Electroweak corrections for LHC physicsmschoenherr/talks/20141118_Freiburg.… · using universal splitting kernels K (t; z)/ s 2ˇt P phase space d 1 = t zd˚ 2ˇ J( ; ) emission

Electroweak effects in multijet merging Electroweak parton showers Electroweak corrections at NLO Conclusions

Electroweak corrections for LHC physics

Marek Schonherr

Universitat Zurich

Freiburg, 18/11/2014

Marek Schonherr Electroweak corrections for LHC physics 1/38


Introduction

Electroweak correction come in two variants: virtual corrections and realemission correction.

Virtual electroweak corrections often studied in the context of jetproduction at large transverse momentum (EW-Sudakov suppression).Usually negative and rising with p⊥.

Real electroweak corrections usually constitute a separate process.However, largest BR of W /Z bosons is hadronic, thus (almost)indistinguishable in jet production. Nonetheless may constitute signal initself.

When large scale differences occur resummation is needed in either case.Practically at LHC13/14 these scale differences are moderate.



Outline

1 Electroweak effects in multijet mergingQCD parton showers and multijet mergingMultijet merging beyond improving parton shower kernels

2 Electroweak parton showersConstruction of EW parton showersCase study: Finding W bosons inside jets

3 Electroweak corrections at NLOPreliminary: pp →W +jetsFirst results

4 Conclusions







4 Conclusions



QCD parton showers and multijet merging

Construction of a parton shower• approximate higher orders in (soft-)collinear limit

dσn+1(t, z , φ) ≈ dσn

∑ı

nspec∑s

dt dzdφ

2π

1

nspecJ(t, z) Kı(s)→ij(s)(t, z)

• using universal splitting kernels K(t, z) ∝ αs

2πt P(z)

• phase space dΦ1 = dt dz dφ2π J(t, z)

emission variable t, splitting variable z , azimuthal angle φ• spectators needed for local recoil,

also ensure colour coherence in non-angular ordered showers• construct emission probability at scale t

dPem(t) =dσn+1(t)

dσn=∑ı

nspec∑s

dt

∫dz

dφ

2π

1





Construction of a parton shower• approximate higher orders in (soft-)collinear limit

dσn+1(t, z , φ) ≈ dσn

∑ı

nspec∑s

dt dzdφ

2π

1


• using universal splitting kernels K(t, z) ∝ αs

2πt P(z)

• phase space dΦ1 = dt dz dφ2π J(t, z)

emission variable t, splitting variable z , azimuthal angle φ• spectators needed for local recoil,

also ensure colour coherence in non-angular ordered showers• construct emission probability at scale t

dPem(t) =dσn+1(t)

dσn=∑ı

nspec∑s

dt

∫dz

dφ

2π

1





Construction of a parton shower• emission probability at scale t

dPem(t) =dσn+1(t)

dσn=∑ı

nspec∑s

dt

∫dz

dφ

2π

1


• Poisson statistics leads to no-emission probability

Pno-em(t, t ′) = exp

−∑ı

nspec∑s

∫ t′

t

dt

∫dz

dφ

2π

1


→ Sudakov form factor ∆(t, t ′) = Pno-em(t, t ′)

⇒ probability of a parton produced at t ′ to radiate/resolve anotherparton at t

dP(t) = dPem(t)dPno-em(t, t ′) = dtd∆(t, t ′)

dt





dPem(t) =dσn+1(t)

dσn=∑ı

nspec∑s

dt

∫dz

dφ

2π

1




−∑ı

nspec∑s

∫ t′

t

dt

∫dz

dφ

2π

1





dt





dPem(t) =dσn+1(t)

dσn=∑ı

nspec∑s

dt

∫dz

dφ

2π

1




−∑ı

nspec∑s

∫ t′

t

dt

∫dz

dφ

2π

1





dt




Construction of a parton showerGeneral form

dσLOPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc

dt ′ Kn(t ′) ∆n(t ′, tmax)

]

• first term: probability of resolving no additional parton in [tmax, tc ]

• second term: probability and distribution of resolving another partonat scale t ′ (but not above)

• iterate:- approximate n + 2 parton matrix element by showering the n + 1parton expression, now t′ being the upper limit (strong ordering)

• Sudakov form factor: (soft-)collinear LL all-orders virtual correctionemission term: (soft-)collinear approximated real correction

• choose αs = αs(k2⊥) to resum certain class of higher logs from

1-loop running




Construction of a parton showerGeneral form

dσLOPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc

dt ′ Kn(t ′) ∆n(t ′, tmax)

]

• first term: probability of resolving no additional parton in [tmax, tc ]

• second term: probability and distribution of resolving another partonat scale t ′ (but not above)

• iterate:- approximate n + 2 parton matrix element by showering the n + 1parton expression, now t′ being the upper limit (strong ordering)

• Sudakov form factor: (soft-)collinear LL all-orders virtual correctionemission term: (soft-)collinear approximated real correction

• choose αs = αs(k2⊥) to resum certain class of higher logs from

1-loop running




Resummation properties of parton showers

Example: Drell-Yan production

tI

• core process: arbitrary scaleµR = µcore

• define initial conditions: settmax = tI

• first emission at t1 with αs(t1)

• second emission at t2 withαs(t2)

• third emission at t3 with αs(t3)


• strong orderingtI > t1 > t2 > t3 > t4 > tc






t1

tI













t2

t1

tI













t3

t2

t1

tI













t4

t3

t2

t1

tI











Improvements through merging• higher order real emission corrections in (soft-)collinear limit→ identify hard region, replace kernel with LO matrix element

dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc

dt ′ Kn(t ′) ∆n(t ′, tmax) Θ(Qcut − Q)

]+ dσLO

n+1 ∆n(t ′, tmax) Θ(Q − Qcut)

= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn

∆n(t ′, tmax) Θ(Q − Qcut)

]+ dσLO

n+1 Θ(t − tmax)

• need to identify scales ti in n + k matrix element to set scales in αs

⇒ must use inverse parton shower• Sudakovs must match ⇒ use trial showers





dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)







dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)







dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)







dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)







dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)







dσMEPS = dσLOn

[∆(tc , tmax) +

∫ tmax

tc


]+ dσLO


= dσLOn

[∆(tc , tmax) +

∫ tmax

tc


+

∫ tmax

tc

dt ′dσLO

n+1

dσLOn


]+ dσLO

n+1 Θ(t − tmax)






Improvements through merging

Example: Drell-Yan production in association with jets

• cluster external particlesusing inverse parton shower→ flavour conscious, initialstate aware, probabilitydetermined through splittingkernels

• identify a shower history(probabilistically), determinescale ti up to predefined tI

• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4

t3



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4

t3

t2



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4

t3

t2

t1



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4

t3

t2

t1

tI



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )






t4

t3

t2

t1µcore



• choose

αn+ks (µ2

R ) = αks (µ2

core)n∏

i=1

αs(ti )



Multijet merging beyond improving parton shower kernels


ME also provides expression beyond tmax

two types of configuration: pp → Z +jets and pp →jets+Z

Electroweak clustering

• different core process, naıvelynot part of pp → Z +jets butindistinguishable

• configuration that wouldhave arisen from dijets plusQCD+EW showering

• necessitates EW splittingkernels to calculate splittingprobability→ see next part

• leads to different scalechoices







t3












t3

t2












t2

t3

t1












t2

t3

t1

tI










vs.




Importance of electroweak clustering

QCD+EW clusteringstrict QCD ordering

10 1

10 2

10 3

10 4

Inclusive jet multiplicity (p⊥ > 20 GeV)

σ(≥

Nje

t)[p

b]

0 1 2 3 4 5

11.21.41.61.8

Njet

Rat

io

QCD+EW clusteringstrict QCD ordering

10−4

10−3

10−2

10−1

1

10 1

10 2

Transverse momentum of leading jet

dσ

/d

p ⊥(j

et1)

[pb/

GeV

]

10 2 10 3

11.21.41.61.8

p⊥(jet 1) [GeV]

Rat

io

⇒ large impact at high p⊥ and multiplicity




Importance of electroweak clustering

) [p

b]je

t N≥

) +

- l

+ l→

*(γ(Z

/σ

-310

-210

-110

1

10

210

310

410

510

610

= 7 TeV)sData 2011 (ALPGENSHERPAMC@NLO

+ SHERPAATHLACKB

ATLAS )µ)+jets (l=e,-l+ l→*(γZ/-1

L dt = 4.6 fb∫ jets, R = 0.4tanti-k

| < 4.4jet

> 30 GeV, |yjet

Tp

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

NLO

/ D

ata

0.60.8

11.21.4 + SHERPAATHLACKB

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

MC

/ D

ata

0.60.8

11.21.4 ALPGEN

jetN

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

MC

/ D

ata

0.60.8

11.21.4 SHERPA

[1/G

eV]

jet

T/d

pσ

) d

- l+ l

→* γZ

/σ

(1/

-710

-610

-510

-410

-310

-210

-110

= 7 TeV)sData 2011 (ALPGENSHERPAMC@NLO

+ SHERPAATHLACKB

ATLAS )µ 1 jet (l=e,≥)+ -l+ l→*(γZ/-1

L dt = 4.6 fb∫ jets, R = 0.4tanti-k

| < 4.4jet

> 30 GeV, |yjet

Tp

100 200 300 400 500 600 700

NLO

/ D

ata

0.60.8

11.21.4 + SHERPAATHLACKB

100 200 300 400 500 600 700

MC

/ D

ata

0.60.8

11.21.4 ALPGEN

(leading jet) [GeV]jetT

p100 200 300 400 500 600 700

MC

/ D

ata

0.60.8

11.21.4 SHERPA




Example: Forward-backward asymetry @ Tevatron

Hoche, Huang, Luisoni, MS, Winter Phys.Rev.D88(2013)1,014040

b

b

b

b

bc

bc

bc

bc

Parton level

Sherpa+GoSam

b CDF dataPhys. Rev. D87 (2013) 092002

bc DØ dataarXiv:1405.0421Meps@Nlo µcore = µQCDperturbative uncertaintyMeps@Nlo µcore = mttperturbative uncertainty

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7Rapidity dependent forward-backward asymmetry

∆y, tt

AFB(∆

y,tt)

b

b

b

b

bcbc

bcbc

bc

bc

Parton level

Sherpa+GoSam

b CDF dataPhys. Rev. D87 (2013) 092002

bc DØ dataarXiv:1405.0421

Meps@Nlo µcore = µQCDperturbative uncertaintyMeps@Nlo µcore = mttperturbative uncertainty

350 400 450 500 550 600 650 700 750

-0.4

-0.2

0

0.2

0.4

0.6

Mass dependent forward-backward asymmetry

mtt [GeV]

AFB(m

tt)

Chose two different µcore → largest impactElectroweak histories not an issue, but merging works nicely




Recent NNLO+NNLL results:Forward-backward asymetry @ Tevatron

Czakon, Fiedler, Mitov arXiv:1411.3007

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2

AFB

|∆Y|

mt=173.3 GeV

MSTW2008 pdf

NLONNLOCDFD0

-0.4

-0.2

0

0.2

0.4

0.6

350 400 450 500 550 600 650 700 750

AFB

Mtt [GeV]

mt=173.3 GeV

MSTW2008 pdf

NLONNLOCDFD0

MEPS@NLO result very well reproduced by higher order calculation







4 Conclusions



Construction of EW parton showers

Collinear limit with E � m

• approximation to collinear (vector) boson emission in limit E � m,in dipole language (splitter-spectator pairs): f (s)→ f (′)V (s)

dσn+V = dσn

∑f

nspec∑s

dt dzdφ

2π

1

nspecJ(t, z) Kf (s)→f (′)V (s)(t, z)

• emitter fermion f , suitable spectator s

• flavour change f → f ′ in case of W emissions

• IS kernels contain ratio of PDFs (change in x,Q,flavour)

• similar ansatz with diff. kernels in Christiansen, Sjostrand JHEP04(2014)115

• same ansatz as used for clustering in multijet merging




Choice of spectator

Role of the spectator:

• needed for momentum conservation in splitting 1(s)→ 2(s)

• colour coherence for soft emissions

Which particles are allowed as spectators?

• kernels are derived in collinear limit→ collinear emissions exhibit no coherence, any spectator would dofor momentum conservation

• to fit into dipole shower picture choose any other electroweakparticle, in particular any fermion




Splitting kernelsDenner, Hebenstreit unpublished

• use Denner-Hebenstreit expressions modified into CDST form

Kf (s)→f ′W (s)(t, z) =α

2πt

[fW cW

⊥ VCDSTf (s)→f ′b(s)(t, z) + fh cW

L12 (1− z)

]Kf (s)→fZ(s)(t, z) =

α

2πt

[fZ cZ⊥ VCDST

f (s)→fb(s)(t, z) + fh cZL

12 (1− z)

]• contain a transverse component as standard splitting functions→ in limit E � m revert to CDST splitting functions for emission ofa massless gauge boson

Catani, Dittmaier, Seymour, Trocsanyi Nucl.Phys.B627(2002)189-265

• contain a longitudinal component→ in limit E � m this is the emission of the corresponding scalarHiggs component/Goldstone boson

• construct phase space with massive bosons (fully differential)→ emulates some mass effects a la ACOT




Splitting kernelsDenner, Hebenstreit unpublished

• use Denner-Hebenstreit expressions modified into CDST form

Kf (s)→f ′W (s)(t, z) =α

2πt

[fW cW

⊥ VCDSTf (s)→f ′b(s)(t, z) + fh cW

L12 (1− z)

]Kf (s)→fZ(s)(t, z) =

α

2πt

[fZ cZ⊥ VCDST

f (s)→fb(s)(t, z) + fh cZL

12 (1− z)

]with

cW⊥ = seff

12s2

W|Vff ′ |2 , cZ

⊥ = seffs2

W

c2W

Q2f + (1− seff)

(I 3f −s2

W Qf )2

s2W c2

W,

cWL = 1

2s2W|Vff ′ |2

[seff

m2f ′

m2W

+ (1− seff)m2

f

m2W

], cZ

L =I 3f

s2W

m2f

m2W,

• couplings ff (′)V depend on spin of f , but standard parton showersare spin avaraged (no spin information)

• process dependent avarage spin of fermion line seff

⇒ pp → jj : seff = 12 , pp →W : seff = 1, undefined in general

• factors fW , fZ , fh modify couplings to test sensitivity




Interaction with QCD shower

Want to have simultaneous evolution of QCD+EW:→ emissions compete for phase space

• combined evolution kernel

Ktot(t, z) = KQCD(t, z) +KEW(t, z) +KQED(t, z)

⇒ emissions occur in correct proportions⇒ splittings into heavy bosons are suppressed at small t

How to embed decays into parton evolution?

• decay bosons immediately

• ensures that evolution of singlet q − q pair is consistently embedded

• neglects secondary splittings of the type W± →W±γ,W± →W±Z or Z →W±W∓



Case study: Finding W bosons inside jets

Krauss, Petrov, MS, Spannowsky Phys.Rev.D89(2014)114006

Can we see radiated W bosons inside jets at the LHC (14 TeV)?

• need high-p⊥ jets to produce real W bosons at sufficient rate

• need high-p⊥ jets to satisfy assumption E � m

Boosted analysis:

• isolated leptons (p⊥ > 25 GeV, |η| < 2.5, max. 10% in ∆R = 0.2)

• find jets (anti-k⊥, R = 1.5, p⊥ > 200 GeV) on remainder

• two cases: no isolated leptons ⇒ hadronic analysisone isolated lepton ⇒ leptonic analysis

• require further two jets with p⊥ > 500, 750, 1000 GeV to drive Wradiation into collinear region




Hadronic analysis• proposed three analysis

strategies, here method B

• recluster fat jets into C/A(R = 0.3, p⊥ > 20 GeV)microjets

• discard leading microjet aslikely from leading quark

• use m23 as em. gluons tendto be softer then decay prod.of em. W

• accept candidate ifm23 ∈ [70, 86] GeV

f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 500GeV

m23 [GeV]

dσ/d

m23[pb/2

GeV

]

1009080706050

3.4

3.2

3

2.8

2.6

2.4

2.2

2

1.8

1.6

1.4

⇒ large, but continuous QCD background, clear signal shape

⇒ more W emissions with hight p⊥, but peak shifts










f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 750GeV

m23 [GeV]

dσ/d

m23[pb/2

GeV

]

1009080706050

0.36

0.34

0.32

0.3

0.28

0.26

0.24

0.22

0.2












f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 1000GeV

m23 [GeV]

dσ/d

m23[pb/2

GeV

]

1009080706050

0.06

0.055

0.05

0.045

0.04

0.035






Hadronic analysis

• use event shape variables onmicrojets of reconstructed Wcandidate to enhance S/B,e.g. ellipticity

t =Tmin

Tmaj

→ small when radiationpattern is 1D (W → qq)

• fat jet p⊥ > 750 GeV optimalbest balance between crosssection and emission rate

f = 2.0

f = 1.1

f = 1.0

f = 0.0

pTJ> 750GeV

tdσ/d

t[pb/0.05]

10.80.60.40.20

2.5

2

1.5

1

0.5

0

⇒ additional discrimination




Hadronic analysis

Can we distinguish between f = 1 and f = 2?(simplified version of: How accurate can we measure the coupling?)

5.0%3.5%2.5%2.0%1.5%Syst. err.

500 GeVpTJ

>

m23

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4 5.0%3.5%2.5%2.0%1.5%Syst. err.

750 GeVpTJ

>

m23

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4 5.0%3.5%2.5%2.0%1.5%Syst. err.

1000 GeVpTJ

>

m23

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4

• signal: f = 2, background: f = 1 (SM)

• moderate sensitivity even under ideal conditionsbenefits from larger emission at large p⊥ despite smaller cross section




Leptonic analysis

• exactly one isolated lepton

• require /ET > 50 GeV

• reconstruct

mT =√

2ETl/ET (1− cos θ)

• accept candidate ifmT ∈ [60, 100] GeV

f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 500GeV

mT [GeV]

dσ/d

mT[pb/3

GeV

]

200150100500

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

⇒ provides good background rejection

⇒ loose some sensitivity for higher fat jet p⊥ as isolation iscompromised for more collinear W emissions




Leptonic analysis



• reconstruct

mT =√



f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 750GeV

mT [GeV]

dσ/d

mT[pb/3

GeV

]

200150100500

0.006

0.005

0.004

0.003

0.002

0.001

0






Leptonic analysis



• reconstruct

mT =√



f = 2.0

f = 1.1

f = 1.0

f = 0.0pTJ> 1000GeV

mT [GeV]

dσ/d

mT[pb/3

GeV

]

200150100500

0.0014

0.0012

0.001

0.0008

0.0006

0.0004

0.0002

0






Leptonic analysis

Can we distinguish between f = 1 and f = 1.1?(simplified version of: How accurate can we measure the coupling?)

5.0%3.5%2.5%2.0%1.5%Syst. err.

500 GeVpTJ

>

mT

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4 5.0%3.5%2.5%2.0%1.5%Syst. err.

750 GeVpTJ

>

mT

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4 5.0%3.5%2.5%2.0%1.5%Syst. err.

1000 GeVpTJ

>

mT

99.9%CL

95%CL

L [pb−1]

Confidence

Level

105104103102101100

100

10−1

10−2

10−3

10−4

• signal: f = 1.1, background: f = 1.0 (SM)

• improved sensitivity, despite small cross sections,benefits from ideal background rejection







4 Conclusions



Preliminary: pp → W +jets

Electroweak corrections at NLO

Kallweit, Lindert, Maierhofer, Pozzorini, MS in preparation

• fixed-order next-to-leading order electroweak corrections topp →W + 1, 2, 3 jets production in on-shell approximation

• OPENLOOPS for virtual corrections using COLLIER for tensor integralsDenner, Dittmaier, Hofer PoS LL2014(2014)071

• SHERPA or private code by S. Kallweit for Born, real emission,subtraction and phase space integration

• combine QCD and EW to leading pp →W + 1, 2, 3 process(O(αn

sα)) in two schemesQCD+EW: σNLO QCD+EW = σLO (1 + δQCD + δEW)QCD×EW: σNLO QCD×EW = σLO (1 + δQCD) (1 + δEW)

• use NNPDF2.3QED with LO QED PDFideally would need NLO QED PDF




Counting orders• same problem as in e.g. Dittmaier, Huss, Speckner JHEP11(2012)095

αnsα

m

α0sα

2α1sα

1

α0sα

1 pp → W + 0 jets

pp → W + 3 jets

pp → W + 2 jets

pp → W + 1 jet

α1sα

3

α1sα

2

α3sα

1

α2sα

1

α2sα

2 α0sα

4

α0sα

3

tree configuration

• consistent definition of orders and signature to be calculated needed





αnsα

m

α0sα

2α1sα

1

α0sα

1 pp → W + 0 jets

pp → W + 3 jets

pp → W + 2 jets

pp → W + 1 jet

α1sα

3

α1sα

2

α3sα

1

α2sα

1

α2sα

2 α0sα

4

α0sα

3

tree configuration






αnsα

m

α0sα

2α1sα

1

α0sα

1 pp → W + 0 jets

pp → W + 3 jets

pp → W + 2 jets

pp → W + 1 jet

α1sα

3

α1sα

2

α3sα

1

α2sα

1

α2sα

2 α0sα

4

α0sα

3

tree configuration






αnsα

m

α0sα

2α1sα

1

α0sα

1 pp → W + 0 jets

pp → W + 3 jets

pp → W + 2 jets

pp → W + 1 jet

α1sα

3

α1sα

2

α3sα

1

α2sα

1

α2sα

2 α0sα

4

α0sα

3

tree configuration+ two loop diagrams






αnsα

m

α0sα

2α1sα

1

α0sα

1 pp → W + 0 jets

pp → W + 3 jets

pp → W + 2 jets

pp → W + 1 jet

α1sα

3

α1sα

2

α3sα

1

α2sα

1

α2sα

2 α0sα

4

α0sα

3

tree configuration

+ two loop diagrams




First results

Preliminary results: pp → Wj

pT [GeV]

pT,j1

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j1

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + j @ 13TeV

103

100

10−3

10−6

10−9

10−12NLO QCD×EWNLO QCD+EWNLO QCDLON

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + j @ 13TeV

103

100

10−3

10−6

10−9

10−12

pT [GeV]

pT,j1

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j1

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j1/103

W+

dσ/d

pT[pb/G

eV]

∆φj1j2 < 3π/4

pp → W+ + j @ 13TeV

103

100

10−3

10−6

10−9

10−12NLO QCD×EWNLO QCD+EWNLO QCDLON

j1/103

W+

dσ/d

pT[pb/G

eV]

∆φj1j2 < 3π/4

pp → W+ + j @ 13TeV

103

100

10−3

10−6

10−9

10−12



First results

Preliminary results: pp → Wjj

pT [GeV]

pT,j2

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j2

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + 2j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18 NLO QCD×EWNLO QCD+EWNLO QCDLON

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + 2j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18

pT [GeV]

pT,j2

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j2

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

HT,tot > 2TeV

pp → W+ + 2j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18

NLO QCD×EWNLO QCD+EWNLO QCDLON

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

HT,tot > 2TeV

pp → W+ + 2j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18



First results

Preliminary results: pp → Wjj

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

dσ/d

∆φj 1j 2[pb]

pp → W+ + jj @ 13TeV

5000

2000

1000

500


dσ/d

∆φj 1j 2[pb]


5000

2000

1000

500

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

dσ/d

∆φj 1j 2[pb]

HT,tot > 2TeV


2

1

0.5

0.2

0.1

0.05

0.02


dσ/d

∆φj 1j 2[pb]

HT,tot > 2TeV


2

1

0.5

0.2

0.1

0.05

0.02



First results

Preliminary results: pp → Wjjj

pT [GeV]

pT,j3

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j3

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT,j2

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j2

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j3/109

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + 3j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18 NLO QCD×EWNLO QCD+EWNLO QCDLON

j3/109

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

pp → W+ + 3j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18

pT [GeV]

pT,j3

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT [GeV]

pT,j3

σ/σNLO

QCD

2000100050020010050

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

pT,j2

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j2

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2 pT,j1

σ/σNLO

QCD

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

σ/σNLO

QCD

pT,W+

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

j3/109

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

HT,tot > 2TeV

pp → W+ + 3j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18


j3/109

j2/106

j1/103

W+

dσ/d

pT[pb/G

eV]

HT,tot > 2TeV

pp → W+ + 3j @ 13TeV

103

100

10−3

10−6

10−9

10−12

10−15

10−18



First results

Preliminary results: pp → Wjjj

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

dσ/d

∆φj 1j 2[pb]

pp → W+ + jjj @ 13TeV

2000

1000

500

200

100


dσ/d

∆φj 1j 2[pb]


2000

1000

500

200

100

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

∆φj1j2

σ/σNLO

QCD

π3π4

π2

π40

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

dσ/d

∆φj 1j 2[pb]

HT,tot > 2TeV


2

1

0.5

0.2

0.1

0.05

0.02

0.01


dσ/d

∆φj 1j 2[pb]

HT,tot > 2TeV


2

1

0.5

0.2

0.1

0.05

0.02

0.01



Conclusions

• electroweak effects are important at LHC at 13/14 TeV

• become large whenever the scale is large compared the electroweakscale

• should be incorporated in multijet merging to correctly describe theregions where a given configuration is rather a electroweakcorrection to a QCD process than a QCD correction to anelectroweak process (pp →W + jets vs. pp → jets + W )

• QCD+QED combined merging methods exist

• proper QCD+EW merging methods need to be defined

• automation of NLO EW follows on the heels of NLO QCD→ much more care with consistent schemes and order counting



Thank you for your attention!



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