2-loop 1-loop 0.4 0.3 0.2 V I N C I A R O O T 0.1 0 0 0.5 1 - - PowerPoint PPT Presentation

(Q/GeV)

10

log

0.5 1 1.5 2

(Q)

s

α

0.1 0.2 0.3 0.4 0.5 0.6

(Q)

s

α

2-loop 1-loop

V I N C I A R O O T

Skands, ¡TASI ¡Lectures, ¡arXiv:1207.2389

1.4 1.5 1.5 1.5 1.75 1.75 1.75 2

• 8
• 6
• 4
• 2
• 8
• 6
• 4
• 2

lnHyijL lnHyjkL

QE=2pT HstrongL

(a) µPS = √s

1.2 1.2 1.2

• 8
• 6
• 4
• 2
• 8
• 6
• 4
• 2

lnHyijL lnHyjkL

QE=2pT HstrongL

(b) µPS = p⊥

Z → 3 Jets

Size of NLO “K” factor

• ver phase space

s h

• w

e r shower

i j k

yij = sij M 2

Z

yjk = sjk M 2

Z

collinear soft collinear collinear soft collinear hard hard

Hartgring, ¡Laenen, ¡Skands, ¡arXiv:1303.4974

1.05 1.1 1.1 1.1 1.2 1.2 1.2 1.2

• 8
• 6
• 4
• 2
• 8
• 6
• 4
• 2

lnHyijL lnHyjkL

QE=2pT HstrongL

µPS = p⊥, with CMW

1.2 1.2 1.2

• 8
• 6
• 4
• 2
• 8
• 6
• 4
• 2

lnHyijL lnHyjkL

QE=2pT HstrongL

(b) µPS = p⊥

Z → 3 Jets

The “CMW” factor

αs 2π β0 2 ln

• k2

CMW

• ∼ 0.07

kCMW = exp ✓67 − 3π2 − 10nF /3 2(33 − 2nF ) ◆ = 8 > > > < > > > : 1.513 nF = 6 1.569 nF = 5 1.618 nF = 4 1.661 nF = 3

: Constant shift by Size of NLO “K” factor over phase space

soft soft

Hartgring, ¡Laenen, ¡Skands, ¡arXiv:1303.4974 Catani, ¡Marchesini, ¡Webber, ¡NPB349 ¡(1991) ¡635

0.2 0.4 0.6 0.8

(Q)

s

α

(MZ)=0.12 (incl var)

(2) s

α (MZ)=0.12 (CMW)

(2) s

α (MZ)=0.14

(1) s

α

V I N C I A R O O T

) [GeV] µ Log10(

1 2 3 4

Ratio

0.8 0.9 1 1.1 1.2

Beware: choosing a larger central scale → a seemingly smaller scale variation!

Λ3 = 0.37 Λ4 = 0.33 Λ5 = 0.26 1 Loop: 2 Loop: αs(MZ)=0.14 αs(MZ)=0.12 Λ3 = 0.37 Λ4 = 0.32 Λ5 = 0.23

(In all cases, 5-flavor running is still used above mt)

Variations in e+e- μR by factor 2 in either direction See mcplots.cern.ch 1-T y23 y56

3j 4j 3-jet observable 6-jet observable Durham kT Durham kT Thrust Event Shape

Pythia 6 “Perugia 2012 : Variations”

∝αs1 ∝αs4

(with central choice μR=pT, and αs(MZ)(1) ~ 0.14)

Beware! αs pileup

→ Factor 2 looks pretty extreme?

Skands, ¡ ¡arXiv:1005.3457 Karneyeu ¡et ¡al, ¡ ¡arXiv:1306.3436

Variations in pp See mcplots.cern.ch μR by factor 2 in either direction

(with central choice μR=pT, and αs(MZ)(1) ~ 0.14) Pythia 6 “Perugia 2012 : Variations”

pTZ pTjet Z W Jets Jet Shape

1/σ dσ/dpT dσ/dpT

→ Factor 2 looks reasonable?

“normalized” “dimensionful” Karneyeu ¡et ¡al, ¡ ¡arXiv:1306.3436 Skands, ¡ ¡arXiv:1005.3457

1 2 3

Ratio to

0.5 1 1.5

jet

N 1 2 3 jets) [pb]

jet

N ≥ (W + σ

2

10

3

10

4

10

P2011 ↑ Alp. Λ , ↑ PS Λ ↓ Alp. Λ , ↓ PS Λ ↑ Alp. Λ ↓ Alp. Λ

mcplots.cern.ch pp, 7 TeV, W+jets, el-chan. Alpgen+Pythia jet multiplicity

Matrix Elements NJets

Jet Shape PS Jet Shape ME+PS

W+jets NJets: dominated by ME (+Sudakov from PS) Jet Shapes: dominated by PS

(E.g., AlpGen/MadGraph + Herwig/Pythia)

Cooper ¡et ¡al., ¡ ¡arXiv:1109.5295

From multi-leg LO to multi-leg NLO

/d(1-T) σ d σ 1/

• 3

10

• 2

10

• 1

10 1 10

2

10

3

10

4

10 1-Thrust (udsc)

Vincia 1.104 + MadGraph 4.4.26 + Pythia 8.186 Data from Phys.Rept. 399 (2004) 71

L3 (MZ)=0.12 (NLO3,CMW)

(2) S

α (MZ)=0.14 (LO3)

(1) S

α (MZ)=0.12 (LO3,CMW)

(2) S

α (MZ)=0.12 (LO3)

(2) S

α

bins

/N

2 5%

χ 0.0 ± 0.5 0.1 ± 0.5 0.1 ± 1.4 0.6 ± 15.0

V I N C I A R O O T

hadrons → ee

91.2 GeV

1-T (udsc)

0.1 0.2 0.3 0.4 0.5

Theory/Data

0.8 0.9 1 1.1 1.2 Hartgring, ¡Laenen, ¡Skands, ¡arXiv:1303.4974

0.0005 0.001 0.0015 0.002 0.0025 0.003 + 3 jets (100, 200, 300)

800

W'

3 s

α

V I N C I A R O O T

Central Choice

1 2 3 4 5

Ratio 0.5 1 1.5 2

Multi-scale problems E.g., in context of ME matching with many legs

0.001 0.002 0.003 0.004 0.005 W + 3 jets (100, 200, 300)

3 s

α

V I N C I A R O O T

Central Choice

1 2 3 4 5

Ratio 0.5 1 1.5 2

0.002 0.004 0.006 0.008 0.01 W + 3 jets (20, 30, 60)

3 s

α

V I N C I A R O O T

Central Choice

1 2 3 4 5

Ratio 0.5 1 1.5 2

Example: W+3

pT1 = 20 pT2 = 30 pT3 = 60 pT1 = 100 pT2 = 200 pT3 = 300 mW = 800 pT1 = 100 pT2 = 200 pT3 = 300

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1: MW 2: MW + Sum(|pT|) 3: -“- (quadratically) 4: Geometric mean pT (~PS) 5: Arithmetic mean pT