High-precision predictions for V+jet production Jonas M. Lindert - - PowerPoint PPT Presentation

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High-precision predictions for V+jet production

Jonas M. Lindert

UCL HEP Seminars 
 UCL, London, 21.04.2017

work in collaboration with: 


• R. Boughezal, A. Denner, S. Dittmaier, A. Huss, A. Gehrmann-De Ridder, 

• T. Gehrmann, N. Glover, S. Kallweit, P. Maierhöfer, M. L. Mangano, 


T.A. Morgan, A. Mück, M. Schönherr, F. Petriello, S. Pozzorini, G. P. Salam

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High-precision predictions for V+jet production Jonas M. Lindert

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• Dominant backgrounds for monojet DM searches
• Important/dominant backgrounds for various 


BSM searches (lepton + missing ET + ets)

• Dominant backgrounds for top physics
• Dominant backgrounds for Higgs physics, e.g. VH(→bb),

H→WW

• Large cross-sections and clean leptonic signatures
• V+jets: Precision QCD at LHC
• Playground to probe different aspects of higher-order

calculations 
 (LO+PS, NLO+PS, NLO-Merging, NLO EW,…)


• Probe and constrain PDFs

pp

total 80 µb−1

Jets

R=0.4 |y|<3.0 0.1 < pT < 2 TeV

Dijets

R=0.4 |y|<3.0 y ∗<3.0 0.3 < mjj < 5 TeV

W

fiducial 35 pb−1 njet ≥ 0 njet ≥ 1 njet ≥ 2 njet ≥ 3 njet ≥ 4 njet ≥ 5 njet ≥ 6 njet ≥ 7

Z

fiducial 35 pb−1 njet ≥ 0 njet ≥ 1 njet ≥ 2 njet ≥ 3 njet ≥ 4 njet ≥ 5 njet ≥ 6 njet ≥ 7

t¯ t

total njet ≥ 0 njet ≥ 4 njet ≥ 5 njet ≥ 6 njet ≥ 7 njet ≥ 8

tt−chan

total WW+ WZ total

WW

total

γγ

fiducial 4.9 fb−1

Wt

total 2.0 fb−1

WZ

total 13.0 fb−1

ZZ

total

t¯ tγ

fiducial 1.0 fb−1

Wγ

fiducial njet=0

Zγ

fiducial njet=0

t¯ tW

total

t¯ tZ

total 95% CL upper limit

Zjj

EWK fiducial

H→γγ

fiducial W±W±jj EWK fiducial

ts−chan

total 95% CL upper limit 0.7 fb−1

σ [pb]

10−3 10−2 10−1 1 101 102 103 104 105 106 1011 LHC pp √s = 7 TeV Theory Data 4.5 − 4.7 fb−1 LHC pp √s = 8 TeV Theory Data 20.3 fb−1

Standard Model Production Cross Section Measurements

Status: July 2014

ATLAS Preliminary Run 1 √s = 7, 8 TeV

V + multijet production

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High-precision predictions for V+jet production Jonas M. Lindert

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V+jets backgrounds in monojet/MET + jets searches

pp→Z(→νν̅)+jets ⟹ MET + jets

irreducible backgrounds:

pp→W(→lv)+jets ⟹ MET + jets (lepton lost)

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High-precision predictions for V+jet production Jonas M. Lindert

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Target precision

10% 1%

• for 500 GeV < pTV < 1000 GeV: background statistics will be at 1% level
• understanding of V+jets backgrounds at this level increases sensitivity in DM searches
• this level of precision is theoretically possible @ NNLO QCD + NNLO EW
• requires solid understanding of uncertainties!

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High-precision predictions for V+jet production Jonas M. Lindert

Determine V+jets backgrounds

5

global fit of Z(→l l ̅ )+jets, W(→lν̅)+jets and ɣ+jets measurements

• to determine Z(→ν̅ν)+jet
• and the visible channels at high-pT
• theory systematics (scales, etc.) via nuisance parameters in fit
• hardly any systematics (just QED dressing)
• very precise at low pT
• but: limited statistics at large pT
• fairly large data samples at large pT
• systematics from transfer factors

pTV Z(→l l ̅ )+jets ɣ+jets Z(→ν̅ν)+jet W(→lν̅)+jets dσ/dpTV

1 TeV

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High-precision predictions for V+jet production Jonas M. Lindert

Goal of the ongoing study

6

• Combination of state-of-the-art predictions: (N)NLO QCD+(N)NLO EW


in order to match (future) experimental sensitivities
 (1-10% accuracy in the few hundred GeV-TeV range)
 
 
 
 
 
 
 
 


d dx d d~ y (V )(~ "MC, ~ "TH) := d dx d d~ y (V )

MC(~

"MC) "

d dx(V ) TH (~

"TH)

d dx(V ) MC(~

"MC) #

• ne-dimensional reweighting of MC samples in

parameter x um, x = p(V )

T ,

dence of the

• Robust uncertainty estimates including

1.Pure QCD uncertainties 2.Pure EW uncertainties 3.Mixed QCD-EW uncertainties 4.PDF, ɣ-induced uncertainties ….

• Prescription for correlation of these uncertainties
• within a process (between low-pT and high-pT)
• across processes

d dx(V )

TH = d

dx(V )

QCD + d

dx(V )

mix + d

dx∆(V )

EW + d

dx(V )

γ−ind..

with

[to be published soon, already available to ATLAS & CMS]

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High-precision predictions for V+jet production Jonas M. Lindert

Prelude: Z+jet vs. ɣ + 1 jet

QCD corrections

• mostly moderate and stable QCD corrections
• (almost) identical QCD corrections in the tail, 


sizeable differences for small pT

7

EW corrections

• correction in pT(Z) > correction in pT(ɣ)
• -20/-8% for Z/ɣ at 1 TeV
• EW corrections > QCD uncertainties for pT,Z > 350 GeV

ɣ+jet

pT,γ [GeV]

dσ/dσNLO

QCD

1500 1000 500 1.1 1 0.9 0.8 0.7 0.6 0.5

pT,γ [GeV]

dσ/dσNLO

QCD

1500 1000 500 1.1 1 0.9 0.8 0.7 0.6 0.5

dσ/dpT,γ [fb/GeV]

∆φ(j1, j2) < 2.5 preliminary! Munich+OpenLoops pp → γ + 1j @ 8 TeV

103 102 101 100 10−1 10−2 10−3

NLO QCD×EW NLO QCD+EW NLO QCD LON

dσ/dpT,γ [fb/GeV]

∆φ(j1, j2) < 2.5 preliminary! Munich+OpenLoops pp → γ + 1j @ 8 TeV

103 102 101 100 10−1 10−2 10−3 pT,Z [GeV]

dσ/dσNLO

QCD

1500 1250 1000 750 500 250 1.1 1 0.9 0.8 0.7 0.6 0.5

pT,Z [GeV]

dσ/dσNLO

QCD

1500 1250 1000 750 500 250 1.1 1 0.9 0.8 0.7 0.6 0.5

dσ/dpT,Z [fb/GeV]

∆φ(j1, j2) < 2.5 preliminary! Munich+OpenLoops pp → Z + 1j @ 13 TeV

103 102 101 100 10−1 10−2 10−3

NLO QCD×EW NLO QCD+EW NLO QCD LON

dσ/dpT,Z [fb/GeV]

∆φ(j1, j2) < 2.5 preliminary! Munich+OpenLoops pp → Z + 1j @ 13 TeV

103 102 101 100 10−1 10−2 10−3

Z+jet

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High-precision predictions for V+jet production Jonas M. Lindert

Prelude: Z/ɣ pT-ratio

8

Overall

• mild dependence on the boson pT

QCD corrections

• 10-15% below 250 GeV
• ≲ 5% above 350 GeV

EW corrections

• sizeable difference in EW corrections results in 


10-15% corrections at several hundred GeV

• ~5% difference between NLO QCD+EW 


and NLO QCDxEW

(dσZj/dσγj) / (dσLO

Zj /dσLO γj )

pT,Z/γ [GeV]

1500 1250 1000 750 500 250 1.05 1 0.95 0.9 0.85 0.8 0.75 (dσZj/dσγj) / (dσLO

Zj /dσLO γj )

pT,Z/γ [GeV]

1500 1250 1000 750 500 250 1.05 1 0.95 0.9 0.85 0.8 0.75 dφ(j1, j2) < 2.5 preliminary! Munich+OpenLoops dσZj × BRZ→ν¯

ν/dσγj

pp → Z/γ + 1j @ 8 TeV 0.3 0.28 0.26 0.24 0.22 0.2 0.18 0.16 NLO QCD×EW NLO QCD+EW NLO QCD LON dφ(j1, j2) < 2.5 preliminary! Munich+OpenLoops dσZj × BRZ→ν¯

ν/dσγj

pp → Z/γ + 1j @ 8 TeV 0.3 0.28 0.26 0.24 0.22 0.2 0.18 0.16

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High-precision predictions for V+jet production Jonas M. Lindert

Prelude: compare against Z/γ-data

9

Sherpa+OpenLoops NLO QCD NLO QCD+EW CMS data JHEP10(2015)128 0.01 0.02 0.03 0.04 0.05 Z/γ ratio for events with njets ≥ 1 dσ/dpZ

T / dσ/dpγ T

100 200 300 400 500 600 700 800 0.8 0.9 1.0 1.1 1.2 pZ/γ

T

[GeV]

MC/Data

• remarkable agreement with data at @ NLO QCD+EW!

[Ciulli, Kallweit, JML, Pozzorini, Schönherr 
 for LH’15]

[JHEP10(2015)128]

SLIDE 10

• 1. pure QCD uncertainties

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High-precision predictions for V+jet production Jonas M. Lindert

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QCD effects

O d dx(V )

QCD = d

dx(V )

LO QCD + d

dx(V )

NLO QCD + d

dx(V )

NNLO QCD.

δ(1)KNkLO

LO NLO QCD NNLO QCD 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσNLO QCD [A. Huss, A. Gehrmann-De Ridder, 


• T. Gehrmann, N. Glove, T.A. Morgan]

NNLO from this is a ‘good’ scale for V+jets

• at large pTV: HT’/2 ≈ pTV
• modest higher-order corrections
• sufficient convergence

scale uncertainties due to 7-pt variations yields 
 O(20%) uncertainties at LO 
 O(10%) uncertainties at NLO 
 O(5%) uncertainties at NNLO µR,F = ξR,Fµ0

ariations (ξR, ξF) = (2, 2), (2, 1), (1, 2), (1, 1), (1, 0.5), (0.5, 1),

• ur M P predictions are assessed by applying the scale

(0.5, 0.5), variation µ0 = 1 2 @ q p2

T,`+`− + m2 `+`− +

X

i∈{q,g,}

|pT,i| 1 A

with minor shape variations

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High-precision predictions for V+jet production Jonas M. Lindert

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Correlation of scale variations

Z+jet/W+jet LO (uncorrelated errors) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 pp → e+e−j vs. pp → e− ¯ νj @ 13 TeV Z(→ ℓ+ℓ−)+jet / W(→ e− ¯ ν) +jet 10 2 10 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,V [GeV] dσ/dσLO

consider Z+jet / W+jet pT,V-ratio @ LO uncorrelated treatment yields 
 O(40%) uncertainties

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High-precision predictions for V+jet production Jonas M. Lindert

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Correlation of scale variations

consider Z+jet / W+jet pT,V-ratio @ LO uncorrelated treatment yields 
 O(40%) uncertainties correlated treatment yields tiny 
 O(<~ 1%) uncertainties check against NLO QCD!

Z+jet/W+jet LO (uncorrelated errors) Z+jet/W+jet LO (correlated errors) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 pp → e+e−j vs. pp → e− ¯ νj @ 13 TeV Z(→ ℓ+ℓ−)+jet / W(→ e− ¯ ν) +jet 10 2 10 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,V [GeV] dσ/dσLO

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High-precision predictions for V+jet production Jonas M. Lindert

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Correlation of scale variations

consider Z+jet / W+jet pT,V-ratio @ LO uncorrelated treatment yields 
 O(40%) uncertainties correlated treatment yields tiny 
 O(<~ 1%) uncertainties check against NLO QCD! NLO QCD corrections remarkably flat in Z+jet / W+jet ratio! → supports correlated treatment of uncertainties!

Z+jet/W+jet LO (uncorrelated errors) Z+jet/W+jet LO (correlated errors) Z+jet/W+jet NLO QCD 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 pp → e+e−j vs. pp → e− ¯ νj @ 13 TeV Z(→ ℓ+ℓ−)+jet / W(→ e− ¯ ν) +jet 10 2 10 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,V [GeV] dσ/dσLO

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High-precision predictions for V+jet production Jonas M. Lindert

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Correlation of scale variations

consider Z+jet / W+jet pT,V-ratio @ LO uncorrelated treatment yields 
 O(40%) uncertainties correlated treatment yields tiny 
 O(<~ 1%) uncertainties check against NLO QCD! NLO QCD corrections remarkably flat in Z+jet / W+jet ratio! → supports correlated treatment of uncertainties! Also holds for higher jet-multiplicities → indication of correlation also in higher-order corrections beyond NLO!

Z+jet/W+jet LO (uncorrelated errors) Z+jet/W+jet LO (correlated errors) Z+jet/W+jet NLO QCD Z+2 jets/W+2 jets LO Z+3 jets/W+3 jets LO 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 pp → e+e−j vs. pp → e− ¯ νj @ 13 TeV Z(→ ℓ+ℓ−)+jet / W(→ e− ¯ ν) +jet 10 2 10 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,V [GeV] dσ/dσLO

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High-precision predictions for V+jet production Jonas M. Lindert

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QCD uncertainties

d dx(V )

NkLO QCD(~

"QCD) = " K(V )

NkLO(x) + 3

X

i=1

"QCD,i (i)K(V )

NkLO(x)

# ⇥ d dx(V )

LO QCD(~

µ0).

nuisance parameters: interpreted as 1σ Gaussian

δ(1)KNkLO δ(2)KNkLO δ(3)KNkLO

LO NLO QCD 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 10 2 pp →W(→ `ν)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 0.4 0.6 0.8 1 1.2 dσ/dσNLO QCD 0.4 0.6 0.8 1 1.2 dσ/dσNLO QCD 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσNLO QCD

• ✏(Z)

QCD,i = ✏(W ±) QCD,i = ✏(γ) QCD,i = ✏QCD,i

• correlated across processes
• correlated across pT bins
• 100

200 500 1000 3000 pT [GeV] 1

± shape(pT)

δ(2)KV

NkLO = p2 T − 650 GeV

p2

T + 650 GeVδ(1)KV NkLO

δ(1)KV

NkLO = 1

2 h KV,max

NkLO − KV,min NkLO

i

yields max shape distortion within scale variation band symmetrized scale uncertainty

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High-precision predictions for V+jet production Jonas M. Lindert

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QCD uncertainties

d dx(V )

NkLO QCD(~

"QCD) = " K(V )

NkLO(x) + 3

X

i=1

"QCD,i (i)K(V )

NkLO(x)

# ⇥ d dx(V )

LO QCD(~

µ0).

nuisance parameters: interpreted as 1σ Gaussian

δ(1)KNkLO δ(2)KNkLO δ(3)KNkLO

LO NLO QCD 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 10 2 pp →W(→ `ν)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 0.4 0.6 0.8 1 1.2 dσ/dσNLO QCD 0.4 0.6 0.8 1 1.2 dσ/dσNLO QCD 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσNLO QCD

• ✏(Z)

QCD,i = ✏(W ±) QCD,i = ✏(γ) QCD,i = ✏QCD,i

• correlated across processes
• correlated across pT bins
• yields max shape distortion within scale variation band

δ(2)KV

NkLO = p2 T − 650 GeV

p2

T + 650 GeVδ(1)KV NkLO

δ(1)KV

NkLO = 1

2 h KV,max

NkLO − KV,min NkLO

i

• δ(3)KV

NkLO =

KV

NkLO

KV

Nk−1LO

− KZ

NkLO

KZ

Nk−1LO

Difference of (N)NLO corrections as process correlation uncertainty symmetrized scale uncertainty

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High-precision predictions for V+jet production Jonas M. Lindert

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Caveat: ɣ+jet

Note: this modelling of process correlations assumes close similarity

• f QCD effects between different V+jets processes
• apart from PDF effects it is the case for W+jets vs. Z+jets
• at pT > 200 GeV it is also the case for ɣ+jets vs. Z+jets.
• σ(V )

NLO

σ(V )

LO

σ(Z)

NLO

σ(Z)

LO

• ⌧
• σ(Z)

NLO

σ(Z)

LO

• Different logarithmic effects from fragmentation

W/Z+jet: masscut-off MVj ≥MV
 γ+ jet: Frixione-isolation cone of radius R0 Consider dynamic γ-isolation with Rdyn(pT,γ) = min{1.0, MZ/pTγ}

pT,V [GeV] dσNLO QCD

V+j

/dσLO

V+j

3000 1000 500 200 100 50 2.2 2 1.8 1.6 1.4 1.2

γ(dyn)+j γ(fix)+j W+j Z+j

pT,V [GeV] dσNLO QCD

V+j

/dσLO

V+j

3000 1000 500 200 100 50 2.2 2 1.8 1.6 1.4 1.2

• γdyn behaves like W/Z at pT > MZ


⇒justifies process-correlation estimate

• remnant part γfix − γdyn uncorrelated 


(uncertainty through extra reweighting and MC)

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High-precision predictions for V+jet production Jonas M. Lindert

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QCD uncertainties

δ(1)KNLO δ(2)KNLO δ(3)KNLO

Z(→ ℓ+ℓ−)+ jet W(→ ℓν)+ jet γ+ jet 1 1.2 1.4 1.6 1.8 2 2.2 NLO QCD for V+jet @ 13 TeV KNLO 0.05 0.1 0.15 0.2 δ(1)KNLO/KNLO

• 0.1
• 0.05

0.05 0.1 0.15 0.2 δ(2)KNLO/KNLO 10 2 10 3

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2 pT,V [GeV] δ(3)KNLO/KNLO

NLO QCD corrections and uncertainties

• almost identical for W/Z/ɣ for pTV > 200 GeV
• sizeable ɣ+jet fragmentation for pTV > 200 GeV

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High-precision predictions for V+jet production Jonas M. Lindert

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QCD uncertainties in pT-ratios

Z/W Z/γ

δ(1)KNkLO δ(2)KNkLO δ(3)KNkLO

LO NLO QCD 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 pp →Z(→ ℓ+ℓ−)+ jet / W(→ ℓν)+ jet @ 13 TeV Z(→ ℓ+ℓ−)+ jet / W(→ ℓν)+ jet 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 10 2 10 3 0.9 0.95 1.0 1.05 pT,V [GeV] dσ/dσNLO QCD

δ(1)KNkLO δ(2)KNkLO δ(3)KNkLO

LO NLO QCD 0.01 0.02 0.03 0.04 0.05 pp →Z(→ ℓ+ℓ−)+ jet / γ+ jet @ 13 TeV Z(→ ℓ+ℓ−)+ jet / γ+ jet 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 10 2 10 3 0.9 0.95 1.0 1.05 pT,V [GeV] dσ/dσNLO QCD

Z/W± ≃1% Z/γ ≃3%

δ(1)KNkLO δ(2)KNkLO δ(3)KNkLO

LO NLO QCD 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 pp →W(→ ℓ− ¯ ν)+ jet / W(→ ℓ+ν)+ jet @ 13 TeV W(→ ℓ− ¯ ν)+ jet / W(→ ℓ+ν)+ jet 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 0.9 0.95 1.0 1.05 dσ/dσNLO QCD 10 2 10 3 0.9 0.95 1.0 1.05 pT,V [GeV] dσ/dσNLO QCD

0.8 0.7 0.6 0.5 0.4

W+/W− ≃1–3%

W-/W+

SLIDE 21

• 2. pure EW effects uncertainties

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High-precision predictions for V+jet production Jonas M. Lindert

22

Originate from soft/collinear virtual EW bosons coupling to on-shell legs Universality and factorisation similar as in QCD [Denner, Pozzorini; ’01]

Virtual EW Sudakov logarithms

• process-independent, simple structure
• typical size at 1, 5, 10 TeV:

➡ large (negative) corrections at high energies 
 (pT, MET, HT, Minv) ➡ sizeable cancellations between leading and subleading terms possible

δLL ⇠ α πs2

W

log2 ˆ s M 2

W

' 28, 76, 104%, δNLL ⇠ + 3α πs4

W

log ˆ s M 2

W

' +16, +28, +32%

√ ˆ s =

δM1loop

LL+NLL = α

4π

n

X

k=1

8 < : 1 2 X

l6=k

X

a=γ,Z,W ±

Ia(k)I¯

a(l) ln2

✓ ˆ skl M 2

W

◆ + γew(k) ln ✓ ˆ s M 2

W

◆9 = ; M0

• γ,Z, W ±

γ,Z, W ± γ,Z, W ±, H, t, . . .

SLIDE 23

High-precision predictions for V+jet production Jonas M. Lindert

Pure EW uncertainties

23

EW corrections become sizeable 
 at large pT,V Origin: virtual EW Sudakov logarithms How to estimate corresponding pure
 EW uncertainties of relative ?

tive O(α2)

Z+jet

Note: real EW Sudakov logarithms 
 included as separate VV(+jets) 
 backgrounds

κEW ± δ(1)κEW

LO NLO EW 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

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High-precision predictions for V+jet production Jonas M. Lindert

κEW ± δ(1)κEW

LO NLO EW SudakovNLO 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

Pure EW uncertainties

24

Z+jet

Large EW corrections dominated by Sudakov logs

Uncertainty estimate of NLO EW from naive exponentiation x 2:

α(L2 + L1)

κNLO EW(ˆ s, ˆ t) = α π h δ(1)

hard + δ(1) Sud

i ⇣ ⌘

δ(1)κEW ' 2 k! ⇣ κNLO,EW ⌘k

SLIDE 25

High-precision predictions for V+jet production Jonas M. Lindert

κEW ± δ(1)κEW

LO NLO EW SudakovNLO 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

Pure EW uncertainties

25

Z+jet

Large EW corrections dominated by Sudakov logs

Uncertainty estimate of NLO EW from naive exponentiation x 2:

α(L2 + L1)

κNLO EW(ˆ s, ˆ t) = α π h δ(1)

hard + δ(1) Sud

i ⇣ ⌘

δ(1)κEW ' 2 k! ⇣ κNLO,EW ⌘k

SLIDE 26

High-precision predictions for V+jet production Jonas M. Lindert

κEW ± δ(1)κEW

LO NLO EW SudakovNLO NLO EW + SudakovNNLO 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

Pure EW uncertainties

26

Z+jet

Large EW corrections dominated by Sudakov logs

Uncertainty estimate of NLO EW from naive exponentiation x 2:

α(L2 + L1)

check against two-loop Sudakov logs

[Kühn, Kulesza, Pozzorini, Schulze; 05-07]

α2(L4 + L3) κNLO EW(ˆ s, ˆ t) = α π h δ(1)

hard + δ(1) Sud

i ⇣ ⌘ π h κNNLO Sud(ˆ s, ˆ t) = ⇣α π ⌘2 δ(2)

Sud.

3 n 1 2

tree

+ X

i,j

1 2

i j V1 +

X

i,j,k,l

1 2 "

i j V1 V2

+

i j V1 V2

# +

i j V1 V3 V2

+

i j V1 V2

+

i j V1 V2

+ 1 2

i j V1 V2

+

j i k V1 V2

+ 1 6

j i k V2 V1 V3

+ 1 8

i j k l V1 V2

= exp 2 4X

j<i i j ∆γ

3 5 exp 2 4X

j<i i j W,Z,γ

3 5

3 n 1 2 tree

δ(1)κEW ' 2 k! ⇣ κNLO,EW ⌘k

SLIDE 27

High-precision predictions for V+jet production Jonas M. Lindert

κEW ± δ(1)κEW

LO NLO EW SudakovNLO NLO EW + SudakovNNLO 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

Pure EW uncertainties

27

Z+jet

Large EW corrections dominated by Sudakov logs

Uncertainty estimate of NLO EW from naive exponentiation x 2:

α(L2 + L1)

check against two-loop Sudakov logs

[Kühn, Kulesza, Pozzorini, Schulze; 05-07]

Uncertainty estimate of NNLO EW:

δ(1)κ(V )

EW(x)

=

) = 2 3κ(V )

NLO EW(x) κ(V ) NNLO Sud(x),

α2(L4 + L3) κNLO EW(ˆ s, ˆ t) = α π h δ(1)

hard + δ(1) Sud

i ⇣ ⌘ π h κNNLO Sud(ˆ s, ˆ t) = ⇣α π ⌘2 δ(2)

Sud.

δ(1)κEW ' 2 k! ⇣ κNLO,EW ⌘k

SLIDE 28

High-precision predictions for V+jet production Jonas M. Lindert

Pure EW uncertainties

28

κEW ± δ(1)κEW κEW ± δ(2)κEW κEW ± δ(3)κEW

LO NLO EW SudakovNLO NLO EW + SudakovNNLO 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 0.4 0.6 0.8 1 1.2 dσ/dσLO 0.4 0.6 0.8 1 1.2 dσ/dσLO 10 2 10 3 0.4 0.6 0.8 1 1.2 pT,V [GeV] dσ/dσLO

δ(2)κ(V )

EW(x) = 0.05 κ(V ) NLO EW(x).

δ(1)κ(V )

EW(x)

=

) = 2 3κ(V )

NLO EW(x) κ(V ) NNLO Sud(x),

‘higher-order logs’ ‘hard non-log NNLO effects I’ 


• (correlated)

(uncorrelated) (uncorrelated) d, δ(2)

hard  0.05π α

δ(1)

hard ' 20 δ(1) hard,

the NLO hard corretion is acci- ⇔ ‘hard non-log NNLO effects II’ 


• δ(3)κ(V )

EW(x)

= κ(V )

NNLO Sud(x) 1

2[κ(V )

NLO EW(x)]2.

estimate of typical size of pe h δ(1)

hard

i2 and δ(1)

hard ⇥ δ(1) Sud.

In Fig. 4 we

• r

Additional uncorrelated uncertainties:

SLIDE 29

High-precision predictions for V+jet production Jonas M. Lindert

Pure EW uncertainties

29

δ(1)κEW δ(2)κEW δ(3)κEW

Z(→ ℓ+ℓ−)+ jet W(→ ℓν)+ jet γ+ jet 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V+jet @ NNLO EW, 13 TeV κEW ± δ(1)κEW 0.02 0.04 0.06 0.08 0.1 δ(1)κEW 0.02 0.04 0.06 0.08 0.1 δ(2)κEW 10 2 10 3

• 0.1
• 0.05

0.05 0.1 pT,V [GeV] δ(3)κEW

NLO NNLO

Pure EW uncertainties

• tiny at low pT and only 1-2% at 1 TeV
• thanks to NNLO Sudakov logs


(up to ∼ 5%)

δ(1)κEW δ(2)κEW δ(3)κEW

Z(→ ℓ+ℓ−)+ jet W(→ ℓν)+ jet γ+ jet 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V+jet @ NLO EW, 13 TeV κEW ± δ(1)κEW 0.05 0.1 0.15 0.2 0.25 0.3 δ(1)κEW 0.05 0.1 0.15 0.2 0.25 0.3 δ(2)κEW 10 2 10 3 0.05 0.1 0.15 0.2 0.25 0.3 pT,V [GeV] δ(3)κEW

NNLO EW corrections at 1 TeV

• -10% for ɣ+jets
• -20% for Z+jet
• -25% for W+jet

SLIDE 30

High-precision predictions for V+jet production Jonas M. Lindert

30

EW uncertainties in pT-ratios

Z/W Z/γ

δ(1)κEW δ(2)κEW δ(3)κEW

LO NLO EW NLO EW + SudakovNNLO 0.1 0.12 0.14 0.16 0.18 0.2 0.22 pp →Z(→ ℓ+ℓ−)+ jet / W(→ ℓν)+ jet @ 13 TeV Z(→ ℓ+ℓ−)+ jet / W(→ ℓν)+ jet 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 10 2 10 3 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 pT,V [GeV] dσ/dσNNLO EW

δ(1)κEW δ(2)κEW δ(3)κEW

LO NLO EW NLO EW + SudakovNNLO 0.01 0.02 0.03 0.04 0.05 pp →Z(→ ℓ+ℓ−)+ jet / γ+ jet @ 13 TeV Z(→ ℓ+ℓ−)+ jet / γ+ jet 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 10 2 10 3 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 pT,V [GeV] dσ/dσNNLO EW

Z/W± ≃2-3% Z/γ ≃2-3%

0.8 0.7 0.6 0.5 0.4

W+/W− ≃2–3%

δ(1)κEW δ(2)κEW δ(3)κEW

LO NLO EW NLO EW + SudakovNNLO 0.2 0.4 0.6 0.8 1 1.2 pp →W(→ ℓ− ¯ ν)+ jet / W(→ ℓ+ν)+ jet @ 13 TeV W(→ ℓ− ¯ ν)+ jet / W(→ ℓ+ν)+ jet 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 dσ/dσNNLO EW 10 2 10 3 0.85 0.9 0.95 1.0 1.05 1.1 1.15 1.2 pT,V [GeV] dσ/dσNNLO EW

W-/W+

SLIDE 31

• 3. mixed QCD-EW uncertainties

SLIDE 32

High-precision predictions for V+jet production Jonas M. Lindert

Mixed QCD-EW uncertainties

32

σNLO

QCD+EW = σLO + δσNLO QCD + δσNLO EW ,

σNLO

QCD×EW = σNLO QCD

✓ 1 + δσNLO

EW

σLO ◆ = σNLO

EW

1 + δσNLO

QCD

σLO !

Difference between these two approaches indicates size of missing mixed EW-QCD corrections. Given QCD and EW corrections are sizeable, also mixed QCD-EW uncertainties of relative have to be considered.

O(ααs)

Too conservative!?
 
 For dominant Sudakov EW logarithms factorization should be exact!

LO NLO QCD NLO QCD⊕EW NLO QCD⊗EW 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 pT,V [GeV] dσ/dσNLO QCD

Additive combination Multiplicative combination (no contributions)

O(ααs)

(some dominant contributions, 
 e.g. EW Sudakov logs × soft QCD)

O(ααs)

KQCD⊗EW − KQCD⊕EW ∼ 10% at 1 TeV

SLIDE 33

High-precision predictions for V+jet production Jonas M. Lindert

Mixed QCD-EW uncertainties

33

NLO QCD NLO QCD⊕EW NLO QCD⊗EW 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 dσ/dσNLO QCD 10 2 10 3

• 0.1
• 0.05

0.05 0.1 pT,V [GeV] δKmix

K(V )

mix(x)

= 0.1 h K(V )

TH,⊕(x, ~

µ0) − K(V )

TH,⊗(x, ~

µ0) i

(correlated)

Vj Vjj full NLO EW Vj w.o. NLO EW interference 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 pp →Z(→ ℓ+ℓ−)+ jets @ 13 TeV dσLO/dpT,V [pb/GeV]

• 0.7
• 0.6
• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 κNLO EW 10 2 10 3

• 0.1
• 0.05

0.05 0.1 pT,V [GeV] κVjj

NLO EW − κVj NLO EW

Bold estimate:

O(ααs)

Consider real correction to V+jet

' NLO EW to V+2jets

and we observe

' dσNLO EW dσLO

• V +2jet dσNLO EW

dσLO

• V +1jet

< ⇠ 1%

strong support for

• factorization
• multiplicative QCD x EW combination

Estimate of non-factorising contributions (tuned to cover above difference of EW K-factors )

SLIDE 34

• 4. Other issues (PDFs, ɣ-induced )

SLIDE 35

High-precision predictions for V+jet production Jonas M. Lindert

Photon-induced production

35

Z+jet W+jet

• photon-induced production irrelevant for Z+jet (and ɣ+jet)
• in W+jet O(5%) contribution with LUXqed (consistent with CT14qed)


(due to t-channel enhancement)

• ~1% uncertainties in photon PDFs due to LUXqed

ve~ 4 e- 3 w- d 1 u 5 w- a 2

LO qq+qg LUXqed LO qγ LUXqed LO qγ CT14qed inc LO qγ NNPDF30qed 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 qq+qg/qγ →Z(→ ℓ+ℓ−)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.05 0.1 0.15 0.2 pT,V [GeV] dσ/dσLO LO qq+qg LUXqed LO qγ LUXqed LO qγ CT14qed inc LO qγ NNPDF30qed 10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 1 10 1 qq+qg/qγ →W(→ ℓ− ¯ ν)+ jet @ 13 TeV dσ/dpT,V [pb/GeV] 10 2 10 3 0.05 0.1 0.15 0.2 pT,V [GeV] dσ/dσLO

SLIDE 36

PDFs

• small percent-level QED effects on qg/qq luminosities (included via LUXqed)

• 1.5-5% PDF uncertainties

SLIDE 37

Exclusive V+jets

SLIDE 38

High-precision predictions for V+jet production Jonas M. Lindert

soft W/Z q g

Interplay between QCD and EW

38

MUNICH + OpenLoops

j1 W+


 
 
 pT of jet

• “giant QCD K-factors” in the tail 


[Rubin, Salam, Sapeta ’10]

• dominated by dijet configurations
• positive 10-50% EW corrections from quark


bremsstrahlung 
 
 
 
 
 


⟹ pathologic with large uncertainties!

⟹ exclusive jet observables require
 merging W+1jet with W+2 jets at
 NLO QCD+EW!

pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

dσ/dpT [pb/GeV]

j1 / 103 W ∆φj1j2 < 3π/4 pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

NLO QCD×EW NLO QCD+EW NLO QCD LON

dσ/dpT [pb/GeV]

j1 / 103 W ∆φj1j2 < 3π/4 pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

dσ/dpT [pb/GeV]

j1 / 103 W pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

NLO QCD×EW NLO QCD+EW NLO QCD LON

dσ/dpT [pb/GeV]

j1 / 103 W pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

ℓ ¯ ℓ V V ′ ℓ ¯ ℓ V

⊗

SLIDE 39

High-precision predictions for V+jet production Jonas M. Lindert

MEPS@NLO QCD+EWvirt

39

pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT [GeV] pT,j1 dσ/dσNLO

QCD

2000 1000 500 200 100 50 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 pT,W dσ/dσNLO

QCD

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

dσ/dpT [pb/GeV]

j1 / 103 W pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

NLO QCD×EW NLO QCD+EW NLO QCD LON

dσ/dpT [pb/GeV]

j1 / 103 W pp → ℓ−¯ ν + 1j @ 13 TeV

100 10−3 10−6 10−9 10−12 10−15

MEPS@LO MEPS@NLO QCD MEPS@NLO QCD+EWvirt MEPS@NLO QCD+EWvirt w.o. LO mix 100 10–3 10–6 10–9 pp → ℓ− ¯ ν + 0,1,2 j @ 13 TeV dσ/dpT,j1 [pb/GeV] 50 100 200 500 1000 2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,j1 [GeV] dσ/dσNLO

QCD

MEPS@LO MEPS@NLO QCD MEPS@NLO QCD+EWvirt MEPS@NLO QCD+EWvirt w.o. LO mix 100 10–3 10–6 10–9 pp → ℓ− ¯ ν + 0,1,2 j @ 13 TeV dσ/dpT,V [pb/GeV] 50 100 200 500 1000 2000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 pT,V [GeV] dσ/dσNLO

QCD

• Stable NLO QCD+EW

predictions in all of the 
 phase-space…

• …including Parton-Shower

effects.

• Can directly be used by the

experimental collaborations
 


• pT, V : MEPS@NLO QCD+EW

in agreement with 
 QCDxEW (fixed-order) ★again: support for factorization!!

• pT, j1 : compensation between

negative Sudakov and LO mix

W- W- j1 j1

pT [GeV]

SLIDE 40

High-precision predictions for V+jet production Jonas M. Lindert

• monojet / MET+jets searches soon limited by V+jets background systematics
• MC reweighting allows to promote V + jet to NNLO QCD+(N)NLO EW:
• inclusion of EW corrections crucial due to large Sudakov logs
• Perturbative systematics in pTV under control at the level of 1-10% up to the TeV





• percent precision requires scrutiny of many subtleties and close TH/EXP interplay
• Experimental closure tests in control regions
• Applicability to other more exclusive observables / process classes

Conclusions

40

Outlook

SLIDE 41

https://indico.cern.ch/event/624982

SLIDE 42

BACKUP

SLIDE 43

High-precision predictions for V+jet production Jonas M. Lindert

Putting everything together

43

K(V )

TH (x, ~

"QCD, ~ "EW, "mix) = K(V )

TH,⊗(x, ~

"QCD, ~ "EW) + "mix K(V )

mix(x),

= " K(V )

NkLO(x) + 3

X

i=1

"QCD,i (i)K(V )

NkLO(x)

# × " 1 + (V )

EW(x) + 3

X

i=1

"(V )

EW,i (i)(V ) EW(x)

# + "mix K(V )

mix(x),

(45)

d dx(V )

TH (~

µ) = K(V )

TH (x, ~

µ) d dx(V )

LO QCD(~

µ0) + d dx(V )

γ−ind.(x, ~

µ) re

O d dx(V )

QCD = d

dx(V )

LO QCD + d

dx(V )

NLO QCD + d

dx(V )

NNLO QCD.

with nuisance parameters ~ "TH = (~ "QCD, ˆ ", ~ "EW, "γ)

202

d dxσ(V )

EW = d

dxσ(V )

NLO EW + d

dxσ(V )

Sudakov NNLO EW

SLIDE 44

High-precision predictions for V+jet production Jonas M. Lindert

NNLO for Z+jet

44

[Gehrmann-De Ridder, Gehrmann, Glover, A. Huss, Morgan; ‘16]

SLIDE 45

High-precision predictions for V+jet production Jonas M. Lindert

NNLO for W/Z+jet

45

• [Gehrmann-De Ridder, Gehrmann, 


Glover, A. Huss, Morgan; ‘16] [Boughezal, Liu, Petriello; ‘16]

Z+jet W+jet

• unprecedented reduction of scale uncertainties at NNLO: O(~ 5%)
• we can now check the correlation of the uncertainties going from NLO to NNLO

SLIDE 46

High-precision predictions for V+jet production Jonas M. Lindert

NNLO for Z/γ+jet

46

• MCFM

CMS

19.7 fb-1 (8 TeV)

||< μ= /γ

• /γ
• ⩾
• (σ/

)/(σ/ γ)

• []

/

[Campbell, Ellis, Williams; ’17]

NNLO/NLO ~ 1 for large pT!

SLIDE 47

High-precision predictions for V+jet production Jonas M. Lindert

Combination of NLO QCD and EW & Setup

Two alternatives: Difference between the two approaches indicates uncertainties due to missing two-loop 
 EW-QCD corrections of O(ααs)

σNLO

QCD+EW = σLO + δσNLO QCD + δσNLO EW ,

σNLO

QCD×EW = σNLO QCD

✓ 1 + δσNLO

EW

σLO ◆ = σNLO

EW

1 + δσNLO

QCD

σLO !

σNLO

QCD+EW

σNLO

QCD

= 1 + δσNLO

EW

σNLO

QCD

! ✓ ◆

Relative corrections w.r.t. NLO QCD:

σNLO

QCD×EW

σNLO

QCD

= ✓ 1 + δσNLO

EW

σLO ◆

“usual” NLO EW w.r.t. LO suppressed by large NLO QCD corrections

47

• in Gμ -scheme with 


α = √ 2 π GµM 2

W

✓ 1 − M 2

W

M 2

Z

◆

• stable. The electroweak coupl

Gµ = 1.16637×10−5 GeV−2, i

SLIDE 48

High-precision predictions for V+jet production Jonas M. Lindert

LUXqed

48

• [Manohar, Nason, Salam, Zanderighi, ’16]

SLIDE 49

pTV Z(→l l ̅ )+jets ɣ+jets Z(→ν̅ν)+jet W(→lν̅)+jets dσ/dpTV

1 TeV