bins, and count the fraction of events that pass cuts

• Only interested in Relative acceptance for each bin

• Estimate systematic uncertainty by recomputing results for most important systematic errors

Unsmearing Methodology

Break the data sample up into two subsamples and perform an unbinned likelihood fit to the data

• No Tag Hadronic (k=1)

• Tagged Hadronic (k=2) Then perform simultaneous maximization of the following likelihood function in each of the tagging subsamples:

− ln[L_{k}] = ∑_{i=1}^{n_{data}}− ln[(1 − B_{k}) ∑_{j=1}^{n_{bin}}R_{j}T_{jk}(P_{T}^{i}) + B_{k}V (P_{T}^{i})]  (2)

• R_{i} is the fraction of top quarks produced in true bin i

• B_{1} is the background fraction in the untagged events.

• B_{2} is the background fraction in the tagged events.

• The T_{k}, V are the response functions for the signal and

background, respectively.

The signal (T_{jk}(P_{T})) and background (V (P_{T})) response functions are normalized to unity. The B_{i} are constrained via Gaussian probability distributions about the background estimates.

HEP Seminar, 15 February 1999

The Bootstrap

• Methodology appears to be reasonably successful

• However, have overlooked one potential problem

• A given set of response functions is only valid for a particular assumption about how the P_{T} distribution varies within each true P_{T} bin!

Thus, we bootstrap:

After each iteration, perform rejection against new true P_{T} distribution to generate next set of response functions

Summary

Our work on top using Run I data coming to close

• Will complete P_{T} measurements

• Have W′ → tb̄ analysis underway

• Would like to complete branching fraction study

All this sets the stage for Run II

• Will start data taking sometime in 2000 (April-Sep?)

• Run for 2-4 years, with goal to collect ∼ 2 fb^{−1}

• Increase top quark sample ×50

By the time ATLAS turns on,

• Top will be well-studied – Understood as a background

• We will be able to focus on those properties that are most crucial to extending our understanding of elementary particles