Improving MC@NLO simulationsmschoenherr/talks/20120227... · 2019. 1. 21. · 1 1=p 2? +1= R p?!1!...
Transcript of Improving MC@NLO simulationsmschoenherr/talks/20120227... · 2019. 1. 21. · 1 1=p 2? +1= R p?!1!...
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Improving MC@NLO simulations
S. Höche, F. Krauss, M. Schönherr, F. Siegert
Institute for Particle Physics Phenomenology
22/11/2011
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 1
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Choice of exponentiated phase space
from Stefan’s talk: limit phase space for exponentiation by α
Sherpa
NLO
α = 1α = 0.3α = 0.1α = 0.03α = 0.01α = 0.003α = 0.001
10−6
10−5
10−4
10−3
10−2
10−1Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
10 1 10 2 10 30.5
11.5
22.5
3
ph⊥ [GeV]
Ratio
Sherpa
NLO
α = 1α = 0.3α = 0.1
α = 0.03α = 0.01α = 0.003α = 0.001
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1Rapidity separation betw. Higgs and leading jet in pp → h+ X
dσ/d
∆y(h,
1stjet)
[pb]
-4 -3 -2 -1 0 1 2 3 40.5
1
1.5
2
∆y(h, 1st jet)
Ratio
however, α no sensible parameter w.r.t. exponentiation region→ restricts emissions to small opening angle wrt. beam→ bias towards hard collinear emissions
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 2
Höche et.al. arXiv:1111.1220
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Choice of exponentiated phase space
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1Phase space boundaries in II dipoles, η = 10 . . . 0.01
xi,ab
ṽi Real emission phase space
ṽi =pa · kpa · pb
xi,ab = 1−(pa + pb) · kpa · pb
• restriction in α permits very hard(xi,ab → 0), not too collinearradiation at larger ṽi
• restriction in k2⊥ = Q2 ṽi
1−xi,abxi,ab
permits only very soft (xi,ab → 1)radiation at larger ṽi
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 3
Höche et.al. arXiv:1111.1220
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Choice of exponentiated phase space
〈O〉 =∫
dΦB B̄(A)
∆(A)(t0, µ2Q)O(ΦB) +µ2Q∫t0
dΦ1D(A)
B∆(A)(t, µ2Q)O(ΦR)
+
∫dΦR
[R−D(A)
]O(ΦR)
with
B̄(A) = B + Ṽ + I(S) +
∫dΦ1
[D(A) −D(S)
]• maintain D(A) = D(S) scheme• to recover physical resummation phase space→ limit phase space in PS evolution variable t = k2⊥ < kmax⊥ 2 = µ2Q
D(A) = D(S) −→ D(S)Θ(kmax⊥ − k⊥)
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 4
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Choice of exponentiated phase space
Assessment of uncertainties
• limit discussion to gg → h because effects are largest and cleanest here(large NLO k-factor, very simple colour/dipole structure)→ large rate difference for S and H events
• setup: k⊥-ordered parton shower based on Catani-Seymour dipoles→ highlights what happens at resummation scale kmax⊥
• renormalisation scale µR = mh, µexpR =
√1
1/p2⊥+1/µ2R
p⊥→∞−→ µR• vary resummation scale kmax⊥ , i.e. starting conditions of MC@NLO-shower• starting conditions of POWHEG-shower fixed at kmax⊥ =
12
√shad
• effect of suppression function not investigated• introduces arbitrary free parameter (not fixed to be of order of mh)• uncertainties as large as with α variation→ investigated in Alioli et.al. JHEP04(2009)002
⇒ uncertainties in (N)LL-LO matching in MC@NLO and POWHEGMarek Schönherr IPPP Durham
Improving MC@NLO simulations 5
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Choice of exponentiated phase space
Assessment of uncertainties
• limit discussion to gg → h because effects are largest and cleanest here(large NLO k-factor, very simple colour/dipole structure)→ large rate difference for S and H events
• setup: k⊥-ordered parton shower based on Catani-Seymour dipoles→ highlights what happens at resummation scale kmax⊥
• renormalisation scale µR = mh, µexpR =
√1
1/p2⊥+1/µ2R
p⊥→∞−→ µR• vary resummation scale kmax⊥ , i.e. starting conditions of MC@NLO-shower• starting conditions of POWHEG-shower fixed at kmax⊥ =
12
√shad
• effect of suppression function not investigated• introduces arbitrary free parameter (not fixed to be of order of mh)• uncertainties as large as with α variation→ investigated in Alioli et.al. JHEP04(2009)002
⇒ uncertainties in (N)LL-LO matching in MC@NLO and POWHEGMarek Schönherr IPPP Durham
Improving MC@NLO simulations 6
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Choice of exponentiated phase space
Assessment of uncertainties
• limit discussion to gg → h because effects are largest and cleanest here(large NLO k-factor, very simple colour/dipole structure)→ large rate difference for S and H events
• setup: k⊥-ordered parton shower based on Catani-Seymour dipoles→ highlights what happens at resummation scale kmax⊥
• renormalisation scale µR = mh, µexpR =
√1
1/p2⊥+1/µ2R
p⊥→∞−→ µR• vary resummation scale kmax⊥ , i.e. starting conditions of MC@NLO-shower• starting conditions of POWHEG-shower fixed at kmax⊥ =
12
√shad
• effect of suppression function not investigated• introduces arbitrary free parameter (not fixed to be of order of mh)• uncertainties as large as with α variation→ investigated in Alioli et.al. JHEP04(2009)002
⇒ uncertainties in (N)LL-LO matching in MC@NLO and POWHEGMarek Schönherr IPPP Durham
Improving MC@NLO simulations 7
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Choice of splitting kernel – D(A)/B
traditional MC@NLO and POWHEG choices of splitting kernels
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−7
10−6
10−5
10−4
10−3
10−2
10−1Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
10 1 10 2 10 3
1
2
3
ph⊥ [GeV]
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.01
0.02
0.03
0.04
0.05
0.06Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
0 5 10 15 20 25
0.6
0.8
1
1.2
1.4
ph⊥ [GeV]
Ratio
I large uncertainties when varying kmax⊥I driven by diff. in normalisation of S- and H-events and size of ln2(k2⊥/µ2Q)I shape difference driven by unitarity constraint
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 8
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Choice of splitting kernel – D(A)/B
traditional MC@NLO and POWHEG choices of splitting kernels
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.02
0.04
0.06
0.08
0.1
Rapidity separation betw. Higgs and leading jet in pp → h+ X
dσ/d
∆y(h,
1stjet)
[pb]
-4 -3 -2 -1 0 1 2 3 4
1
2
3
∆y(h, 1st jet)
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−6
10−5
10−4
10−3
10−2Transverse momentum of leading jet in pp → h+ X
dσ/dp⊥(jet
1)[pb/GeV
]
0 100 200 300 400 500
1
2
3
p⊥(jet 1) [GeV]
Ratio
I uncertainty on jet rates with p⊥ ∼ 100GeV: 2.5I no dip in ∆y → originates in HERWIG’s radiation pattern
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 9
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Choice of splitting kernel – D(A)/B̄(A)
here: change splitting kernels K −→ (1 + αs · const.) K
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−7
10−6
10−5
10−4
10−3
10−2
10−1Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
10 1 10 2 10 30.6
0.8
1
1.2
1.4
ph⊥ [GeV]
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.01
0.02
0.03
0.04
0.05
0.06Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
0 5 10 15 20 25
0.6
0.8
1
1.2
1.4
ph⊥ [GeV]
Ratio
I uncertainties much lower, smooth transition at µ2QI much closer to NLO fixed order result for “hard”emissionsI price of spuriously large LL prefactor → Sudakov peak differs
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 10
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Choice of splitting kernel – D(A)/B̄(A)
here: change splitting kernels K −→ (1 + αs · const.) K
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.02
0.04
0.06
0.08
0.1
Rapidity separation betw. Higgs and leading jet in pp → h+ X
dσ/d
∆y(h,
1stjet)
[pb]
-4 -3 -2 -1 0 1 2 3 4
0.6
0.8
1
1.2
1.4
∆y(h, 1st jet)
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−6
10−5
10−4
10−3
10−2Transverse momentum of leading jet in pp → h+ X
dσ/dp⊥(jet
1)[pb/GeV
]
0 100 200 300 400 500
0.6
0.8
1
1.2
1.4
p⊥(jet 1) [GeV]
Ratio
I uncertainties much lower, smooth transition at µ2QI much closer to NLO fixed order result for “hard”emissionsI price of spuriously large LL prefactor
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 11
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Choice of higher order correction – B̄(A)/B ·Hhere: modify H-term with arbitrary higher order corrections H→ B̄(A)B H
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−7
10−6
10−5
10−4
10−3
10−2
10−1Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
10 1 10 2 10 3
1
2
3
ph⊥ [GeV]
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.01
0.02
0.03
0.04
0.05
0.06Transverse momentum of Higgs boson in pp → h+ X
dσ/dph ⊥[pb/GeV
]
0 5 10 15 20 25
0.6
0.8
1
1.2
1.4
ph⊥ [GeV]
Ratio
I PS resummation left void of higher order termsI equivalent to MENLOPS prescription in Höche et.al. JHEP04(2011)024I uncontrolled O(α2s) terms in H-events
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 12
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Choice of higher order correction – B̄(A)/B ·Hhere: modify H-term with arbitrary higher order corrections H→ B̄(A)B H
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
0
0.02
0.04
0.06
0.08
0.1
Rapidity separation betw. Higgs and leading jet in pp → h+ X
dσ/d
∆y(h,
1stjet)
[pb]
-4 -3 -2 -1 0 1 2 3 4
1
2
3
∆y(h, 1st jet)
Ratio
NLO
Powheg
MC@NLO kmax⊥ =12 mh
MC@NLO kmax⊥ = mhMC@NLO kmax⊥ = 2mh
10−6
10−5
10−4
10−3
10−2Transverse momentum of leading jet in pp → h+ X
dσ/dp⊥(jet
1)[pb/GeV
]
0 100 200 300 400 500
1
2
3
p⊥(jet 1) [GeV]
Ratio
I PS resummation left void of higher order termsI equivalent to MENLOPS prescription in Höche et.al. JHEP04(2011)024I uncontrolled O(α2s) terms in H-events
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 13
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Conclusions
• uncertainties studied occur in every process and are inherent to methods→ gg → h just presents a clean environment
• exploit freedom left at the respective level of accuracy→ each with merrits and drawbacks
• choices constrained by adding higher order calculations• (N)NLL resummation• NNLO corrections• NLO⊗NLO merging with Qcut < µ2Q
Marek Schönherr IPPP Durham
Improving MC@NLO simulations 14