Top to Bottom

New Results on Top and Bottom Quark Decays

Pekka K. Sinervo University of Toronto

1. Top and Bottom Quark Decays in the SM 2. Summary of Run I Data Samples

3. Top Quark Branching Fractions

4. Bottom Meson Hadronic Decays

5. Summary and Outlook for Run II

University of Rochester

HEP Seminar September 1996

SM Top Quark Phenomenology

Top quarks decay via the weak force

• Predict ∼ 100% t → W + b

• Lifetime depends on mass

• For heavy top (Mtop > ∼ 100 − 120 GeV/c2), decays before it hadronises

Can be viewed as a “pure” charged current

Γtop = \frac{GF M3 t}{8√2π} (1 − \frac{M2 W}{M2 t} )2 (1 + 2\frac{M2 W}{M2 t} )
∼ 175 MeV (\frac{Mt}{MW} )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{Wlong}{WT} ∼ \frac{1}{2} (\frac{Mt}{MW} )2 ∼ 2.2

• Vts CKM matrix elements

• Constraints on other SM parameters (eg. ALR)

• 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

|_{⟶}τ+ ντ

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

SM Bottom Quark Decays

SM predicts similar charged-current decays

• Dominated by weak matrix element

• However, b is imbedded in “brown muck” – Strong interaction effects are important – higher-order diagrams also play a role

Have resorted to an effective Hamiltonian approach

• Use a basis convenient for a Qq̄ system ⇒ Heavy Quark Effective Theory

• Assume that decay amplitude “factors” (BSW)

• Determine parameters empirically

Hadronic Bottom Decays

Start with

H = \frac{GF}{√2} Vcb \{[(d̄u) + (s̄c)] (c̄b)\}

• Renormalise H to take into account QCD corrections

Heff = \frac{GF}{√2} Vcb \{c1(μ) [(d̄u) + (s̄c)] (c̄b) + c2(μ) [(c̄u)(d̄b) + (c̄c)(c̄b)] \}

• For B → J/ψ decays, employ BSW factorisation:

dΓ(B+ → J/ψX) ∝ a2(mb)2|VcbV{∗ \atop cs}|2 |⟨J/ψ|(c̄c)|0⟩ |2 |⟨X|(s̄b)|B⟩|2

• Have to put in b quark form factors by hand

Model is fundamental enough to warrant detailed study

• CLEO/ARGUS have looked at many decays systematically

• But studies have had limitations – low statistics

– only have access to B∘ and B+ ∗ cannot produce B∘ s or b baryons

Hadron collider experiment overcomes some limitations

• Tevatron has produced ∼ 3 × 109 bb̄ events

• CDF has measured a number of B branching fractions

Run I Results from CDF

CDF is general-purpose detector designed to study p p collisions

• approximately hermetic calorimeters in |η| < 4.2

• 84-layer drift chamber in 1.4 T solenoidal B field

• muon chambers outside calorimeter

• electron ID based on shower profiles & tracking

The CDF experiment ran from 1992-96

• Collected 20 pb−1 in 1992-93 (Run Ia)

• Collected 85 pb−1 in 1994-96 (Run Ib)

• Maximum L of ∼ 2.7 × 1031 cm−2s−1

Top Quark Production

Top quark production is mediated by

qq̄, gg → tt̄
qq̄ → tb̄X  and  qq̄ → W + → tb̄ both small

Because top is heavy, need large x for initial partons

• Implies that cross section falls with mass

• t t system approximately at rest – < PT >∼ Mtop/2

Higher order corrections to σ_{t t} have been calculated

• Most recently by Laenen, Smith and Neerven, NP B369, (1992) 543.

• Biggest effects due to “soft gluon emission”

Top Decays and Detection Requirements

SM top quark decays via the weak force

t → W + b

|_{⟶}ud̄ or cs̄ (2/3)

|_{⟶}e+ νe or μ+ νμ or τ+ ντ (1/3)

In proton-antiproton collisions,

This results in several distinct decay signatures

• Six jet final states (36/81)

• Lepton (e± or μ±) + Jet events (24/81)

• Dilepton events with 2 energetic e± and μ∓ (4/81)

• Decay modes with τ’s hard! (∼ 12/81)

Triggering Issues

Use multi-level trigger to tag events in real-time

• Interaction rate of (50 × 10−27 cm 2) ×(1.5 × 1031 cm −2s−1) = 7.5 × 105 Hz has to be reduced to of order 1-10 Hz

• Most challenging aspect of experiment – Depends critically on all subsystems

– Need efficiency > 75% to be competitive

Triggering for “heavy” top is relatively easy

• Tag high PT (> 15 − 20 GeV/c) lepton(s)

• Missing energy requirements (E̸T > 20 − 25 GeV)

• Multijet topologies

• Trigger efficiencies ≥ 90 − 95% in most cases

Top Signals

Have detected signals for t t production & decay

1. Lepton + jets channel • Require e± or μ± with PT > 20 GeV/c • Require E̸T > 20 GeV to tag neutrino

• Require ≥ 3 jets with ET > 15 GeV

• Require at least one jet with b tag

2. Dilepton channel • Require two e± or μ± with PT > 20 GeV/c • Require E̸T > 25 GeV to tag neutrino

• Require ≥ 2 jets with ET > 10 GeV

3. Dileptons with τ’s • Require τ candidate + additional lepton

• Similar requirements to standard dileptons

4. Hadronic channel • Require 6 jets with ET > 20 GeV

• Require at least two jets with b tags

• Make kinematic cuts to increase S/N

W+Jet Selection

Selection of W candidates straightforward

• Require high PT isolated lepton candidate

• Require significant E̸T

• Require three or more high PT jets

Have large W^{+} samples

• CDF has 31,000 eνe and 21,000 μνμ candidates

Run IA CDF data shows clear “W” signal:

W + Jet Sample

Require ≥ 3 or 4 jets (from other W and b quarks)

• ≥ 3 jets with ET > 15 GeV and |η| < 2.0

• find 274 W+≥ 3 jet events

Most background sources are small:

Background  Fraction of Events (%)
Fake leptons and bb̄  9 ± 5
W W, W Z and ZZ  4 ± 2
Z → ττ, ee, μμ  7 ± 2
Total  20 ± 6

QCD W+jets production is largest expected background

Mtop (GeV/c2) Number of Events (CDF)
120  176 ± 28
140  105 ± 14
160  57 ± 10
180  16 ± 3.2
W+jets  238{+76 \atop −38}

b Quark Tagging in W+Jet Events

Have two different techniques for b-tagging

1. About 20% of b’s decay via

b → e−νeX and b → μ−νμX

• Look for jets with “soft” leptons in them (SLT tags)

2. “Long” b lifetime – cτ ∼ 450 microns

• Use Silicon Vertex Detector to identify jets with a secondary vertex

• Expect 42% of t t events to have at least one SVX tag

Applied b tagging techniques to W+jet events

• The W + 1 and W + 2 jet samples are ultimate control – Don’t expect significant top contribution

– Theory predicts low b hadron content

Sample  SVX bkg SVX tags  SLT bkg  SLT tags
W+1 jet  69 ± 15  70  272 ± 24  245
W+2 jet  29 ± 4  45  78 ± 7  82
W+≥ 3 jet  9.3 ± 1.1  34  25.2 ± 3.0  40

Dilepton Top Sample

t t decaying into 2 leptons create unique signature

• Two charged leptons from W ± decay

• Imbalance in total energy due to undetected neutrinos • Two jets from bottom quarks

Select sample by requiring

• Two clean, high PT lepton candidates

• Missing transverse energy E̸T > 25 GeV

• Require two jets with ET > 10 GeV and |η| < 2.0 • Reject specific backgrounds (e.g. Z∘)

Dilepton Channel

Significant dilepton background is Drell-Yan production

• E̸T signature created by mismeasured jet

• Harden E̸T cut to > 50 GeV if correlated with jet

a) Z+1 jet, b) Z+ 2 jet, and c) t t (Mtop = 160 GeV/c2)

Dielectron Data for Run 1A and 1B

16

DiMuon Data for Run 1A and 1B

17

Electron-Muon Data for Run 1A and 1B

18

Summary of CDF Dilepton Search

Observe a total of 10 candidate events

• Observe 1 e+ e− event, 2 μ+ μ− event and 7 eμ events – One μ+ μ− event suspicious (but we keep it)

– Has μ+ μ−γ mass close to Z∘

• Expect 2.1 ± 0.4 events from background

Acceptance × SM branching fraction = 0.77 ± 0.08%

σtt̄ = 9.3{+4.4 \atop −3.4} pb

Top Quark Mass from Lepton + Jets

In this mode, have measured almost all t t daughters

• Lepton 4-momentum solid and νl is missing only pz

• W → qq̄′ observed as 2 jets

• bottom quarks observed as jets (perhaps tagged)

Problems:

• QCD radiation generates additional jets

• Combinatorics in identifying jets ↔ partons

• Background events

Top Mass Results

Estimate mass based on 34 W + ≥ 4 jet sample

• Use known fake tag rates and W bb̄

• Background shape in Mtop comes from MC calculation • Estimate background to be 6.4{+2.1 \atop −1.4} events

– Primarily QCD W+jet

Evidence for W → qq̄

Observation of W → qq̄ is important

• Strong evidence of signal in W + W −bb̄ channel • Can calibrate jet energy scale

Have to refit data relaxing W mass constraint

• Look for W signal plotting all mass combinations – Makes it tough since 6 combos/event

• Reduce backgrounds by requiring H > 300 GeV

Top Quark Branching Fractions

Indication of new physics would be if B(t → W^{±}b) ≠ 1

• SM expects Vtb to be unity

– Unitarity constraints ∗ Vud large from nuclear β and μ decay ∗ Vus constrained by Ke3 decays

∗ Vcd comes from νn → cX

∗ Vcs constrained by De3 decays

∗ Vcb small because large τb

∗ Vub even smaller (b → u)

– Expect Vts and Vtd much smaller than Vtb

• Vtb < ∼ 0.9985 violates (or bends) SM

Experimentally, we determine

R ≡ \frac{B(t → W b)}{B(t → W q)} = \frac{|Vtb|2}{|Vtb|2 + |Vts|2 + |Vtd|2}

Measure the rate of 0, 1 and 2 b-tagged events

• Need to be able to b tag

• Have to deal with large backgrounds in 0-tagged sample

B Technique

Fraction of zero, single and double-tagged events is

f0 = (1 − Rϵ)2
f1 = 2Rϵ(1 − Rϵ)
f2 = (Rϵ)2

• ϵ is tagging efficiency

Rate of single vs double tags gives

R = \frac{2}{ϵ(f1/f2 + 2)}

Rate of zero vs single tags gives

R = \frac{1}{ϵ(2f0/f1 + 1)}

Estimate R using maximum likelihood technique

• For a given number of observed events, – calculate probability of observing 0, 1 and 2 tags – maximize probability by varying R

• Can use probability to constraint R

Event Selection Details

Increase sensitivity by relaxing b tag requirement

• Reject large QCD background by cutting on

1. Relative likelihood of t t vs W +jets – based on 2nd and 3rd leading jet ET

– Rejects 75% of W +jet background

– Has efficiency of 75% for t t

2. Use sample with | cos θ∗| < 0.7 as check – Expected to be enriched in t t

– But fairly large systematic uncertainty

• Only using Run Ib data (∼ 90 pb−1)

After applying likelihood cut,

• Have 68 events after relative likelihood cut – Expect non-t t background to be ∼ 40 events – Have 24 events after additional cos θ∗ cut

• Have 10 and 5 single and double-tagged events

CDF BR Results

For dilepton events

• Have 5, 2 and 0 events with 0, 1 and 2 b-tags

• Backgrounds are very small (< ∼ 2 events)

Fit B(t → W^{+} b) using observed event rates

Class of Events  Observed  Fitted
Lepton + Jets – 0 tags  51.5  53
Lepton + Jets – 1 tags  10.4  10
Lepton + Jets – 2 tags  4.9  5
Dileptons – 0 tags  4.9  5
Dileptons – 1 tags  1.4  2
Dileptons – 2 tags  0.2  0

Fit results are:

R = 1.42{+0.41 \atop −0.39} (lepton + jets )
R = 0.72{+0.66 \atop −0.44} (dileptons )
R = 1.23{+0.38 \atop −0.33} (combined )

• Values > 1 allowed because of background fluctuations

Relating Back to V_{tb}

Find that R > 0.61 at 95% C.L.

• Can relate that to Vtb using average values of – 0.004 ≤ |Vtd| ≤ 0.015 and 0.030 ≤ |Vts| ≤ 0.048

Vtb > 0.78 (95%C.L. ) assuming CKM unitary
Vtb > 0.38 (95%C.L. ) without CKM unitary

• Really saying that |Vtb| ≫ |Vts| or |Vtd|

Bottom Meson Decays at CDF

Hadron collider b experiment has serious S/N problem

• b cross section is of order ∼ 30 μb

• light quark and gluon jet σ ∼ 5 mb

• solution is to trigger on “unique” topologies – require semileptonic decays

– require tag such as J/ψ → μ+ μ− in final state • All CDF studies have been based on these triggers

However, can extract clean samples efficiently

• Will focus on B → J/ψX and B → ψ(2S)X decays

• Now have world’s largest sample

Why are J/ψ and ψ(2S) States Interesting?

Expect decays to result from “internal” diagrams

• Theoretically expected to be very clean

• Strong test of factorisation – Technically considered type 2 decays – Only depend on a2 in BSW model

• Test details of calculations

There has also been some controversy

• Polarisation in B → J/ψK∗(890) decay larger than predicted • Hard to reconcile this with branching fractions

• Few ways out – Measurements are wrong!

– Factorisation only approximate

– Form factors are just wrong

Measurement Technique

The observed cross section (e.g.B^{+} → J/ψK^{+} ) is

σobs = σ(pp̄ → b̄)fuB(B+ → J/ψK+ )ϵK+

There are large uncertainties in σ(pp̄ → b̄)

• Also significant systematic uncertainties in ϵK+

• Strategy is to measure ratios of σobs

R{K∘ \atop K+} = \frac{fd}{fu} \frac{B(B∘ → J/ψK∘)}{B(B+ → J/ψK+ )}

• We also get ratios of fi for “free”

– Have to use independent data or theory

– However, tests “independent” fragmentation ansatzs

Selection of Exclusive B → J/ψX Decays

Search for exclusive decays

B^{+} → J/ψK^{+} ,
B^{∘} → J/ψK^{∘},
B^{+} → J/ψK^{∗}(892)^{+} ,
B^{∘} → J/ψK^{∗}(892)^{0},
B_{s}^{∘} → J/ψϕ(1020)

Select decays by requiring

• Two muon candidates with PT > ∼ 3 GeV/c

• Require muons to come from common vertex

• Search combinatorially for daughter mesons

• Require B candidate PT > 6 or 8 GeV/c

• Require meson daughter PT > 1.5 or 2.0 GeV/c

• Require decay length of B candidate to be > 0

J/ψ Candidates

CDF dimuon trigger upgraded in Run I for J/ψ’s

• Now extends over |η| < ∼ 1.0

• Added steel and chambers to reduce backgrounds ⇒ efficient trigger for J/ψ PT > ∼ 6 GeV/c

Run IA Results

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Ratios of Branching Fractions

R{K∘ \atop K+} = \frac{fd}{fu} \frac{B(B∘ → J/ψK∘)}{B(B+ → J/ψK+ )} = 1.15 ± 0.27 ± 0.09,

R{K∗+ \atop K+} = \frac{B(B+ → J/ψK∗+ )}{B(B+ → J/ψK+ )} = 1.92 ± 0.60 ± 0.17,

R{K∗∘ \atop K+} = \frac{fd}{fu} \frac{B(B∘ → J/ψK∗∘)}{B(B+ → J/ψK+ )} = 1.59 ± 0.33 ± 0.12,

R{Kϕ \atop K+} = \frac{fs}{fu} \frac{B(B∘ s → J/ψϕ)}{B(B+ → J/ψK+ )} = 0.41 ± 0.12 ± 0.04,

R{K∗+ \atop K∘} = \frac{fu}{fd} \frac{B(B+ → J/ψK∗+ )}{B(B∘ → J/ψK∘)} = 1.68 ± 0.58 ± 0.11,
R{K∗∘ \atop K∘} = \frac{B(B∘ → J/ψK∗∘)}{B(B∘ → J/ψK∘)} = 1.39 ± 0.36 ± 0.10, nonumber(1)
R{Kϕ \atop K∘} = \frac{fs}{fd} \frac{B(B∘ s → J/ψϕ)}{B(B∘ → J/ψK∘)} = 0.35 ± 0.12 ± 0.03,
R{K∗∘ \atop K∗+} = \frac{fd}{fu} \frac{B(B∘ → J/ψK∗∘)}{B(B+ → J/ψK∗+ )} = 0.83 ± 0.27 ± 0.07,

R{Kϕ \atop K∗+} = \frac{fs}{fu} \frac{B(B∘ s → J/ψϕ)}{B(B+ → J/ψK∗+ )} = 0.21 ± 0.08 ± 0.02,

R{Kϕ \atop K∗∘} = \frac{fs}{fd} \frac{B(B∘ s → J/ψϕ)}{B(B∘ → J/ψK∗∘)} = 0.26 ± 0.08 ± 0.02,  (2)

Comparison with HQET and BSW

Have compared results with several model predictions

• A. Deandrea, N. Di Bartolomeo, R. Gatto and G. Nardulli, Phys. Lett. B 318, 549 (1993).

• Other calculations give similar results

Fragmentation Fractions

Can extract fragmentation fractions

• Use Deandra et al. model predictions

• Combine measurements from different channels

\frac{fd}{fu} = 0.99 ± 0.19 ± 0.08 and \frac{fs}{(fu, fd)} = 0.34 ± 0.10 ± 0.03.

Can estimate absolute fragmentation fractions

• Assume that fu + fd + fs + fΛb = 1

• Assume that fΛb ∼ 0.115

fu = \frac{1 − fΛb}{1 + \frac{fd}{fu} + \frac{fs}{fu}}

• This gives us

fu = 0.39 ± 0.04 ± 0.04,
fd = 0.38 ± 0.04 ± 0.04 and
fs = 0.13 ± 0.03 ± 0.01.

In good agreement with PDG “LEP” values

• fu : fd : fs = 0.378 ± 0.022 : 0.378 ± 0.022 : 0.112 ± 0.019

ψ(2S) Branching Fractions

Currently working on measuring ratios

\frac{B(B+ → ψ(2S)K+ )}{B(B+ → J/ψK+ )}

\frac{B(B0 → ψ(2S)K∗0)}{B(B0 → J/ψK∗0)}

• Using full Run I data sample

• See clean inclusive ψ(2S) signal ψ(2S) → J/ψπ+ π− and ψ(2S) → μ+ μ−

Run IB B → ψ(2S)X Signals

38

Preliminary Results

The ratios of branching fractions are

\frac{B(B+ → ψ(2S)K+ )}{B(B+ → J/ψK+ )} = 0.666 ± 0.093 ± 0.101
\frac{B(B0 → ψ(2S)K∗0)}{B(B0 → J/ψK∗0)} = 0.569 ± 0.131 ± 0.074

Can turn these into absolute branching fractions using

B(B+ → J/ψK+ ) = (1.02 ± 0.14) × 10−3
B(B0 → J/ψK∗0) = (1.58 ± 0.28) × 10−3

This gives us the branching fractions

B(B+ → ψ(2S)K+ ) = (6.8 ± 1.0 ± 1.4) × 10−4
B(B0 → ψ(2S)K∗0) = (9.0 ± 2.1 ± 2.0) × 10−4

Comparison with Other Measurements

These results can be compared with CLEO results

Now the world’s best measurement

Summary

So far, top decays just like the SM predicts

• Constraints on Vtb > 0.38 at 95% C.L.

• Polarisation studies underway

• Nothing anomolous found

Bottom decay studies really only starting

• Expect to have the most precise B → J/ψ and B → ψ(2S) measurements in next year

• Polarisation studies of entire Run I sample underway

• Will allow tests of HQET and BSW factorisation

Run II expected to start in 1999

• Integrated luminosity of ∼ 2 fb−1

• Upgraded tracking, calorimetry and DAQ

• Will increase top and bottom samples by ×50