The Discovery of the Top Quark

Pekka Sinervo University of Toronto

Overview

• Standard Model Framework

• The Role of the Top Quark

• The Discovery of Top

• What We Know About Top Today – Top Quark Mass

– Production and Decay Rates

– Single Top

• Prognostications

The Standard Model

The ingredients of the SM are

• 12 fermions – 6 quarks (u, d, s, c, b, t)

– 6 leptons (e^{−}, ν_{e}, μ, ν_{μ}, τ, ν_{τ})

• 3 electroweak bosons (W^{+} , W^{−}, Z^{∘}, γ)

• 8 gluons to describe the strong force

• ?? to describe gravity

Enormously successful paradigm since ∼ 1975

• Predicted rich phenomenology

• Accurate! (eg. δ_{M_{z}}/M_{z} ∼ 8 × 10^{−5})

Predicted existence of top quark in late 1970’s

• Higgs boson the only other “essential” missing element

Why a Top Quark?

In 1977, Lederman et al. reported a new resonance • Mass of 9.54 ± 0.04 GeV/c^{2}

• Decayed to μ^{+} μ^{−} pairs ⇒ A fifth quark

– e^{+} e^{−} production rate ⇒ Q = −1/3

Studies implied that the b quark had a missing partner

• “Flavour-changing neutral current” decays didn’t occur – decays like b → μ^{+} μ^{−}d not observed

• e^{+} e^{−} → bb̄ scattering suggested an SU(2) state ⇒ A sixth quark, known as “top” or “truth”

– Would have Q = +2/3

The Top Quark in the Standard Model

The SM “needs” a heavy top quark

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

– b − b̄ mixing

However, exact value of M_{top} not constrained

• In 1983, knew it had to be large (> ∼ 20 GeV/c^{2})

• Searches limited by collider centre-of-mass energies

SM Top Quark Phenomenology

Top quarks decay via the weak force

• Predict ∼ 100% t → W^{+} b

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

Can be viewed as “pure” β decay

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 (tt̄) doesn’t have time to form

• T mesons (tq̄) ∼ degenerate (if they had time...)

Decay dominated by “longitudinal W^{+} ”

• Means the W^{+} prefers helicity 0

• Result of large top and W^{+} mass

The Hunt for the Top Quark

SM didn’t tell us the top quark mass

• Search for top quark production in e^{+} e^{−} and pp̄ – Rate decreases sharply with M_{top}

– Production and decay signature change with mass ∗ pp̄ → W → tb̄

∗ e^{+} e^{−} → tt̄

∗ pp̄ → tt̄ → W^{+} b W^{−}b̄

UA1 experiment at CERN had one “false call”

• Observed a handful of W → tb̄ candidates in 1983 – Turned into a limit of M_{top} > 42 GeV/c^{2} by 1985

• A search by CDF in 1988-89 found M_{top} > 77 GeV/c^{2}

By 1992, had new measurements of M_{Z} and M_{W}

• SM predicted top quark with M_{top} > ∼ 140 GeV/c^{2}

• Only place to look was in high-energy pp̄ collisions • Two experiments

– D0 / and Collider Detector at Fermilab (CDF) Guelph Colloquium, 6 Feb 2001

Reconstructing Top

Since top is pair-produced and β decays

• Expect to see 6 final state particles

Life is normally not that easy – in reality:

Identifying Top Decays in pp̄ Collisions

In order to identify top candidates

• Search for W → lν_{l} candidate – Electron or muon with P_{T} > 20 GeV/c

– Missing transverse energy E̸_{T} > 20 GeV

• Search for at least one b jet – Most effective tool is to find a secondary vertex

• Some evidence of other W in event – Either two more jets or another lepton

Strategy for Detection

Identify events with a W^{+} → l^{+} ν_{l} signature

• Require evidence of a second W boson – W → e^{+} ν_{e} or μ^{+} ν_{μ} – W → q′q̄

• At least one more jet “tagged” as a b quark jet

Look for an excess of such events

Convincing “Smoking Gun” Events

Guelph Colloquium, 6 Feb 2001

Discovery of Top

Hints of top production appeared as early as 1993

• CDF published a 61 page PRD in Sep 1994

• Gave “cagey” label to the reports – “Evidence for top quark production...”

• D0 / ’s analysis not as definitive

With a factor of two more data, result was unequivocal

• April 1995, both collaborations announced discovery

• Confirmed SM predictions – M_{top} ∼ 170 − 190 GeV/c^{2} • Gave us a “free quark” system to study

⇒ New frontier in particle physics

Status of Collider Experiments

CDF and D0 / collected ∼ 110 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)

Studies have strengthened top quark interpretation

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

– Neural network approaches

• Verified that all decay modes appear to be OK – See reasonable signals in τ lepton final states – All hadronic modes are also understood

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)

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

– Look for t → H^{+} b

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

– Have made first measurement of polarization

• Single Top Production

Top Quark Mass

Measurements now limited by statistical uncertainties

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

– Dominated by uncertainties in soft gluon contributions

and energy scale

• Run I statistics limit systematic uncertainty

The final Run I values are

M_{top} = 176.1 ± 6.6 GeV c^{2} (CDF)
M_{top} = 172.1 ± 7.1 GeV c^{2} (D0 / )
M_{top} = 174.3 ± 5.1 GeV c^{2} (RunI)

Guelph Colloquium, 6 Feb 2001

Latest W boson mass results

M_{W} = 80.433 ± 0.079 GeV c^{2} CDF
M_{W} = 80.482 ± 0.091 GeV c^{2} D0
M_{W} = 80.427 ± 0.046 GeV c^{2} LEP2

Top Quark Production Cross Section

The cross section obtained by a fit to

• Lepton + jets, dileptons and all hadronic event rates

• Depends on M_{top} because of acceptance

• Recent improvement is more accurate b-tagging efficiency

σ_{t t} = 6.5_{−1.4}^{+1.7} pb

• Theory predictions range from 4.7 to 5.5 pb

Comparison with D0 /

Measurements by D0 / also quite consistent

Top Quark Transverse Momentum

SM predicts top quarks produced “back-to-back”

• Broad P_{T} distribution – < P_{T} >∼ M_{top}/2

• Non-SM predictions can be quite different – Can test models (such as Top colour or ADD)

Limited statistics and resolution present challenge

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

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

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 signal significance, require that N_{jet15} ≥ 4 the 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

P_{T} Response Functions

Measured P_{T} smearing using MC/detector simulation

• Use standard HERWIG MC calculations

• Most smearing arises from incorrect jet assignments Guelph Colloquium, 6 Feb 2001

Uncorrected P_{T} Distribution

• 61 events pass selection criteria

• Background distribution normalized to estimated rate

– We estimate N_{bgd} = 31.9 ± 4.6 events Guelph Colloquium, 6 Feb 2001

Resulting Fitted P_{T} Distribution

Perform unbinned likelihood fit

• Include four 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}

R_{1} = 0.21_{−0.21}^{+0.22}
R_{2} = 0.45_{−0.23}^{+0.23}
R_{3} = 0.34_{−0.12}^{+0.14}
R_{4} = 0.000_{−0.000}^{+0.031}

Confidence Level Interval on R_{4}

Obtain R_{4}^{fit} = 0 (fraction of top with P_{T} > 225 GeV/c) • Use non-Bayesian technique to infer “true” size of R_{4} • 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 MC samples 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

Agrees with result obtained by integrating the likelihood function

• Including systematics, R_{4} < 0.16 at 95% CL Guelph Colloquium, 6 Feb 2001

Top Quark Differential Cross Section

R_{1} + R_{2} = 0.66_{−0.17}^{+0.17} (stat) _{−0.06}^{+0.06} (syst)
R_{4} < 0.16 at 95% C.L.

P_{T} Bin  Measured Fraction of Top Quarks
0 < P_{T} < 75 GeV/c  R_{1} = 0.21_{−0.21}^{+0.22} (stat) _{−0.08}^{+0.10} (syst)
75 < P_{T} < 150 GeV/c  R_{2} = 0.45_{−0.23}^{+0.23} (stat) _{−0.07}^{+0.04} (syst)
150 < P_{T} < 225 GeV/c  R_{3} = 0.34_{−0.12}^{+0.14} (stat) _{−0.05}^{+0.07} (syst)
225 < P_{T} < 300 GeV/c  R_{4} = 0.000_{−0.000}^{+0.031} (stat) _{−0.000}^{+0.019} (syst)

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 production processes different

• Use the same selection for both processes – 1, 2 or 3 jets with E_{T} > 15 Gev and |η| < 2.0

– At least one b-tagged jet

– Require 140 ≤ M_{top} ≤ 210 GeV/c^{2}

• Fit H_{T} distribution with signal and background terms

H_{T} ≡ ∑_{partons} E_{T}

W^{∗}  W -gluon
σ_{theory} (pb)  0.73 ± 0.10  1.7 ± 0.3
Integrated luminosity (pb^{−1})  106 ± 4  106 ± 4
W + n jet acceptance (%)  4.5 ± 0.7  6.7 ± 1.0
SVX b-tag efficiency (%)  37.5 ± 3.1  24.8 ± 2.0
Number of expected events  1.3 ± 0.3  3.0 ± 0.6

Top Mass Reconstruction

Guelph Colloquium, 6 Feb 2001

H_{T} Reconstruction

The variable H_{T} is an effective discriminator

• QCD Background

• t t background

• Single top signal

Results of Search

Observed 65 events in this sample

• Largest single background are mistags

– tt̄ itself is a problem now

Process  Event Yield
Mistags  25.9 ± 7.5
W bb̄ + W cc̄  28.7 ± 7.5
W c  17.2 ± 6.2
Non-W  12.1 ± 4.1
Miscellaneous  5.1 ± 0.9
After M_{t} cut  54 ± 11
tt̄  8.4 ± 2.7
W -gluon  3.0 ± 0.6
W^{∗}  1.3 ± 0.3
Total expected  67 ± 11
Observed  65

Not yet sensitive to SM single top rate

• Can set limits on total single top rate

Single Top Production Cross Section Limits

Use H_{T} distribution to fit signal and background shapes

• Set upper limit using a Bayesian technique

• Fit gives σ_{t} < 13.5 pb at 95% CL

Still well away from SM rate

• Can conclude that there is no huge anomaly

• It is a feasable measurement for Run II

– Can get S/N = 2.9 on W + 2, 3 jet sample Guelph Colloquium, 6 Feb 2001

Run II Forecasts

Run II will start this summer at √s = 2.0 TeV

• CDF had an “engineering run” (partial SVX II) last fall • Physics running will commence next month 2001

Will be worth the wait

• Begin with ∼ 3 fb^{−1}/year per detector

• Finish up with ∼ 5 fb^{−1}/year

• Literal “Top Factory” with – 300 dilepton events

– 3000 tagged lepton+jet events – 1500 events in “mass sample”

Top Physics Goals in Run II

Mass analysis uncertainties scale with statistics

• Can expect δM_{t} ∼ 3.0˜ GeV/c^{2}

• With δM_{W} ∼ 40 MeV/c^{2}

\frac{δM_{Higgs}}{M_{Higgs}} ∼ 40%

• Powerful “pointer” for LHC searches

Measure angular correlations and decay kinematics

• Polarization of W^{+} will be measurable

• Spin correlations (expect 90%) also detectable

Single top production

• Measure σ_{t} with 10% uncertainty

• Measure V_{tb} with 12% uncertainty

Expected Run IIa Result

Guelph Colloquium, 6 Feb 2001

Summary

Debut of top using Run I data coming to close

• Have seen that it looks much like a SM fermion • But top mass scale is enigmatic

All this sets the stage for Run II

• Run for 2-4 years, with goal of ∼ 2 − 15 fb^{−1} ⇒ Increase top quark sample ×50

By the time next generation collider turns on,

• Top will be pretty well-studied

– Reveal some property that points toward a more complete theory?

– Will at least be an important background

• Will be able to reconstruct millions at the LHC!

– It will become the “high-statistics” probe of the next energy scale