DETECTOR . James Robinson 1 1 DESY Introduction ATLAS has measured - - PowerPoint PPT Presentation

SLIDE 1

STUDIES OF THE UNDERLYING EVENT AND PARTICLE PRODUCTION WITH THE ATLAS DETECTOR.

James Robinson1

• n behalf of the ATLAS Collaboration

1DESY

MPI@LHC 2015, 23nd November 2015

SLIDE 2

Introduction

ATLAS has measured particle production and the underlying event > using various different hard processes > at several centre-of-mass energies Too much to discuss in full, so I will show only most recent results: 13 TeV! Detector-level underlying event distributions

ATL-PHYS-PUB-2015-019

Underlying event in jet events

EPJC 74 (2014) 2965

Underlying event in inclusive Z-boson production

EPJC 74 (2014) 3195

Dijet production with large rapidity gaps

accepted by PLB

Exclusive dilepton production

PLB 749 (2015) 242-61

Transverse polarisation of Λ and ¯ Λ hyperons

PRD 91 (2015) 032004 J.E.M. Robinson | Underlying event and particle production | 23/11/15 | Page 1/23

SLIDE 3

Underlying event

SLIDE 4

What is the underlying event?

Any hadronic activity not associated with hard scattering process > Unavoidable background to collision events > Non-perturbative effects dominate → not well-predicted Typically modelled with > Multiple parton interactions > Initial/final-state radiation > Colour reconnection with beam remnants Impossible to unambiguously assign particles to hard scatter or UE > Measurements must not be dependent on details of model used

J.E.M. Robinson | Underlying event | 23/11/15 | Page 2/23

SLIDE 5

Underlying event topology

> Identify a “hard scatter” using a reference object (eg. jet/Z/track) > Define azimuthal regions with respect to this leading object > Toward and transverse regions most sensitive to the underlying event > High pT recoil important in away region → perturbative QCD > Transverse region can be further divided into trans-max and trans-min depending on the amount

• f activity

J.E.M. Robinson | Underlying event | 23/11/15 | Page 3/23

SLIDE 6

Underlying event observables

Reconstruct kinematics: calorimeter deposits and charged tracks

Densities and averages

> Average pT of charged particles: ⟨pT⟩ > Number density of charged particles: Nch/δηδϕ > pT density of charged particles: ∑ pT/δηδϕ > ET density of all particles: ∑ ET/δηδϕ

Particle spectra

> Charged particle pT spectrum > Charged particle multiplicity spectrum

J.E.M. Robinson | Underlying event | 23/11/15 | Page 4/23

SLIDE 7

Underlying event in 7 TeV jet events

EPJC 74 (2014) 2965

≥ 1 jet Exactly 2 jets

> [GeV] φ δ η δ /

T

p

∑

<

1 2 3 4 5

Data 2010 - trans-max Pythia6 Perugia 2011 - trans-max Data 2010 - trans-min Pythia6 Perugia 2011 - trans-min Data 2010 - trans-diff Pythia6 Perugia 2011 - trans-diff

Inclusive jet ATLAS

= 7 TeV s ,

• 1

= 37 pb

int

L

[GeV]

T lead

p 20 30 40 100 200 300

MC/Data

0.8 0.9 1 1.1 1.2

> [GeV] φ δ η δ /

T

p

∑

<

0.5 1 1.5 2 2.5

Data 2010 - trans-max Pythia6 Perugia 2011 - trans-max Data 2010 - trans-min Pythia6 Perugia 2011 - trans-min Data 2010 - trans-diff Pythia6 Perugia 2011 - trans-diff

Exclusive dijet ATLAS

= 7 TeV s ,

• 1

= 37 pb

int

L

[GeV]

T lead

p 20 30 40 100 200 300

MC/Data

0.8 0.9 1 1.1 1.2

> Trans-min flat (at hard enough scales) → treat UE activity as constant > Increasing activity for trans-max → pQCD > Colour connection to jet? > Both trans-max and trans-min regions flat in pT > Veto on extra hard activity lessens sensitivity to pQCD

J.E.M. Robinson | Underlying event | 23/11/15 | Page 5/23

SLIDE 8

Underlying event in 7 TeV jet events

EPJC 74 (2014) 2965

Inclusive jet selection Exclusive dijet selection

> [GeV] φ δ η δ /

T cent ch+neut

E

∑

<

2 3 4 5 6

Data 2010 Pythia8 AU2 CT10 Pythia6 Perugia 2011 Pythia6 DW Herwig++ UE7-2 MRST LO** Herwig + Jimmy AUET2 LO** Alpgen + Herwig + Jimmy AUET1 Powheg + Pythia6 Perugia 2011

| < 2.5

ch,neut

η > 500(200) MeV, |

ch(neut)

p

Transverse region Inclusive jet ATLAS

= 7 TeV s ,

• 1

= 37 pb

int

L

[GeV]

T lead

p 20 30 40 100 200 300

MC/Data

0.8 0.9 1 1.1 1.2

> [GeV] φ δ η δ /

T cent ch+neut

E

∑

<

1.5 2 2.5 3 3.5 4

Data 2010 Pythia8 AU2 CT10 Pythia6 Perugia 2011 Pythia6 DW Herwig++ UE7-2 MRST LO** Herwig + Jimmy AUET2 LO** Alpgen + Herwig + Jimmy AUET1 Powheg + Pythia6 Perugia 2011

| < 2.5

ch,neut

η > 500(200) MeV, |

ch(neut)

p

Transverse region Exclusive dijet ATLAS

= 7 TeV s ,

• 1

= 37 pb

int

L

[GeV]

T lead

p 20 30 40 100 200 300

MC/Data

0.8 0.9 1 1.1 1.2

> Similar distributions for ∑ ET from calorimeter clusters > Compare to different Monte Carlo models and tunes > Best agreement given by PYTHIA 6 with Perugia 2011 tune

J.E.M. Robinson | Underlying event | 23/11/15 | Page 6/23

SLIDE 9

Underlying event in 7 TeV Drell-Yan events

EPJC 74 (2014) 3195

[GeV]

Z T

p

20 40 60 80 100 120 140 160 180 200

MC/Data

0.85 0.9 0.95 1 1.05 1.1 1.150

20 40 60 80 100 120 140 160 180 200

> φ δ η δ /

ch

<N

0.6 0.7 0.8 0.9 1 1.1 1.2 Toward region

• 1

= 7 TeV, 4.6 fb s ATLAS

Data Pythia8 AU2 Powheg+Pythia8 AU2 Sherpa Pythia6 Perugia2011C Herwig++ UE-EE-3 Alpgen+Herwig+Jimmy AUET2

[GeV]

Z T

p

20 40 60 80 100 120 140 160 180 200

MC/Data

0.85 0.9 0.95 1 1.05 1.1 1.150

20 40 60 80 100 120 140 160 180 200

> φ δ η δ /

ch

<N

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Transverse region

• 1

= 7 TeV, 4.6 fb s ATLAS

Data Pythia8 AU2 Powheg+Pythia8 AU2 Sherpa Pythia6 Perugia2011C Herwig++ UE-EE-3 Alpgen+Herwig+Jimmy AUET2

[GeV]

Z T

p

20 40 60 80 100 120 140 160 180 200

MC/Data

0.85 0.9 0.95 1 1.05 1.1 1.150

20 40 60 80 100 120 140 160 180 200

> φ δ η δ /

ch

<N

1 1.5 2 2.5 3 Away region

• 1

= 7 TeV, 4.6 fb s ATLAS

Data Pythia8 AU2 Powheg+Pythia8 AU2 Sherpa Pythia6 Perugia2011C Herwig++ UE-EE-3 Alpgen+Herwig+Jimmy AUET2

> Measurement of toward UE! > Tune non-perturbative models with low pT region > Away region dominated by Z+j > Toward and transverse regions sensitive to higher Njets

J.E.M. Robinson | Underlying event | 23/11/15 | Page 7/23

SLIDE 10

Particle pT and multiplicity

EPJC 74 (2014) 3195

0.5 1 1.5 2 2.5 3 3.5

φ δ η δ /

ch

dN dN N 1

• 4

10

• 3

10

• 2

10

• 1

10 1

Data 2010 Pythia8 AU2 CT10 Pythia6 Perugia 2011 Pythia6 DW Herwig++ UE7-2 MRST LO** Herwig + Jimmy AUET2 LO** Alpgen + Herwig + Jimmy AUET1 Powheg + Pythia6 Perugia 2011

Transverse region Inclusive jet ATLAS

= 7 TeV s ,

• 1

= 37 pb

int

L

φ δ η δ /

ch

N 0.5 1 1.5 2 2.5 3 3.5

MC/Data

0.6 0.8 1 1.2 1.4

Jet selection

[GeV] φ δ η δ /

T

p ∑

• 1

10 1 10

MC/Data

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

φ δ η δ /

T

p ∑ d

ev

dN

ev

N 1

• 4

10

• 3

10

• 2

10

• 1

10 1

< 50 GeV

Z T

20 GeV < p Dressed Leptons

• 1

= 7 TeV, 4.6 fb s ATLAS Trans-min region Data Pythia8 AU2 Sherpa Pythia6 Perugia2011C Powheg+Pythia8 AU2 Herwig++ UE-EE-3 Alpgen+Herwig+Jimmy AUET2

Z-boson selection

> Double differential charged particle multiplicity and pT spectra > Provide further discrimination between Monte Carlo models > Current models do not describe these observables well

J.E.M. Robinson | Underlying event | 23/11/15 | Page 8/23

SLIDE 11

Universality of MPI model

EPJC 74 (2014) 3195

> Compare UE measurements with different hard scatters > Qualitative test of MPI universality in different hard processes

[GeV]

leadjet T

• r p

leadtrack T

• r p

Z T

p

50 100 150 200 250 300 350 400 450 500

> φ δ η δ /

ch

<N

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

)

• 1

Data 2011: Z events (4.6 fb )

• 1

, 37 pb

• 1

µ Data 2010: Minimum bias and jet events (168 = 7 TeV s

ATLAS

Transverse region Minimum bias events Jet events Z events

[GeV]

T

p 5 10 15 20 25 30 35 40 45 50 > φ δ η δ /

ch

<N 0.2 0.4 0.6 0.8 1 1.2

φ δ η δ /

ch

N

1 2 3 4 5 6 φ δ η δ /

ch

dN

ev

dN

ev

N 1

• 4

10

• 3

10

• 2

10

• 1

10 1 10

)

• 1

Data 2011: Z events (4.6 fb )

• 1

Data 2010: Jet events (137 pb

= 7 TeV s

ATLAS

< 60 GeV

Z, leadjet T

20 GeV < p Trans-min region

Z events Jet events

> Good agreement between jet and Z-boson measurements → especially for trans-min (most sensitive to MPI) > How well does the MPI model extrapolate to higher energies?…

J.E.M. Robinson | Underlying event | 23/11/15 | Page 9/23

SLIDE 12

Leading track underlying event at 13 TeV

ATL-PHYS-PUB-2015-019

5 10 15 20 25 30

> [GeV] φ d η /d

T

p Σ

2

<d

1 2 3 4 5 6 7

Preliminary ATLAS = 13 TeV s Toward region |< 2.5 η > 0.5 GeV, |

T

p > 1 GeV

lead T

p

DATA (uncorrected) EPOS PYTHIA 8 A14 PYTHIA 8 A2 HERWIG++ EE5 PYTHIA 8 Monash

[GeV]

lead T

p

5 10 15 20 25 30

MC/Data

0.7 0.8 0.9 1 1.1 1.2 1.3 5 10 15 20 25 30

> φ d η /d

ch

N

2

<d

0.5 1 1.5 2 2.5

Preliminary ATLAS = 13 TeV s Toward region |< 2.5 η > 0.5 GeV, |

T

p > 1 GeV

lead T

p

DATA (uncorrected) EPOS PYTHIA 8 A14 PYTHIA 8 A2 HERWIG++ EE5 PYTHIA 8 Monash

[GeV]

lead T

p

5 10 15 20 25 30

MC/Data

0.7 0.8 0.9 1 1.1 1.2 1.3

> Detector-level only (preliminary result) > Good agreement with data in toward region

J.E.M. Robinson | Underlying event | 23/11/15 | Page 10/23

SLIDE 13

Leading track underlying event at 13 TeV

ATL-PHYS-PUB-2015-019

5 10 15 20 25 30

> [GeV] φ d η /d

T

p Σ

2

<d

0.5 1 1.5 2 2.5

Preliminary ATLAS = 13 TeV s Transverse region |< 2.5 η > 0.5 GeV, |

T

p > 1 GeV

lead T

p

DATA (uncorrected) EPOS PYTHIA 8 A14 PYTHIA 8 A2 HERWIG++ EE5 PYTHIA 8 Monash

[GeV]

lead T

p

5 10 15 20 25 30

MC/Data

0.7 0.8 0.9 1 1.1 1.2 1.3 5 10 15 20 25 30

> φ d η /d

ch

N

2

<d

0.5 1 1.5 2 2.5

Preliminary ATLAS = 13 TeV s Transverse region |< 2.5 η > 0.5 GeV, |

T

p > 1 GeV

lead T

p

DATA (uncorrected) EPOS PYTHIA 8 A14 PYTHIA 8 A2 HERWIG++ EE5 PYTHIA 8 Monash

[GeV]

lead T

p

5 10 15 20 25 30

MC/Data

0.7 0.8 0.9 1 1.1 1.2 1.3

> Greater discriminating power in transverse region > Still only minor discrepancies from the data → MPI energy extrapolation working well

J.E.M. Robinson | Underlying event | 23/11/15 | Page 11/23

SLIDE 14

Particle Production

SLIDE 15

Dijet production with rapidity gaps

arXiv:1511.00502

[nb]

F

η ∆ / d σ d 1 10

2

10

3

10

4

10

5

10

6

10

7

10

• 1

= 7 TeV, L = 6.8 nb s Data Total exp. uncertainty PYTHIA 8 SD, D-L PYTHIA 8 SD+DD, D-L PYTHIA 8 ND+SD+DD, D-L

ATLAS

R = 0.6

t

Anti-k > 20 GeV

T

p

F

η ∆ 1 2 3 4 5 6 MC/Data 0.5 1 1.5 2

> Use tracks and calorimeter deposits to identify activity > Rapidity gap is largest empty η span from detector edge > Decomposition into diffractive components > Non-negligible contribution from ND even at large ∆ηF

J.E.M. Robinson | Particle Production | 23/11/15 | Page 12/23

SLIDE 16

Cross sections as a function of diffractive mass

arXiv:1511.00502

ξ ∼

10

log 3.2 − 3 − 2.8 − 2.6 − 2.4 − 2.2 − 2 − [nb] ξ ∼

10

/ d log σ d 100 200 300 400 500 600 700

• 1

= 7 TeV, L = 6.8 nb s Data Total exp. uncertainty PYTHIA 8 ND POWHEG ND + PYTHIA 8 PYTHIA 8 DD D-L POMWIG ATLAS R = 0.6

t

Anti-k > 2

F

η ∆

> Consider ξ = M2

X/s

> In region ∆ηF > 2 > ND contribution from PYTHIA or POWHEG+PYTHIA 8 not enough > PYTHIA 8 DD contribution also falls short of the data > POMWIG SD-only overshoots → need gap survival factor

J.E.M. Robinson | Particle Production | 23/11/15 | Page 13/23

SLIDE 17

Scaling by gap survival probability

arXiv:1511.00502

ξ ∼

10

log 3.2 − 3 − 2.8 − 2.6 − 2.4 − 2.2 − 2 − [nb] ξ ∼

10

/ d log σ d 50 100 150 200 250 300 350

• 1

= 7 TeV, L = 6.8 nb s Data Total exp. uncertainty =16%)

2

model (S

2

POMWIG S PYTHIA 8 SD+DD+ND D-L PYTHIA 8 SD+DD+ND S-S PYTHIA 8 SD+DD+ND MBR ATLAS R = 0.6

t

Anti-k > 2

F

η ∆

> Scale POMWIG to lowest log ξ bin → S2 = 16% > PYTHIA 8 for three different Pomeron flux choices → compatible without needing gap survival factor

J.E.M. Robinson | Particle Production | 23/11/15 | Page 14/23

SLIDE 18

Exclusive γγ → ll production

PLB 749 (2015) 242-61 p p p p p p p p p ' X X ℓ+ ℓ− ℓ+ ℓ− ℓ+ ℓ− γ γ γ γ γ γ X ' ''

Dimuon vertex isolation distance [mm] 5 10 15 20 25 30 35 40 45 50 Events / mm 10

2

10

3

10

4

10 ATLAS

• 1

= 7 TeV, 4.6 fb s

Data 2011

• µ

+

µ → * γ Z/

• µ

+

µ → γ γ Double-diss.

• µ

+

µ → γ γ Single-diss.

• µ

+

µ → γ γ Exclusive

+ 2 tracks associated with di-muon vertex 5 10 15 20 25 30 35 40 45 50 Data / MC 0.6 0.8 1 1.2 1.4 Baseline selection [mm]

iso vtx

z ∆

> Large backgrounds dominate > Complex selection to extract signal > Irreducible SD and DD contributions important

J.E.M. Robinson | Particle Production | 23/11/15 | Page 15/23

SLIDE 19

Extracting single-diffractive fraction

PLB 749 (2015) 242-61

π |/

• e

+

e

φ ∆ 1-| 0.01 0.02 0.03 0.04 0.05 0.06 Events / 0.002 50 100 150 200 250 300 350 ATLAS

• 1

= 7 TeV, 4.6 fb s

Data 2011

• e

+

e → γ γ Exclusive

• e

+

e → γ γ Single-diss.

• e

+

e → γ γ Double-diss.

• e

+

e → * γ Z/

> Agreement with world average > For e+e− and µ+µ− channels > Fit acoplanarity distributions > Subtract DD and Drell-Yan backgrounds > Template fit allows extraction

• f SD fraction

Exclusive fraction 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Single-dissociative fraction 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 68% C.L. 95% C.L. Theory ATLAS

• 1

= 7 TeV, 4.6 fb s acoplanarity fit

• e

+

e → γ γ

J.E.M. Robinson | Particle Production | 23/11/15 | Page 16/23

SLIDE 20

Equivalent Photon Approximation

PLB 749 (2015) 242-61 nominal EPA

σ / σ 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 = 7 TeV s ATLAS

• 1

, 40 pb

• µ

+

µ → γ γ CMS | < 2.1)

µ

η > 4 GeV, |

µ T

> 11.5 GeV, p

• µ

+

µ

(m

• 1

, 4.6 fb

• e

+

e → γ γ ATLAS | < 2.4)

e

η > 12 GeV, |

e T

> 24 GeV, p

• e

+

e

(m

• 1

, 4.6 fb

• µ

+

µ → γ γ ATLAS | < 2.4)

µ

η > 10 GeV, |

µ T

> 20 GeV, p

• µ

+

µ

(m

nominal EPA

σ /

meas.

σ

• stat. uncertainty
• syst. uncertainty

⊕ stat.

nominal EPA

σ /

corr. EPA

σ

nominal EPA

σ /

EPA

σ

• theo. uncertainty

=

nominal EPA

σ 4.07 pb =

nominal EPA

σ 0.496 pb =

nominal EPA

σ 0.794 pb

> Corrected for interactions between elastically scattered protons

J.E.M. Robinson | Particle Production | 23/11/15 | Page 17/23

SLIDE 21

Transverse polarization of Λ and ¯ Λ hyperons

PRD 91 (2015) 032004

> Λ hyperon: spin ½ particle > Polarisation, P, defined as: P = N+½ − N−½ N+½ + N−½ Λ → pπ− and ¯ Λ → ¯ pπ+ decays > Angular distribution given by: w(cos θ∗) = 1

2 (1 + αP cos θ∗)

> α = 0.642 ± 0.013 (parity-violating

decay asymmetry) is well-known

No theoretical model exists!

p p

Λ

n n

p π

• Λ

0 rest frame production plane θ*

> polarization measured normal to production plane: > as function of pT and xF = pz/pbeam > in region xF < 0.0025

J.E.M. Robinson | Particle Production | 23/11/15 | Page 18/23

SLIDE 22

Signal extraction

PRD 91 (2015) 032004

> Kinematic cuts to reduce background > Signal from long-lived two-prong decays

Candidates / 1.17 MeV 10000 20000 30000 40000 50000 60000 70000 80000

• 1

b µ = 760 L = 7 TeV s

• π

p → Λ ATLAS Data Fit Signal Background Signal region [MeV]

π p

m 1100 1105 1110 1115 1120 1125 1130 1135 Data/Fit 0.95 1 1.05

[MeV]

π p

m 1100 1105 1110 1115 1120 1125 1130 1135

i sig

f Signal fractions 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

• π

p → Λ

+

π p → Λ

• 1

b µ = 760 L = 7 TeV s ATLAS

> Divide invariant mass range into signal region and sidebands > Multi-parameter fit to Λ candidate distribution → allows extraction of signal fractions, fsig

i

in each region

J.E.M. Robinson | Particle Production | 23/11/15 | Page 19/23

SLIDE 23

Polarisation of background contribution

PRD 91 (2015) 032004

> Expectation value (first moment) of decay angle linear in P

[MeV]

π p

m 1100 1105 1110 1115 1120 1125 1130 1135 E First moment

• 0.1
• 0.05

0.05 0.1 0.15 0.2 0.25 = 0 P Moments for = 1 P Moments for = 7 TeV s

• π

p → Λ ATLAS Simulation

> Use P = 0, 1 templates > Assume polarisation of background events [Ebkg] independent of mass > Calculate moments separately in the signal region and sidebands > Signal fractions already known > Simultaneously fit signal and sidebands to extract Ebkg and P

[MeV]

π p

m 1100 1105 1110 1115 1120 1125 1130 1135 E First moment

• 0.02
• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 0.02

• 1

b µ = 760 L = 7 TeV s

• π

p → Λ ATLAS Data Fit to data Signal Background

J.E.M. Robinson | Particle Production | 23/11/15 | Page 20/23

SLIDE 24

Extracted polarisations

PRD 91 (2015) 032004

F

x 0.0005 0.001 0.0015 0.002 0.0025 P

• 0.04
• 0.02

0.02 0.04 Λ

• stat. uncertainty

total uncertainty Λ

• stat. uncertainty

total uncertainty

• 1

b µ = 760 L = 7 TeV s ATLAS [GeV]

T

p 0.5 1 1.5 2 2.5 3 3.5 4 P

• 0.04
• 0.02

0.02 0.04 Λ

• stat. uncertainty

total uncertainty Λ

• stat. uncertainty

total uncertainty

• 1

b µ = 760 L = 7 TeV s ATLAS

> Measurement binned in xF and pT > Polarization < 2% in all bins > Consistent with zero in full fiducial phase space P(Λ)=−0.010±0.005(stat)±0.004(syst) P(¯ Λ)=0.002±0.006(stat)±0.004(syst)

J.E.M. Robinson | Particle Production | 23/11/15 | Page 21/23

SLIDE 25

Comparison to previous results

PRD 91 (2015) 032004

F

x

• 4

10

• 3

10

• 2

10

• 1

10 1 P

• 0.4
• 0.3
• 0.2
• 0.1

0.1 = 7 TeV s ATLAS = 42 GeV s HERA-B = 39 GeV s E799 = 29 GeV s NA48 = 27 GeV s M2

> ATLAS tests different kinematic phase space → direct comparison of results non-trivial > No theoretically motivated prediction,

• nly empirical models

Propose introduction of energy dependence > about half the Λ produced in ATLAS come from decays > dilutes polarisation → smaller than extrapolation

J.E.M. Robinson | Particle Production | 23/11/15 | Page 22/23

SLIDE 26

Conclusions

Underlying Event

> NEW measurements of underlying event [first Run II results] > Large variety of multiplicity and energy density distributions > MC models tuned to previous LHC data working well → particularly MPI energy extrapolation

Particle Production

> Complex measurements extracting small signals > Measurements provided in well-defined fiducial regions for easy comparison with theory > Many more Run II results on the way

J.E.M. Robinson | Particle Production | 23/11/15 | Page 23/23

SLIDE 27

Backup

SLIDE 28

Method of moments

PRD 91 (2015) 032004

Reconstructed decay angle distribution

w(t) ∝ ϵ(t) [(1 + αPt)] ⊗ R(t′, t) where t′ and t are true and reconstructed decay angles (cos θ∗), ϵ(t) is the efficiency function and R(t′, t) the resolution function

Method of moments

> The expectation value (first moment) of w(t) is linear in P: E(w|P = p) ≡ E(p) = C0 + C1p = E(0) + [E(1) − E(0)]p > E(0) and E(1) estimated from MC with polarisation set to 0 and 1 Eexp

i

( P, Ebkg ) = fsig

i

[ EMC

i

(0) + [ EMC

i

(1)−EMC

i

(0) ] P ] + (1−fsig

i )Ebkg

J.E.M. Robinson | Backup | 23/11/15 | Page 1/2

SLIDE 29

Λ polarisation parametrisation

PRD 40 (1989) 3557

> Many possible parametrisations > B. Lundberg [PRD 40 (1989) 3557] is a popular choice > Assumes energy independence and neglects detector effects P = ( −0.268xF − 0.338x3

F

) × ( 1 − e−4.5pT2) > ATLAS: ⟨pT⟩ ∼ 1.8 – 2.1 GeV and √s = 7 TeV > HERA-B and E799: ⟨pT⟩ ∼ 0.67 – 2.2 GeV and √s ∼ 40 GeV

J.E.M. Robinson | Backup | 23/11/15 | Page 2/2