Multijet merging and jet substructure - Durham...

Multijet merging Jet properties Conclusions

Multijet merging and jet substructure

Marek Schönherr

Institute for Particle Physics Phenomenology

BOOST, London, 20/08/2014

Marek Schönherr IPPP Durham

Multijet merging and jet substructure 1/23


Introduction

Two aspects of event generation are important for boosted observables

1 production of boosted systems• production of hard jets or boosted heavy resonances usually requires

(multiple) jets to recoil against• jet/resonance production at large p⊥ is usually accompagnied by (many)

additional jets

⇒ multijet merging to describe such topologies

2 description of intrajet dynamics• parton evolution well described by parton shower• contributions from multiple interactions• important aspects from hadronisation and hadron decays

⇒ multijet merging must not upset parton shower resummation⇒ good soft-physics models important at high scales as well




Terminology

LOPS/NLOPS matching ⇒ see Keith’s talk• combine LO/NLO description of a single process with parton shower→ only this one process described to LO/NLO accuracy→ subsequent multiplicities added at PS-accuracy

• multiple schemes, different ways to resolve overlap of competingdescriptions

• examples: pp→ h, pp→W + j, ...Multijet merging

• combine multiple LOPS (→MEPS)/NLOPS (→MEPS@NLO) of subsequentmultiplicity→ resums emission scale hierarchies identical to parton shower→ wrt. the most inclusive process considered→ corrects hard emission of jets to LO/NLO accuracy

• multiple schemes, different ways to resolve overlap of competingdescriptions

• examples: pp→ h+jets, pp→ tt̄+jets, ...Marek Schönherr IPPP Durham



MEPSPS LO

LO

LO

Parton showers

resummation of (soft-)collinear limit→ intrajet evolution

• matrix elements (ME) and parton showers (PS) are approximations indifferent regions of phase space

• MEPS combines multiple LOPS – keeping either accuracy• NLOPS elevate LOPS to NLO accuracy• MENLOPS supplements core NLOPS with higher multiplicities LOPS




MEPS

ME

LO LO LO LO

Matrix elements

fixed-order in αs→ hard wide-angle emissions→ interference terms






MEPS

ME

PS LO

LO

LO

LO

LO

LO LO

MEPS (CKKW-like)

Catani, Krauss, Kuhn, Webber JHEP11(2001)063

Lönnblad JHEP05(2002)046

Höche, Krauss, Schumann, Siegert JHEP05(2009)053

Hamilton, Richardson, Tully JHEP11(2009)038






MEPS

ME

PS LO

LO

LO

LO

LO

LO LO

MEPS (CKKW-like)

Catani, Krauss, Kuhn, Webber JHEP11(2001)063

Lönnblad JHEP05(2002)046

Höche, Krauss, Schumann, Siegert JHEP05(2009)053

Hamilton, Richardson, Tully JHEP11(2009)038


• MEPS combines multiple LOPS – keeping either accuracy• NLOPS elevate LOPS to NLO accuracy• MENLOPS supplements core NLOPS with higher multiplicities LOPSα

k+ns (µR) = α

ks (µcore)αs(t1) · · ·αs(tn)




MEPS

pp → h + jetsLoPs

0 50 100 150 200 250 30010−4

10−3

10−2

10−1

Transverse momentum of the Higgs boson

p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]

• first emission by PS,restrict toQn+1 < Qcut

• LOPS pp→ h+ jetfor Qn+1 > Qcut

• restrict emission offpp→ h+ jet toQn+2 < Qcut

• LOPS pp→ h+ 2jetsfor Qn+2 > Qcut

• iterate• sum all contributions• eg. p⊥(h)>200 GeV

has contributions fr.multiple topologies




MEPS

pp → h + jetspp → h + 0j

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS

pp → h + jetspp → h + 0jpp → h + 1j

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS

pp → h + jetspp → h + 0jpp → h + 1jpp → h + 2j

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS

pp → h + jetspp → h + 0jpp → h + 1jpp → h + 2jpp → h + 3j

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS@NLOPS NLO

NLO

NLO

NLOPS (MC@NLO,POWHEG)

Frixione, Webber JHEP06(2002)029

Nason JHEP11(2004)040, Frixione et.al. JHEP11(2007)070

Höche, Krauss, MS, Siegert JHEP09(2012)049


• MEPS combines multiple LOPS – keeping either accuracy• NLOPS elevate LOPS to NLO accuracy• MENLOPS supplements core NLOPS with higher multiplicities LOPS•




MEPS@NLOME

PS NLO

NLO

NLO

LO

LO

LO LO

MENLOPS (CKKW-like)

Hamilton, Nason JHEP06(2010)039


Gehrmann, Höche, Krauss, MS, Siegert JHEP01(2013)144


• MEPS combines multiple LOPS – keeping either accuracy• NLOPS elevate LOPS to NLO accuracy• MENLOPS supplements core NLOPS with higher multiplicities LOPS•




MEPS@NLOME

PS NLO

NLO

NLO

NLO

NLO

NLO NLO

MEPS@NLO (CKKW-like)

Lavesson, Lönnblad JHEP12(2008)070



Lönnblad, Prestel JHEP03(2013)166

Plätzer JHEP08(2013)114


• MEPS combines multiple LOPS – keeping either accuracy• NLOPS elevate LOPS to NLO accuracy• MENLOPS supplements core NLOPS with higher multiplicities LOPS• MEPS@NLO combines multiple NLOPS – keeping either accuracy




MEPS@NLO

pp → h + jetsSherpa S-MC@NLO

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]

• first emission byNLOPS , restrict toQn+1 < Qcut

• NLOPS pp→ h+ jetfor Qn+1 > Qcut


• NLOPSpp→ h+ 2jets forQn+2 > Qcut






MEPS@NLO

pp → h + jetspp → h + 0j @ NLO

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS@NLO

pp → h + jetspp → h + 0j @ NLOpp → h + 1j @ NLO

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS@NLO

pp → h + jetspp → h + 0j @ NLOpp → h + 1j @ NLOpp → h + 2j @ NLO

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










MEPS@NLO

pp → h + jetspp → h + 0j @ NLOpp → h + 1j @ NLOpp → h + 2j @ NLOpp → h + 3j @ LO

0 50 100 150 200 250 30010−4

10−3

10−2

10−1


p⊥(h) [GeV]

dσ

/dp ⊥

[pb/

GeV

]










Recent results in SHERPA

Multijet merging at NLO accuracy (MEPS@NLO)

• pp→W + jets – SHERPA+BLACKHAT Höche, Krauss, MS, Siegert JHEP04(2013)027• e+e− → jets – SHERPA+BLACKHAT


• pp→ h+ jets – SHERPA+GOSAM/MCFMHöche, Krauss, MS, Siegert, contribution to YR3 arXiv:1307.1347

Höche, Krauss, MS arXiv.1401.7971

MS, Zapp, contribution to LH13 arXiv:1405.1067

• pp̄→ tt̄+ jets – SHERPA+GOSAM/OPENLOOPSHöche, Huang, Luisoni, MS, Winter Phys.Rev.D88(2013)014040

Höche, Krauss, Maierhöfer, Pozzorini, MS, Siegert arXiv:1402.6293

• pp→ 4`+ jets – SHERPA+OPENLOOPSCascioli, Höche, Krauss, Maierhöfer, Pozzorini, Siegert JHEP01(2014)046

• pp→ V H+ jets, pp→ V V + jets, pp→ V V V + jets– SHERPA+OPENLOOPS

Höche, Krauss, Pozzorini, MS, Thompson, Zapp Phys.Rev.D89(2014)114006




pp→ tt̄+jetsHöche, Krauss, Maierhöfer, Pozzorini, MS, Siegert in arXiv:1401.7971

Sherpa+OpenLoops

pl-jet⊥ > 40 GeV

pl-jet⊥ > 60 GeV×0.1

pl-jet⊥ > 80 GeV×0.01

[email protected] × MEPS@LOS-MC@NLO

0 1 2 3

10−5

10−4

10−3

10−2

10−1

1Inclusive light jet multiplicity

Nl-jet

σ(≥

Nl-

jet)

[pb]

pp→ tt̄+jets (0,1,2 @ NLO; 3 @ LO)• scales:α2+ns (µR) = α

2s(µcore)

n∏i=1

αs(ti),

µF = µQ = µcore on 2→ 2Qcut = 30 GeV

µcore = −2

1p0p1

+ 1p0p2 +1

p0p3

• µR/F ∈ [ 12 , 2]µdefR/F• µQ ∈ [ 1√2 ,

√2]µdefQ

• Qcut ∈ {20, 30, 40} GeV• spin-correlated dileptonic decays

at LO accuracy




pp→ tt̄+jets

Sherpa+OpenLoops

[email protected] × MEPS@LO

S-MC@NLO

10−6

10−5

10−4

10−3

10−2Transverse momentum of reconstructed top quark

dσ

/d

p T[p

b/G

eV]

0 100 200 300 400 500 600

0.5

1

1.5

pT (top) [GeV]

Rat

ioto

ME

PS@

NL

O

pp→ tt̄+jets (0,1,2 @ NLO; 3 @ LO)Reconstructed top p⊥

• again, shapes are stable• noticable reduction in

uncertainty

• inclusive observable, but largenumber of events with ≥1 jetnecessitates mutlijet merging forbest accuracy




pp→ tt̄+jets

Sherpa+OpenLoops

pp → tt̄ excl.pp → tt̄ + 1j excl.pp → tt̄ + 2j excl.pp → tt̄ + 3j incl.

MEPS@NLO

10−6

10−5

10−4

10−3

10−2Transverse momentum of reconstructed top quark

dσ

/d

p T[p

b/G

eV]

0 100 200 300 400 500 600

0.5

1

pT (top) [GeV]

Rat

ioto

ME

PS@

NL

O

pp→ tt̄+jets (0,1,2 @ NLO; 3 @ LO)Reconstructed top p⊥

• again, shapes are stable• noticable reduction in

uncertainty

• inclusive observable, but largenumber of events with ≥1 jetnecessitates mutlijet merging forbest accuracy




pp→ tt̄+jets

Sherpa+OpenLoops

[email protected] × MEPS@LO

S-MC@NLO

10−5

10−4

10−3

Total transverse energy

dσ

/d

Hto

tT

[pb/

GeV

]

200 400 600 800 1000 1200

0.5

1

1.5

HtotT [GeV]

Rat

ioto

ME

PS@

NL

O

pp→ tt̄+jets (0,1,2 @ NLO; 3 @ LO)Total transverse energyH totT =

∑b-jets

p⊥+∑l-jets

p⊥+∑lep

p⊥+EmissT

• relevant observable for newphysics searches

• slight correction to MEPS shapesat high H totT

• noticable reduction in uncert.,especially at high H totT

• inclusive observable, butdominated by configurationswith different number of jets atsuccessively higher H totT




pp→ tt̄+jets

Sherpa+OpenLoops

MEPS@NLOpp → tt̄ excl.pp → tt̄ + j excl.pp → tt̄ + 2j excl.pp → tt̄ + 3j incl.

10−6

10−5

10−4

10−3

10−2Total transverse energy

dσ

/d

Hto

tT

[pb/

GeV

]

200 400 600 800 1000 1200

0.5

1

HtotT [GeV]

Rat

ioto

ME

PS@

NL

O

pp→ tt̄+jets (0,1,2 @ NLO; 3 @ LO)Total transverse energyH totT =

∑b-jets

p⊥+∑l-jets

p⊥+∑lep

p⊥+EmissT

• relevant observable for newphysics searches

• slight correction to MEPS shapesat high H totT

• noticable reduction in uncert.,especially at high H totT

• inclusive observable, butdominated by configurationswith different number of jets atsuccessively higher H totT




Jet properties

Jet production comprises contributions from all energy regimes:

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• perturbative contributions- hard seed parton(s) → fixed order matrix elements- soft & collinear emissions (parton shower w/ colour coherence)

• non-perturbative contributions- (uncorrelated) contributions from additional partonic interactions- hadronisation and hadron decays

⇒ small scale contributions especially important for intrajet observables

• necessity to describe intrajet observables well to be useful in jetsubstructure analysis

• need to describe hard emissions well• recoil to produce boosted heavy particles (production xsecs/dists)• good chance they will end up in same fat jet (Qcut usally k⊥-type)

⇒ multijet merging must preserve soft physicsMarek Schönherr IPPP Durham



Jet shapes – differential jet shape ρ(r)

0.1 0.2 0.3 0.4 0.5

(r)

ρ

-110

1

10 jets, R = 0.6

tanti-k

< 160 GeVT

p110 GeV <

| < 2.8y|

ATLAS

Data

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2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

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Data

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1.20.1 0.2 0.3 0.4 0.5

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Data

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2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

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Data

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1.2

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ρ

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2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

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Data

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(r)

ρ

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p60 GeV <

| < 2.8y|

ATLAS

Data

6)→Sherpa 1.2.3 (2

2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

r0 0.1 0.2 0.3 0.4 0.5 0.6

Data

/MC

0.81

1.2

ATLAS collaboration Phys.Rev.D83(2011)052003, ATL-PHYS-PUB-2011-010





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b

b

b

bb

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10−1

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ρ(r)

b b b b b b

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b

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ATLAS data Phys.Rev.D83(2011)052003





b

b

b

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Jet shapes – integrated jet shape 1−Ψ(r = 0.3)

0.5 1 1.5 2 2.5

(r =

0.3

)Ψ

1 -

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14 jets, R = 0.6

tanti-k

< 160 GeVT

p110 GeV <

ATLAS

Data 6)→Sherpa 1.2.3 (2 2)→Sherpa 1.2.3 (2 2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

|y|

0 0.5 1 1.5 2 2.5

Data

/MC

0.60.8

11.21.4 0.5 1 1.5 2 2.5

(r =

0.3

)Ψ

1 -

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11 jets, R = 0.6

tanti-k

< 260 GeVT

p210 GeV <

ATLAS


ALPGEN+PYTHIA

|y|

0 0.5 1 1.5 2 2.5

Data

/MC

0.60.8

11.21.4

0.5 1 1.5 2 2.5

(r =

0.3

)Ψ

1 -

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.32

jets, R = 0.6t

anti-k

< 40 GeVT

p30 GeV <

ATLAS


ALPGEN+PYTHIA

|y|

0 0.5 1 1.5 2 2.5

Data

/MC

0.60.8

11.21.4 0.5 1 1.5 2 2.5

(r =

0.3

)Ψ

1 -

0.08

0.1

0.12

0.14

0.16

0.18

0.2 jets, R = 0.6

tanti-k

< 80 GeVT

p60 GeV <

ATLAS


ALPGEN+PYTHIA

|y|

0 0.5 1 1.5 2 2.5

Data

/MC

0.60.8

11.21.4





Jet shapes – integrated jet shape 1−Ψ(r = 0.3)

100 200 300 400 500 600

(r =

0.3

)Ψ

1 -

0.05

0.1

0.15

0.2

0.25

0.3 jets, R = 0.6

tanti-k

| < 2.8y2.1 < |

ATLAS

Data

6)→Sherpa 1.2.3 (2

2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

(GeV)T

p

0 100 200 300 400 500 600

Data

/MC

0.60.8

11.21.4 100 200 300 400 500 600

(r =

0.3

)Ψ

1 -

0.05

0.1

0.15

0.2

0.25

0.3 jets, R = 0.6

tanti-k

| < 2.8y|

ATLAS

Data

6)→Sherpa 1.2.3 (2

2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

(GeV)T

p

0 100 200 300 400 500 600

Data

/MC

0.60.8

11.21.4

100 200 300 400 500 600

(r =

0.3

)Ψ

1 -

0.05

0.1

0.15

0.2

0.25

0.3 jets, R = 0.6

tanti-k

| < 0.3y|

ATLAS

Data

6)→Sherpa 1.2.3 (2

2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

(GeV)T

p

0 100 200 300 400 500 600

Data

/MC

0.60.8

11.21.4 100 200 300 400 500 600

(r =

0.3

)Ψ

1 -

0.05

0.1

0.15

0.2

0.25

0.3 jets, R = 0.6

tanti-k

| < 1.2y0.8 < |

ATLAS

Data

6)→Sherpa 1.2.3 (2

2)→Sherpa 1.2.3 (2

2)→Sherpa 1.3.0 (2

ALPGEN+PYTHIA

(GeV)T

p

0 100 200 300 400 500 600

Data

/MC

0.60.8

11.21.4





Jet shapes – integrated jet shape Ψ(r)

b

bb

b bb


0

0.2

0.4

0.6

0.8

1

1.2Jet shape Ψ for p⊥ ∈ 110–160 GeV, y ∈ 1.2–2.1

Ψ(r)

b b b b b b

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0.81

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Jet shapes – integrated jet shape Ψ(r)

b

bb b

b b


0

0.2

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Ψ(r)

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Jet substructure – background mis-tag rate

BOOST2011 arXiv:1201.0008

Multijet background mis-tag rate in pp→ tt̄+ jets production

0.1 0.2 0.3 0.4 0.5 0.6 0.7Signal efficiency

10-3

10-2

10-1

Back

gro

und m

is-t

ag

ATLASCMSHEPJHNSubPrunedTWTrimmed

0.1 0.2 0.3 0.4 0.5 0.6 0.7Signal efficiency

10-3

10-2

10-1

Back

gro

und m

is-t

ag

ATLASCMSHEPJHNSubPrunedTWTrimmed

• need to properly describe additional hard radiation that can end up in thefat jet leading to large (sub-)jet masses

• otherwise mis-tag rates etc. underestimated

no multijet merging

pp→ jj

multijet merging

pp→ jj + up to 4j




Jet substructure – signal observables

BOOST2012 arXiv:1311.2708

pp→ tt̄+ jets production

• some observablesvery sensitive toadditional hardradiation

• can be reduced byvarious techniques,but effects remain intails




Conclusions

Multijet merging

• describes both hard radiation and intrajet evolution→ reliable estimate of event yields→ good description of jet substructure

• for large cone radii and/or high boosts partons of large relative k⊥, Qij ,etc. land in the fat jet→ multijet merging must preserve resum. accuracy to describe these configs

⇒ tool of choice for boosted observables• various formulations and implementations exist• accuracy for hard emissions has recently been elevated to NLO

accuracy for soft-collinear resummation remains at (N)LL

SHERPA: current release SHERPA-2.1.1http://sherpa.hepforge.org



http://sherpa.hepforge.org


Thank you for your attention!




MEPS

Parton showers (operate in Nc →∞ limit):

PSn(tc, tmax) = ∆n(tc, tmax) +

∫ tmaxtc

dt′Kn(t′) ∆n(t′, tmax)

Multijet merging at leading order:

dσMEPS = dσLOn ⊗ PSn Θ(Qcut −Qn+1)+ dσLOn+1 Θ(Qn+1 −Qcut) ∆n(tn+1, tn) ⊗ PSn+1 Θ(Qcut −Qn+2)+ dσLOn+2 Θ(Qn+2 −Qcut) ∆n(tn+1, tn) ∆n+1(tn+2, tn+1) ⊗ PSn+2

• restrict the parton shower on 2→ n to emit only below Qcut• arbitrary jet measure Qn = Qn(Φn)• add the n+ 1 ME and its parton shower• multiply by Sudakov wrt. 2→ n process to restore resummation• iterate• if tn(Φn) 6= Qn(Φn) truncated shower needed to fill gaps




MEPS



∫ tmaxtc




• restrict the parton shower on 2→ n to emit only below Qcut• arbitrary jet measure Qn = Qn(Φn)• add the n+ 1 ME and its parton shower• multiply by Sudakov wrt. 2→ n process to restore resummation• iterate• if tn(Φn) 6= Qn(Φn) truncated shower needed to fill gaps

αk+ns (µR) = αks (µcore)αs(t1) · · ·αs(tn)




MEPS



∫ tmaxtc




• restrict the parton shower on 2→ n to emit only below Qcut• arbitrary jet measure Qn = Qn(Φn)• add the n+ 1 ME and its parton shower• multiply by Sudakov wrt. 2→ n process to restore resummation• iterate• if tn(Φn) 6= Qn(Φn) truncated shower needed to fill gaps Nason JHEP11(2004)040




MEPS@NLO

Parton showers for NLOPS (need to reproduce Nc = 3 singular limits for 1st em.):

P̃Sn(tc, tmax) = ∆̃n(tc, tmax) +

∫ tmaxtc

dt′K̃n(t′) ∆̃n(t′, tmax)

Multijet merging at next-to-leading order:

dσMEPS@NLO = dσNLOn ⊗ P̃Sn Θ(Qcut −Qn+1)+ dσNLOn+1 Θ(Qn+1 −Qcut)

(∆n(tn+1, tn) −∆(1)n (tn+1, tn)

)⊗ P̃Sn+1 Θ(Qcut −Qn+2)

+ dσNLOn+2 Θ(Qn+2 −Qcut)(

∆n(tn+1, tn)−∆(1)n (tn+1, tn))

×(

∆n+1(tn+2, tn+1)−∆(1)n+1(tn+2, tn+1))⊗ P̃Sn+2

• NLOPS for 2→ n, restricted to emit only below Qcut• add the NLOPS for 2→ n+ 1• multiply by Sudakov wrt. 2→ n process to restore resummation• remove overlap of ∆n and dσNLOn+1, iterate• if tn(Φn) 6= Qn(Φn) truncated shower needed to fill gaps




MEPS@NLO

Parton showers for NLOPS (need to reproduce Nc = 3 singular limits for 1st em.):

P̃Sn(tc, tmax) = ∆̃n(tc, tmax) +

∫ tmaxtc

dt′K̃n(t′) ∆̃n(t′, tmax)

Multijet merging at next-to-leading order:

dσMEPS@NLO = dσNLOn ⊗ P̃Sn Θ(Qcut −Qn+1)+ dσNLOn+1 Θ(Qn+1 −Qcut)

(∆n(tn+1, tn) −∆(1)n (tn+1, tn)

)⊗ P̃Sn+1 Θ(Qcut −Qn+2)

+ dσNLOn+2 Θ(Qn+2 −Qcut)(

∆n(tn+1, tn)−∆(1)n (tn+1, tn))

×(

∆n+1(tn+2, tn+1)−∆(1)n+1(tn+2, tn+1))⊗ P̃Sn+2

• NLOPS for 2→ n, restricted to emit only below Qcut• add the NLOPS for 2→ n+ 1• multiply by Sudakov wrt. 2→ n process to restore resummation• remove overlap of ∆n and dσNLOn+1, iterate

αn+ks (µR) = αks (µcore)αs(t1) · · ·αs(tn)




MENLOPS

dσMENLOPS = dσNLOn ⊗ P̃Sn Θ(Qcut −Qn+1)+ kn(Φn+1) dσ

LOn+1 Θ(Qn+1 −Qcut) ∆n(tn+1, tn)

⊗ PSn+1 Θ(Qcut −Qn+2)+ kn(Φn+1(Φn+2)) dσ

LOn+2 Θ(Qn+2 −Qcut)

×∆n(tn+1, tn) ∆n+1(tn+2, tn+1) ⊗ PSn+2

• restrict MC@NLO expression to region Q < Qcut• add in real radiation explicitly, as in MEPS• restore logarithmic behaviour by explicit Sudakov• local K-factor for continuity at Qcut

kn(Φn+1) =B̄n (Φn(Φn+1))

Bn (Φn(Φn+1))

(1− Hn(Φn+1)

Rn(Φn+1)

)+

Hn(Φn+1)

Rn(Φn+1)

• iterateMarek Schönherr IPPP Durham



Scale choices

CKKW scales

αn+ks (µ2R) = α

ks (µ

2core)αs(t1) · · ·αs(tn) µ2F,a/b = text,a/b µ2Q = µ2core

Free choices

1 µcore – scale of core process identified through clustering with inverseparton shower

2 µR/F beyond 1-loop running

- calculate with chosen µR/F- include renormalisation and factorisation terms to shift the 1-loop running

to above

Bnαs(µR)

πβ0

(log

µRµR,CKKW

)n+kand

Bnαs2π

logµFtext

∑c=q,g

∫ 1xa

dz

zPac(z)fc(xa/z, µ

2F )

→ same as in UNLOPS Lönnblad, Prestel JHEP03(2013)166, Plätzer JHEP08(2013)114Marek Schönherr IPPP Durham


Multijet mergingJet propertiesConclusions

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