Improving MC@NLO simulationsmschoenherr/talks/20120227... · 2019. 1. 21. · 1 1=p 2? +1= R p?!1!...

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

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



Höche et.al. arXiv:1111.1220


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



Höche et.al. arXiv:1111.1220


〈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⊥)




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







√1

1/p2⊥+1/µ2R


12

√shad




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


dσ/dph ⊥[pb/GeV

]

10 1 10 2 10 3

1

2

3

ph⊥ [GeV]

Ratio

NLO

Powheg



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



Choice of splitting kernel – D(A)/B

traditional MC@NLO and POWHEG choices of splitting kernels

NLO

Powheg



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



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



Choice of splitting kernel – D(A)/B̄(A)

here: change splitting kernels K −→ (1 + αs · const.) K

NLO

Powheg



10−7

10−6

10−5

10−4

10−3

10−2


dσ/dph ⊥[pb/GeV

]

10 1 10 2 10 30.6

0.8

1

1.2

1.4

ph⊥ [GeV]

Ratio

NLO

Powheg



0

0.01

0.02

0.03

0.04

0.05


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



Choice of splitting kernel – D(A)/B̄(A)

here: change splitting kernels K −→ (1 + αs · const.) K

NLO

Powheg



0

0.02

0.04

0.06

0.08

0.1


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



10−6

10−5

10−4

10−3


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



Choice of higher order correction – B̄(A)/B ·Hhere: modify H-term with arbitrary higher order corrections H→ B̄(A)B H

NLO

Powheg



10−7

10−6

10−5

10−4

10−3

10−2


dσ/dph ⊥[pb/GeV

]

10 1 10 2 10 3

1

2

3

ph⊥ [GeV]

Ratio

NLO

Powheg



0

0.01

0.02

0.03

0.04

0.05


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



Choice of higher order correction – B̄(A)/B ·Hhere: modify H-term with arbitrary higher order corrections H→ B̄(A)B H

NLO

Powheg



0

0.02

0.04

0.06

0.08

0.1


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



10−6

10−5

10−4

10−3


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



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



Improving MC@NLO simulationsmschoenherr/talks/20120227... · 2019. 1. 21. · 1 1=p 2? +1= R p?!1!...

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