Top Quark Mass Measurements at Hadron CollidersG. WATTS (UW/SEATTLE, CPPM)

For the DZERO, CDF, CMS, and ATLAS collaborations

July 15, 2014

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ille2The Top Quark

Just like other Fermions

Except:

𝑚𝑡 40×𝑚𝑏

The next heaviest quark!

The Mass gives the top quark a special role in the Standard Model

• Only fermion which has a significant coupling to the Higgs• Plays key roll in many important physics processes

• Flavor physics, Electro-weak processes• It plays a special roll in a number of Beyond the Standard

Model theories as well

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ille3The Top Mass

We have known almost since it was discovered.

By far the most precisely measured quark mass!

While it behaves like any other quark in the Standard Model, its mass gives it a unique role.

• Only version for which the coupling to the Higgs is important• Stability of the SM Higgs

potential at high scales

A consistency check for the Standard Model!

• Shows up in a number of production loops• at the LHC contains a top loop• Heavy Flavor physics (e.g. )

production

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ille4Top Mass Is A

Precision Measurement

Each measurement deserves at least a

seminar

I have chosen a few extra results

Current World Average: 173.3 GeV.Known to better than 0.5 %!!

Higgs mass is known to better than 0.3%

Top is easier to discover: at TeV

at TeV

No clean easy to see peak l!All final states involve jets

Top is harder to reconstruct:

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Tevatr

on

LHC

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ille6Decays

Dilepton events

Clean, but low statistics~4%

Lepton + Jet events

Good compromiseReasonable background~30%

All Hadronic events

Huge multi-jet background~44%

Top mass has been measured in all decay

channels.

𝑡 𝑡→𝑊+¿𝑏𝑊 −𝑏¿

Classified by the Ws’ decay

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ille7The Tevatron & The LHC

The Tevatron is coming out with its final results

• of data at TeV• Well understood detector• Sophisticated analysis techniques

The LHC is just coming online in the world

• TeV results well developed• 8 TeV results just appearing• Statistics are much better due to the much higher

The much larger statistics will eventually open the door to new measurement techniques.

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ille8Extracting from Data

• Does not always give you 4-vectors (neutrinos!)• Detector/Object resolutions (e.g. Jet Energy Scale)• Background contamination• Incorrect reconstruction (e.g. bad jet assignment)• Top mass width• Etc.

Two common methods to address this:

Matrix ElementUses all the informationComputationally very expensive

Template MethodFlexible, subsets the information used“Fairly easy” to implement

Detector gives you 4-vectors. Use Griffiths!

What do we measure? The Pole mass? The MC mass?

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ille9The Jet Energy Scale

Common curse for all methods

• Experiments normally measure in independent control sample.

• Resolution not good enough for a state-of-the-art top mass measurement.

In situ Jet Energy Scale measurement

𝑊→𝑞𝑞 ′

Two poorly measured

objects

One very well

measured object

Many techniques will constrain to be as part of the global fitting process.

Global fit over the full sample• Scale all jets by a constant

factor to achieve constraint

Lepton+Jets

Flavor Jet Energy Scale

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The Matrix Element ApproachA reverse Monte Carlo

MC Generates

100K events

Distributions of kinematic

variables for all objects

“Map of kinematic

phase space”

Turn that around

Given a single event in data, how dense a part of kinematic phase space is it in?

Repeat for all major backgrounds and signal:

𝑃

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ME – Multiple Steps

ALPGEN + Pythia

Detector Simulation

Reconstruction

4 vectors of reconstructed objects

𝑃 (𝑚𝑡𝑜𝑝 )= 1𝜎𝑜𝑏𝑠

𝑡 𝑡 (𝑚𝑡𝑜𝑝 )∑𝑖=1

24

𝑤 𝑖

Normalization

Sum over all possible jet assignments• Which jet is the first tops?• Which jets belong to the

W?

A weight reflecting the probability of those jet assignments• -tagging

probabilities

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ME – Multiple Steps

ALPGEN + Pythia

Detector Simulation

Reconstruction

4 vectors of reconstructed objects

𝑃 (𝑚𝑡𝑜𝑝 )= 1𝜎𝑜𝑏𝑠

𝑡 𝑡 (𝑚𝑡𝑜𝑝 )∑𝑖=1

24

𝑤 𝑖∫𝑑𝜌 𝑑𝑚12𝑑𝑀1

2 𝑑𝑚22𝑑𝑀 2

2𝑑𝜌 ℓ𝑑𝑞1𝑥𝑑𝑞1

𝑦 𝑑𝑞2𝑥𝑑𝑞2

𝑦

10 dimensional integral over phase space• Mass of the tops, W’s• Directions of the b-quarks• Lepton and neutrino direction

Note no mention of data 4-vectors yet!

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ME – Multiple Steps

ALPGEN + Pythia

Detector Simulation

Reconstruction

4 vectors of reconstructed objects

𝑃 (𝑚𝑡𝑜𝑝 )= 1𝜎𝑜𝑏𝑠

𝑡 𝑡 (𝑚𝑡𝑜𝑝 )∑𝑖=1

24

𝑤 𝑖∫𝑑𝜌 𝑑𝑚12𝑑𝑀1

2 𝑑𝑚22𝑑𝑀 2

2𝑑𝜌 ℓ𝑑𝑞1𝑥𝑑𝑞1

𝑦 𝑑𝑞2𝑥𝑑𝑞2

𝑦

∑𝑝 𝑎𝑟𝑡𝑜𝑛 𝑓𝑙𝑎𝑣𝑜𝑟𝑠 ,𝜈

❑

|𝔐𝑡 𝑡|2

Sum over incoming parton flavorsAll neutrino solutions

The Leading Order Matrix Element• Given all the phase space

parameters• Weight for the kinematics

values• Uses all available

information• At leading order

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ME – Multiple Steps

ALPGEN + Pythia

Detector Simulation

Reconstruction

4 vectors of reconstructed objects

𝑃 (𝑚𝑡𝑜𝑝 )= 1𝜎𝑜𝑏𝑠

𝑡 𝑡 (𝑚𝑡𝑜𝑝 )∑𝑖=1

24

𝑤 𝑖∫𝑑𝜌 𝑑𝑚12𝑑𝑀1

2 𝑑𝑚22𝑑𝑀 2

2𝑑𝜌 ℓ𝑑𝑞1𝑥𝑑𝑞1

𝑦 𝑑𝑞2𝑥𝑑𝑞2

𝑦

∑𝑝 𝑎𝑟𝑡𝑜𝑛 𝑓𝑙𝑎𝑣𝑜𝑟𝑠 ,𝜈

❑

|𝔐𝑡 𝑡|2 𝑓 ′ (𝑞1 ) 𝑓 ′ (𝑞2 )

√ (𝜂𝛼𝛽𝑞1𝛼𝑞2

𝛽 )2−𝑚𝑞 1

2 𝑚𝑞 2

2Φ6

PDF’s

Phase Space FactorTransverse

momenta of incoming partons

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ME – Multiple Steps

ALPGEN + Pythia

Detector Simulation

Reconstruction

4 vectors of reconstructed objects

𝑃 (𝑚𝑡𝑜𝑝 )= 1𝜎𝑜𝑏𝑠

𝑡 𝑡 (𝑚𝑡𝑜𝑝 )∑𝑖=1

24

𝑤 𝑖∫𝑑𝜌 𝑑𝑚12𝑑𝑀1

2 𝑑𝑚22𝑑𝑀 2

2𝑑𝜌 ℓ𝑑𝑞1𝑥𝑑𝑞1

𝑦 𝑑𝑞2𝑥𝑑𝑞2

𝑦

∑𝑝 𝑎𝑟𝑡𝑜𝑛 𝑓𝑙𝑎𝑣𝑜𝑟𝑠 ,𝜈

❑

|𝔐𝑡 𝑡|2 𝑓 ′ (𝑞1 ) 𝑓 ′ (𝑞2 )

√ (𝜂𝛼𝛽𝑞1𝛼𝑞2

𝛽 )2−𝑚𝑞 1

2 𝑚𝑞 2

2Φ6𝑊 (𝑥 , 𝑦 ;𝜌 , 𝜌 ℓ ,…)

Transfer Functions• Given a generated jet with what is the probability DZERO

will reconstruct values x and y?• Detector and reconstruction resolution

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DZERO using the ME Method

In used at DZERO since Run I

GeV3.6

GeV

Total error is equivalent to March world average!

3 years of work (old result):

• Use different top mass in the Matrix Elements

• Vary the Jet Energy Scale in the transfer functions

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What Did 3 years get?• Speed (CPU) to allow better MC stats

• X100 increase means MC stats error drops from ~0.25 GeV to ~0.05 GeV.

• New Jet Energy Scale Calibrations• ISR modeling

• Constrain by studies in Drell-Yan data

• General modeling improvements

The variable is sensitive to Z boson recoil ().

Gives an experimental bound to ISR mis-modeling

Systematic error on reduced from ~0.25 to 0.06 GeV

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Template MethodUsing a distribution sensitive to :

Simulated sample at GeV

Simulated sample at GeV

Simulated sample at GeV

Use a likelihood to estimate template

compatibility

Make it for each sample

𝑚𝑡

Can do in two dimension• Jet energy scale• Top mass

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Top Mass In Dilepton Events

4% of all decays, split into , and .

Very little SM background!

CDF’s basic selection: Observe 520 events, expect 78% purityATLAS’ basic selection: Observe 2913, expect 96% purity

Really excellent top lab

Except…

For 2 !!!There are no 4-vectors for the two!!

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Template Method

Need distributions that are strongly correlated

with the top mass

Template method to figure out the top mass

ATLAS

The average in the eventTwo permutations (take smallest)Avoid the missing resolution

Good separatio

n power

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CDF Template VariablesFully reconstruct the top mass

Problem: detector measures missing

There are not enough constraints to solve for solution!

The weighting method𝜙1

𝜙2

Grid in the azimuthal angles

• Fit for the top mass at each grid location.

• Resulting is the template variable.• Weight by fit .

The fit includes terms for:• All the measurements (2 leptons, two jets, missing )• Top mass and the (constrained) W mass

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Statistics Isn’t The Problem… Broad peak, but decent

separation power.

Leading systematic:Jet Energy Scale!

This measurement is statistics limited.Can something be done?

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Statistics Isn’t The Problem… Broad peak, but decent

separation power.

Leading systematic:Jet Energy Scale!

This measurement is statistics limited.Can something be done?

CDF creates a second template variable:

GeV • Depends on 4-vector of leptons• Direction of jets• No Jet Energy Scale, no Missing

And combines the two, optimizing for minimal error

𝑀 𝑡𝑓𝑖𝑡=𝑤 ∙𝑚𝑡

𝑓𝑖𝑡+ (1−𝑤 ) ∙𝑚𝑡𝑎𝑙𝑡

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Dilepton Top Mass ResultsStandard Template MethodJet Energy Scale isn’t fit: not enough constraints

Statistics already making a big difference here

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Top Mass in All Hadronic Decays (CDF & CMS)

44% of all decays. Largest single decay class.

Overwhelmed by SM QCD background!

6 Jets

After CMS requires 6 jets

4 jets with GeV5th with GeV6th with GeV

Estimated signal purity is 3%Signal Efficiency is 3.5%!

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Improving the Purity

Unique Handles:

2 -jets

2

Look for -tagged jets

Perform kinematic fit:• Know • The two are the same2

(CDF)

Mass of the pairs of light quark jets

is the well measured value of 80.4 GeV

Mass of the pairs of light quark jets

free parameters

Every jet permutation is triedMinimum is kept

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Improving the Purity

1. Requiring the fit to converge2. Very basic cuts on the

Raise CMS’s purity to 39%

Additional kinematic selection

CMS: CDF: Neural Network

Raise CMS’s purity to 54%CDF has a purity of 57%

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Extracting the Mass

𝑚𝑡𝑟𝑒𝑐𝑜 𝑚𝑡

❑

The Template Method

Fit for both Jet Energy Scale and

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Lepton + Jets From CMSFull TeV result:

Analysis is very similar to the All-Jets analysis from CMS

Initial selection is > 100K events and 94% pure

QCD background is negligible!

A simple kinematic fit to clean up incorrect jet assignments

• Each possible jet assignment gives • Each is weighted by the fit probability

Largest systematic error is the flavor dependent Jet Energy Scale (0.41 GeV)

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Conclusions

Field is still rapidly evolving

World average submitted in March

CDF dilptons and all-hadronic

DZERO matrix element

CMS all-hadronic and lepton+jets

What is next?

Tevatron will finish putting out “final” mass measurements

LHC’s statistics and purity mean it should quickly surpass the Tevatron.

LHC Run 2 projections

Other measurements with the

quark mass

Top and anti-top have consistent masses

measurements that can clarify which mass we measure.

Becoming like the W mass…

If you believe BICEP2

!

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Awaiting the next world Combination…

Current World Combination

Tevatron Combination

CMS Combination

±0.95 ±0.76 ±0.64

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Systematic Errors

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ille33ATLAS Lepton+Jets Template

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ille34ATLAS dilepton 7 TeV CDF dilepton

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CDF all jets CMS all jets

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CMS All Jets 7 TeV

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Tevatron Combination

DZERO Lepton+Jets ME