multijet merging and jet substructure - durham...
TRANSCRIPT
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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
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 2/23
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 2/23
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Multijet merging Jet properties Conclusions
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
Multijet merging and jet substructure 3/23
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 4/23
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Multijet merging Jet properties Conclusions
MEPS
ME
LO LO LO LO
Matrix elements
fixed-order in αs→ hard wide-angle emissions→ interference terms
• 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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 4/23
-
Multijet merging Jet properties Conclusions
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
• 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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 4/23
-
Multijet merging Jet properties Conclusions
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
• 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 LOPSα
k+ns (µR) = α
ks (µcore)αs(t1) · · ·αs(tn)
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 4/23
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
MEPS
pp → h + jetspp → h + 0j
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
MEPS
pp → h + jetspp → h + 0jpp → h + 1j
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
MEPS
pp → h + jetspp → h + 0jpp → h + 1j
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
MEPS
pp → h + jetspp → h + 0jpp → h + 1jpp → h + 2j
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
MEPS
pp → h + jetspp → h + 0jpp → h + 1jpp → h + 2j
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
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
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
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
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
-
Multijet merging Jet properties Conclusions
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
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 5/23
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Multijet merging Jet properties Conclusions
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
• 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•
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 6/23
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Multijet merging Jet properties Conclusions
MEPS@NLOME
PS NLO
NLO
NLO
LO
LO
LO LO
MENLOPS (CKKW-like)
Hamilton, Nason JHEP06(2010)039
Höche, Krauss, MS, Siegert JHEP08(2011)123
Gehrmann, Höche, Krauss, MS, Siegert JHEP01(2013)144
• 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•
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 6/23
-
Multijet merging Jet properties Conclusions
MEPS@NLOME
PS NLO
NLO
NLO
NLO
NLO
NLO NLO
MEPS@NLO (CKKW-like)
Lavesson, Lönnblad JHEP12(2008)070
Höche, Krauss, MS, Siegert JHEP04(2013)027
Gehrmann, Höche, Krauss, MS, Siegert JHEP01(2013)144
Lönnblad, Prestel JHEP03(2013)166
Plätzer JHEP08(2013)114
• 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@NLO combines multiple NLOPS – keeping either accuracy
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 6/23
-
Multijet merging Jet properties Conclusions
MEPS@NLOME
PS NLO
NLO
NLO
NLO
NLO
NLO NLO
MEPS@NLO (CKKW-like)
Lavesson, Lönnblad JHEP12(2008)070
Höche, Krauss, MS, Siegert JHEP04(2013)027
Gehrmann, Höche, Krauss, MS, Siegert JHEP01(2013)144
Lönnblad, Prestel JHEP03(2013)166
Plätzer JHEP08(2013)114
• 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@NLO combines multiple NLOPS – keeping either accuracy
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 6/23
-
Multijet merging Jet properties Conclusions
MEPS@NLO
pp → h + jetsSherpa S-MC@NLO
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 byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
MEPS@NLO
pp → h + jetspp → h + 0j @ NLO
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 byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Transverse momentum of the Higgs boson
p⊥(h) [GeV]
dσ
/dp ⊥
[pb/
GeV
]
• first emission byNLOPS , restrict toQn+1 < Qcut
• NLOPS pp→ h+ jetfor Qn+1 > Qcut
• restrict emission offpp→ h+ jet toQn+2 < Qcut
• NLOPSpp→ h+ 2jets forQn+2 > Qcut
• iterate• sum all contributions• eg. p⊥(h)>200 GeV
has contributions fr.multiple topologies
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 7/23
-
Multijet merging Jet properties Conclusions
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
Gehrmann, Höche, Krauss, MS, Siegert JHEP01(2013)144
• 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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 8/23
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 9/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 10/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 10/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 11/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 11/23
-
Multijet merging Jet properties Conclusions
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
Multijet merging and jet substructure 12/23
-
Multijet merging Jet properties Conclusions
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
Multijet merging and jet substructure 12/23
-
Multijet merging Jet properties Conclusions
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
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
1.20.1 0.2 0.3 0.4 0.5
(r)
ρ
-110
1
10 jets, R = 0.6
tanti-k
< 260 GeVT
p210 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
0.1 0.2 0.3 0.4 0.5
(r)
ρ
-110
1
10 jets, R = 0.6
tanti-k
< 40 GeVT
p30 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
1.20.1 0.2 0.3 0.4 0.5
(r)
ρ
-110
1
10 jets, R = 0.6
tanti-k
< 80 GeVT
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 13/23
-
Multijet merging Jet properties Conclusions
Jet shapes – differential jet shape ρ(r)
b
b
b
b
bb
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 110–160 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
b
b
b
b
b
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 210–260 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
bb
b
bb
b
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 30–40 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
b
b
bb
b
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 60–80 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
ATLAS data Phys.Rev.D83(2011)052003
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 14/23
-
Multijet merging Jet properties Conclusions
Jet shapes – differential jet shape ρ(r)
b
b
b
b
b
b
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 400–500 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
b
b
b
b
b
b ATLAS dataSherpa-2.0.0
10−1
1
10 1Jet shape ρ for p⊥ ∈ 500–600 GeV, y ∈ 0.0–2.8
ρ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
ATLAS data Phys.Rev.D83(2011)052003
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 15/23
-
Multijet merging Jet properties Conclusions
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
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 -
0.12
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
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 -
0.08
0.1
0.12
0.14
0.16
0.18
0.2 jets, R = 0.6
tanti-k
< 80 GeVT
p60 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
ATLAS collaboration Phys.Rev.D83(2011)052003, ATL-PHYS-PUB-2011-010
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 16/23
-
Multijet merging Jet properties Conclusions
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
ATLAS collaboration Phys.Rev.D83(2011)052003, ATL-PHYS-PUB-2011-010
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 17/23
-
Multijet merging Jet properties Conclusions
Jet shapes – integrated jet shape Ψ(r)
b
bb
b bb
b ATLAS dataSherpa-2.0.0
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
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
bb b
b b
b ATLAS dataSherpa-2.0.0
0
0.2
0.4
0.6
0.8
1
1.2Jet shape Ψ for p⊥ ∈ 210–260 GeV, y ∈ 2.1–2.8
Ψ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
b
b
bb
b
b ATLAS dataSherpa-2.0.0
0
0.2
0.4
0.6
0.8
1
1.2Jet shape Ψ for p⊥ ∈ 30–40 GeV, y ∈ 0.0–0.3
Ψ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
b
bb
b b
b ATLAS dataSherpa-2.0.0
0
0.2
0.4
0.6
0.8
1
1.2Jet shape Ψ for p⊥ ∈ 60–80 GeV, y ∈ 0.8–1.2
Ψ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
ATLAS data Phys.Rev.D83(2011)052003
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 18/23
-
Multijet merging Jet properties Conclusions
Jet shapes – integrated jet shape Ψ(r)
b
bb b
b b
b ATLAS dataSherpa-2.0.0
0
0.2
0.4
0.6
0.8
1
1.2Jet shape Ψ for p⊥ ∈ 400–500 GeV, y ∈ 0.0–2.8
Ψ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
b
bb b
b b
b ATLAS dataSherpa-2.0.0
0
0.2
0.4
0.6
0.8
1
1.2Jet shape Ψ for p⊥ ∈ 500–600 GeV, y ∈ 0.0–2.8
Ψ(r)
b b b b b b
0 0.1 0.2 0.3 0.4 0.5 0.6
0.81
1.2
r
MC
/Dat
a
ATLAS data Phys.Rev.D83(2011)052003
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 19/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 20/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 21/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 22/23
http://sherpa.hepforge.org
-
Multijet merging Jet properties Conclusions
Thank you for your attention!
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 23/23
-
Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 24/23
-
Multijet merging Jet properties Conclusions
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
αk+ns (µR) = αks (µcore)αs(t1) · · ·αs(tn)
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 24/23
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Multijet merging Jet properties Conclusions
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 Nason JHEP11(2004)040
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 24/23
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Multijet merging Jet properties Conclusions
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
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 25/23
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Multijet merging Jet properties Conclusions
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)
Marek Schönherr IPPP Durham
Multijet merging and jet substructure 25/23
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Multijet merging Jet properties Conclusions
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
Multijet merging and jet substructure 26/23
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Multijet merging Jet properties Conclusions
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 merging and jet substructure 27/23
Multijet mergingJet propertiesConclusions