The Role of Calorimetry in Top Physics

Pekka Sinervo University of Toronto

Overview

• The Standard Model Top Quark

• Detecting and Reconstructing Top

• Intrinsic Limitations – Top mass and p_{T}

• Limitations and Expected Improvements

Work done in collaboration with Pierre Savard and Andrew Robinson

Standard Model Top Quark Phenomenology

Produced in collider environment

• Produced through annihilation ff̄ → tt̄

• In pp̄ collisions at √s = 1.8 TeV, σ ∼ 5 pb

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 doesn’t have time to form

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

• Decay dominated by “longitudinal W^{+} ”

Reconstructing Top

Since top is pair-produced and β decays

• Expect to see 6 final state particles

• tt̄ → lν_{l}+ jets (24/81 for l = e^{−}/μ^{−})

• tt̄ → lν_{l}l′ν_{l′} (2/81 for l = e^{−}/μ^{−})

• tt̄ → n jets (36/81)

Backgrounds are large:

• Fake lepton candidates from QCD multijet events • W + jets production ⇒ Controlled by requiring ≥ 1 b-tagged jet

Effect of b-Tagging

Require b-tag in W + ≥ 3 jet sample

• Expect S/B ∼ 7

Identifying Top Decays in pp̄ Collisions

In order to identify lepton + jets 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

Today’s Technology

Both CDF and D0 / detector employ 1980’s calorimetry

• CDF has a Pb-scintillator/Fe-scintillator sandwich – For |η| > 1.2, employs PWC wire/pad readout – σ_{E} ∼ 0.15√E for EM

– σ_{E} ∼ 1.1√E for jets

• D0 / has a more uniform U-liquid Ar calorimeter – σ_{E} ∼ 0.07√E + 0.016E_{0}.66 for EM

– σ_{E} ∼ 1.15√E for jets

Calorimetry extends to |η| ∼ 4

• Region |η| < ∼ 2.5 most important for top

• Missing E_{T} calculated over region |η| < 3.6

Will be using CDF as example in this talk

• b-tagging is more effective

• Has most complete set of top kinematic results

CDF Run I Detector

• Pb/Fe-scintillator for |η| < 1.1 • Pb/Fe-PWC for 1.1 < |η| < 4.2

Calorimetry in HEP, 15 Jun 1999

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)

These are purest samples for top quark measurements

What are the Interesting Top Properties?

• Top Quark Production Cross Section – Discovery technique

– Predicted by QCD with less uncertainties than σ_{b} – Look for single top production

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

– Important consistency check of theory

• Top Quark Production and Decay Kinematics – p_{T} distribution sensitive to “new” physics

– SM expects decay to be polarized

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

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

Role of Calorimetry in Top Physics

Calorimetry plays crucial role in top quark studies

• Lepton identification – Principle tool for electron ID

• Neutrino detection – Use technique of “missing transverse energy”

• Quark → jet reconstruction – Need to reconstruct b quark jets for tagging – Have to efficiently reconstruct W → qq̄′

• Energy flow in event – Have to understand recoil system

Charged Lepton ID

Electron ID places stringent criteria

• E_{T} measurement

• Shower shape discrimination (lateral and longitudinal)

• Charged track ↔ cluster match

• Can achieve efficiencies ∼ 85% – Rejection of ∼ 10^{3} for QCD-induced backgrounds

Criteria on calorimetry fairly stringent

• Fine tower segmentation - Δη × Δϕ < ∼ 0.1 × 0.05 – Finer transverse segmentation for shower shape – Longitudinal segmentation necessary

∗ > ∼ 2 samples

• Good resolution for energy - charged track matching – typically σ_{E} ∼ 0.1 − 0.15√E is sufficient

Used for muon ID

• Look for minimum-ionizing tracks

Calorimetry in HEP, 15 Jun 1999

Neutrino Identification

Use standard definition of “missing E_{T} ”

E̸_{T} = − ∑ E_{i}n̂_{i}
= p⃗_{T}^{ν}
= − ∑_{i=1}^{n_{l}} p⃗_{T}^{l} − ∑_{i=1}^{n_{j}} p⃗_{T}^{j} − X⃗ − U⃗E

• Non-linear calorimetry response for jets • Fluctuations in underlying event(s) (UE)

• Response to recoil system (X)

• Cracks and holes in detector

Calorimeter Response to Jets

Jets are messy objects

• High-energy parton fragments and hadronizes – “Core” of jet contains most energy

– Calorimetry non-linearities, e/h, ....

• Have to use “clustering” algorithm – Use narrow cone R ≡ √(Δη)^{2} + (Δϕ)^{2} = 0.4 – Fluctuations due to “out-of-cone” losses

– Overlapping showers

• Fluctuations coming from UE contributions – Mean is ∼ 1GeV per steradian

Lots of extra (and missing) jets

Jets Data tt̄ MC
3  35%  33%
4  50%  50%
5  11%  14%
> 5  0%  2.5%

Jet Systematics

Can measure the response in situ

• Systematics are complex mix of effects • Use dijet-balancing, Z+ jet events and MC

Putting tt̄ Event Together

First correct for jet response

• Correct E̸_{T} using known jet corrections

E̸_{T}^{(cor)} = − ∑_{i=1}^{n_{l}} p⃗_{T}^{l} − ∑_{i=1}^{n_{j}} p⃗_{T}^{j}^{(cor)} − X^{(cor)}

Put events together in following way

• Choose 4 leading jets

• Identify any b-jets

• Fit kinematics (masses equal, W boson mass constraint)

• Select parton-jet assignment with smallest χ^{2} – This works about 40% of the time

Overall works reasonably well for single-tagged events

Calorimetry in HEP, 15 Jun 1999

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

• Run I statistics limit systematic uncertainty

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)

Calorimetry in HEP, 15 Jun 1999 Calorimetry in HEP, 15 Jun 1999

Top Quark p_{T} Distribution

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

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

• p_{T} of tt̄ system expected to be low

Statistics limit any measurement

• Use data to set confidence limits on \frac{dσ_{t}}{dp_{T}}

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

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

• In principle can measure p_{T} (tt̄) system

• Simply no resolution to do so with statistics

p_{T} Response Functions

Measured p_{T} smearing using MC/detector simulation

• Use HERWIG MC and full detector model

• Most smearing arises from incorrect jet assignments

• Blame it mostly on “stupid” algorithm Calorimetry in HEP, 15 Jun 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 Calorimetry in HEP, 15 Jun 1999

Resulting Fitted p_{T} Distribution

Perform likelihood fit to response functions and bkg shape

• 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 ∼ 35% with p_{T}

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}

Magnitude of Systematic Uncertainties in p_{T}

Used combination of MC and data to estimate systematic uncertainties

• Largest relates to how well we “unfold” data – Assume standard model distribution within bin

– “Bootstrap” removes most of the bias

• Worst case δR_{i} is ∼ 0.06

• Uncertainties are dominated by small sample size

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}

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)

Limitations from Calorimetry

Have “stepped back” and considered limitations

1. Have difficulty reconstructing jet “objects”

2. Not able to properly reconstruct events

3. Intrinsic calorimeter resolution plays little role

Can demonstrate using “standard” CDF simulation

• Reconstruct and identify correct partons

• Vary calorimeter response – Back-of-the-envelope implies σ_{M} ∼ 6 − 8 GeV/c^{2} – Reality is σ_{M} ∼ 25 − 30 GeV/c^{2}

Effects on Top Mass

Have investigated source of these resolution effects

• “Hard gluon radiation” plays pivotal role – Also create dominate systematic uncertainty

• Getting parton-jet assignments right next

• Intrinsic calorimeter resolution comes third

Mass Resolution of Double Tagged Events

Calorimetry in HEP, 15 Jun 1999

Contributions to p_{T} Resolution

Top quark p_{T} resolution insensitive to intrinsic response

Jet resolution dominated by “hard” gluon radiation/hadronization

• Can get p_{T} RMS to 7 GeV/c when turned off

• Increases rate of “correct” combinations by ∼ 50%

Summary of Kinematic Limitations

Gains have to come from improved jet/event reconstruction

• Tagging both b-jets makes significant difference – Loose 40 − 50% of data

– OK if lots of events to begin with

• Improvements in jet algorithms

– R = 0.4 fixed cone algorithm not perfect ∗ Need sophisticated “pattern recognition”

∗ Reduce out-of-cone corrections

∗ Reduce UE contribution?

– Hard to make big improvements

• Use improved resolution to enhance kinematic constraints

– Makes χ^{2} technique more effective at selecting right combination

– Allows one to sort out 5 and 6-jet combinations

Expected Improvements for Run II

For Run II at Tevatron

• Will have the same fundamental calorimetry • Advantage will be in larger statistics

– Biggest gain will come from improving reconstruction algorithm

Also can control systematics better

• Systematics in M_{top} limited by gluon radiation • Calorimetery response will continue to challenge

– Use W → qq̄′ shape

Most favourable estimates give

• Jet-parton energy scales 1 − 2 GeV

• Event modelling 1 GeV

Top at the Large Hadron Collider

Top physics at the LHC looks a lot easier

• Trick is that the σL is ×10^{4} − 10^{5}

• Can now literally throw away tt̄ events – Concentrate on events with high top p_{T}

– Avoid combinatorial problems

– High E_{T} jets that are more collimated

Have essentially the same problems

• Limited by large jet multiplicities

• Effects of overlapping jets, UE events

Summary

Calorimetry plays crucial role in top quark physics

• Charged lepton ID

• Neutrino measurement

• Jet reconstruction

Biggest effects have to do with sorting out the physics

• Real gains will come from using data more intelligently – Improve jet clustering algorithms

– Deal with combinatorial problems more effectively – Employ b-tagging more creatively

• Better intrinsic resolution helps (but slowly)

Certainly much to do for Run II

• Expect ×50 more data

• Much opportunity to optimize