mc tools and nlo monte carlos - institut national de

Introduction The Good: Fixed Order The Bad: Matching & Merging The Ugly

MC Tools and NLO Monte Carlosor

The Good, the Bad & the Ugly

Frank Krauss

Institute for Particle Physics PhenomenologyDurham University

“Higgs Hunting 2016”, Paris, 1.9.2016

F. Krauss IPPP

MC Tools and NLO Monte Carlos


what the talk is about

the cutting edge in theory inputs

matching & merging with parton showers

where we are and where we (should/could/would) go

F. Krauss IPPP



motivation & introduction

F. Krauss IPPP



motivation: the need for (more) accurate tools

- to date no survivors in searches for new physics & phenomena(a pity, but that’s what Nature hands to us)

- push into precision tests of the Standard Model(find it or constrain it!)

- statistical uncertainties approach zero(because of the fantastic work of accelerator, DAQ, etc.)

- systematic experimental uncertainties decrease(because of ingenious experimental work)

- theoretical uncertainties are or become dominant(it would be good to change this to fully exploit LHC’s potential)

=⇒ more accurate tools for more precise physics needed!

F. Krauss IPPP



motivation: aim of the exercise

review the state of the art in precision simulations(celebrate success)

highlight missing or ambiguous theoretical ingredients(acknowledge failure)

suggest some further studies – experiment and theory(. . . )

F. Krauss IPPP



reminder: fixed-order and its limits

F. Krauss IPPP



the aftermath of the NLO (QCD) revolution

establishing a wide variety of automated tools for NLO calculationsBLACKHAT, GOSAM, MADGRAPH, NJET, OPENLOOPS, RECOLA + automated IR subtraction methods (MADGRAPH, SHERPA)

first full NLO (EW) results with such tools

technical improvements still mandatory(higher multis, higher speed, higher efficiency, easier handling, . . . )

start discussing scale setting prescriptions(simple central scales for complicated multi-scale processes? test smarter prescriptions?)

steep learning curve still ahead: “NLO phenomenology”(example: methods for uncertainty estimates beyond variation around central scale)

F. Krauss IPPP



the looming revolution: going beyond NLO

H in ggF at N3LO (Anastasiou, Duhr and others)

explosive growth in NNLO (QCD) 2→ 2 results(apologies for any unintended omissions)

tt̄ (1303.6254; 1508.03585;1511.00549)

single-t (1404.7116)

VV (1507.06257; 1605.02716;1604.08576; 1605.02716)

HH (1606.09519)

VH (1407.4747; 1601.00658)

Vγ (1504.01330)

γγ (1110.2375; 1603.02663)

Vj (1507.02850; 1512.01291; 1602.06965)

Hj (1408.5325; 1504.07922; 1505.03893; 1508.02684)

jj (1310.3993)

WBF at NNLO and N3LO (1506.02660 and N3LO 1606.00840)

different IR subtraction schemes:N-jettiness slicing, antenna subtraction, sector decomposition,

F. Krauss IPPP



challenging the revolution

some technical issues at NNLO (and beyond)(stability of automated NLO, robustness under integration, subtraction vs. slicing)

more scales (internal or external) complicated – need integrals

going to higher power of N often driven by need to include larger FSmultiplicity – maybe not the most efficient method

structural questions concerning convergence/importance

limitations of perturbative expansion:

breakdown of factorisation at HO (Seymour et al.)higher-twist: compare (αS/π)n with ΛQCD/MZ

(see Melnikov’s talk last week)

F. Krauss IPPP



matching @ (N)NLO

merging @ (N)LO

F. Krauss IPPP



prequel: parton showers vs. resummation calculations

various schemes for various logs in analytic resummation

concentrate on parton shower instead ←→ compare with QT

resummation(transverse momentum of Higgs boson etc.)

parametric accuracy by comparing Sudakov form factors:

∆ = exp

{−∫

dk2⊥

k2⊥

[A log

k2⊥

Q2+ B

]},

where A and B can be expanded in αS(k2⊥)

showers usually include terms A1,2 and B1 (NLL)

A2 often realised by pre-factor multiplying scale µR ' k⊥

F. Krauss IPPP



some parton shower fun with DY(example of accuracy in description of standard precision observable)

b

b b b b b b b bb

bbbbb b b b

bbb

b

b

b

b

b

b

b b b b b b b bb

bbbbbb b b b

bb

b

b

b

b

b

b

b b b b b b b b bbb b

bb b b b b

bb

b

b

b

b

b

Sher

paM

C

0 ≤ |yZ| ≤ 1

1 ≤ |yZ| ≤ 2 (×0.1)

2 < |yZ| ≤ 2.4 (×0.01)

b ATLAS dataJHEP 09 (2014) 145ME+PS (1-jet)5 ≤ Qcut ≤ 20 GeV

1 210−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1pT spectrum, Z→ ee (dressed)

1σ

fidd

σfid

dp T

[GeV

−1 ]

b b b b b b b b b b b b b b b b b b b bbbbbb

b

b

b

b

b

b

b

b

b

b b b b b b b b b b b b b b b b b bb b

bbbbb

b

b

b

b

b

b

b

b

b

b b b b b b b b b b b b b b b b b b bb b

bbbb

b

b

b

b

b

b

b

bb

Sher

paM

C

|yZ| < 0.8

0.8 ≤ |yZ| ≤ 1.6 (×0.1)

1.6 < |yZ| (×0.01)

b ATLAS dataPhys.Lett. B720 (2013) 32ME+PS (1-jet)5 ≤ Qcut ≤ 20 GeV

3 2 1

10−4

10−3

10−2

10−1

1

10 1

φ∗η spectrum, Z→ ee (dressed)

1σ

fid.

dσ

fid.

dφ∗ η

b b b b b b b b b b b b b b b b b b b b b b b b b b

0 ≤ |yZ| ≤ 1

1 2

0.80.91.01.11.2

| |

MC

/Dat

a

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

|yZ| < 0.8

3 2 1

0.80.91.01.11.2

→ | |

MC

/Dat

ab b b b b b b b b b b b b b b b b b b b b b b b b b

1 ≤ |yZ| ≤ 2

1 2

0.80.91.01.11.2

| |

MC

/Dat

a


0.8 ≤ |yZ| ≤ 1.6

3 2 1

0.80.91.01.11.2

→ ≤ | |

MC

/Dat

a

b b b b b b b b b b b b b b b b b b b b b b b b b b

2 < |yZ| ≤ 2.4

1 10 1 10 2

0.80.91.01.11.2

| |

pT,ll [GeV]

MC

/Dat

a


1.6 < |yZ|

10−3 10−2 10−1 1

0.80.91.01.11.2

→ | | ≥

φ∗η

MC

/Dat

a

F. Krauss IPPP



matching at NLO and NNLO

avoid double-counting of emissions

two schemes at NLO: MC@NLO and POWHEG

mismatches of K factors in transition to hard jet regionMC@NLO: −→ visible structures, especially in gg → HPOWHEG: −→: high tails, cured by h dampening factorwell-established and well-known methods

(no need to discuss them any further)

two schemes at NNLO: MINLO & UN2LOPS (singlets S only)

different basic ideasMINLO: S + j at NLO with p

(S)T → 0 and capture divergences by

reweighting internal line with analytic Sudakov, NNLO accuracyensured by reweighting with full NNLO calculation for S productionUN2

LOPS identifies and subtracts and adds parton shower terms atFO from S + j contributions, maintaining unitarityavailable for two simple processes only: DY and gg → H

F. Krauss IPPP



NNLOPS for H production: MINLO

K. Hamilton, P. Nason, E. Re & G. Zanderighi, JHEP 1310

also available for Z production

F. Krauss IPPP



NNLOPS for Z production: UN2LOPS

S. Hoche, Y. Li, & S. Prestel, Phys.Rev.D90 & D91

She

rpa+

Bla

ckH

at

NNLONLO'FEWZ

= 7 TeVs<120 GeV

ll60 GeV<m

NLO'll<2mR/F

µ/2< ll m NNLOll<2m

R/Fµ/2< ll m

[pb]

-e

+e

/dy

σd

20

40

60

80

100

120

140

160

180

200

Rat

io to

NLO

0.960.98

11.021.04

-e+ey

-4 -3 -2 -1 0 1 2 3 4

b

bb

b bb

bbb b

bbb b

b

b

b

b

b

ATLAS PLB705(2011)415b

UN2LOPSmll/2 < µR/F < 2 mllmll/2 < µQ < 2 mll

10−6

10−5

10−4

10−3

10−2

10−1Z pT reconstructed from dressed electrons

1/σ

dσ

/d

p T,Z

[1/G

eV]

b b b b b b b b b b b b b b b b b b b

1 10 1 10 2

0.6

0.8

1

1.2

1.4

pT,Z [GeV]

MC

/Dat

a

also available for H production

F. Krauss IPPP



NNLOPS: shortcomings/limitations

MINLO relies on knowledge of B2 terms from analytic resummation−→ to date only known for colour singlet production

MINLO relies on reweighting with full NNLO result−→ one parameter for H (yH), more complicated for Z , . . .

UN2LOPS relies on integrating single- and double emission to lowscales and combination of unresolved with virtual emissions−→ potential efficiency issues, need NNLO subtraction

UN2LOPS puts unresolved & virtuals in “zero-emission” bin−→ no parton showering for virtuals (?)

F. Krauss IPPP



merging example: p⊥,γγ in MEPS@LO vs. NNLO(arXiv:1211.1913 [hep-ex])

[p

b/G

eV

]γγ

T,

/dp

σd

510

410

310

210

110

1

10

1Ldt = 4.9 fb ∫ Data 2011,

1.3 (MRST2007)×PYTHIA MC11c

1.3 (CTEQ6L1)×SHERPA MC11c

ATLAS

= 7 TeVs

data

/SH

ER

PA

00.5

11.5

22.5

3

[GeV]γγT,

p

0 50 100 150 200 250 300 350 400 450 500

da

ta/P

YT

HIA

00.5

11.5

22.5

3 [

pb

/Ge

V]

γγT,

/dp

σd

510

410

310

210

110

1

10

1Ldt = 4.9 fb ∫ Data 2011,

DIPHOX+GAMMA2MC (CT10)

NNLO (MSTW2008)γ2

ATLAS

= 7 TeVs

da

ta/D

IPH

OX

00.5

11.5

22.5

3

[GeV]γγT,

p

0 50 100 150 200 250 300 350 400 450 500

NN

LO

γd

ata

/2

00.5

11.5

22.5

3

F. Krauss IPPP



multijet-merging at NLO

sometimes “more legs” wins over more loops

basic idea like at LO: towers of MEs with increasing jet multi(but this time at NLO)

combine them into one sample, remove overlap/double-counting

maintain NLO and LL accuracy of ME and PS

this effectively translates into a merging of MC@NLO simulations andcan be further supplemented with LO simulations for even higherfinal state multiplicities

different implementations, parametric accuracy not always clear(MEPS@NLO, FxFx, UNLOPS)

starts being used, still lacks careful cross-validation

F. Krauss IPPP



illustration: pH⊥ in 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 byMC@NLO

MC@NLO pp → h + jetfor Qn+1 > Qcut

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

MC@NLO

pp → h + 2jets forQn+2 > Qcut

iterate

sum all contributions

eg. p⊥(h)>200 GeVhas contributions fr.multiple topologies

F. Krauss IPPP




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

]

first emission byMC@NLO , restrict toQn+1 < Qcut



MC@NLO


iterate



F. Krauss IPPP




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

]




MC@NLO


iterate



F. Krauss IPPP




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

]




MC@NLO


iterate



F. Krauss IPPP




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

]




MC@NLO


iterate



F. Krauss IPPP



results from various schemes in H+jets through ggF

F. Krauss IPPP



F. Krauss IPPP



aside: quark mass effects

include effects of quark masses

reweight NLO HEFT with LO ratio:(reweight virtual with Born ratio, real with real ratio)

dσ(NLO)mass ≈ dσ

(NLO)HEFT ×

dσ(LO)mass

dσ(LO)HEFT

F. Krauss IPPP



b–mass effects: playtime

use LO multijet merging for tb-interference

vary around µQ = mb vary around µQ = mh vary µF ,R

with Qcut = mb fixed

HEFTmt effects onlymt and mb effects, µb

s =√

2mbmt and mb effects, µb

s = mb

0

0.1

0.2

0.3

0.4

0.5

0.6

Higgs boson transverse momentum

dσ

/dp ⊥

[pb/

GeV

]

0 10 20 30 40 50

00.20.40.60.8

1

p⊥(H) [GeV]

Rat

ioto

HE

FT

HEFTmt effects onlymt and mb effects, µb

s = mh/√

2mt and mb effects, µb

s = mh√

2

10−5

10−4

10−3

10−2

10−1

1Higgs boson transverse momentum

dσ

/dp ⊥

[pb/

GeV

]

1 10 1 10 2 10 30.9

0.95

1.0

1.05

p⊥(H) [GeV]

Rat

ioto

HE

FT

HEFTµ f ∈ [0.5, 2]mhµr ∈ [0.5, 2]mhmt and mb effects, Qcut = mb

10−5

10−4

10−3

10−2

10−1

1Higgs boson transverse momentum

dσ

/dp ⊥

[pb/

GeV

]

1 10 1 10 2 10 30.70.80.91.01.11.21.3

p⊥(H) [GeV]

Rat

ioto

HE

FT

F. Krauss IPPP



limitations of full simulations

lots of routinely used tools for large FS multis (4 and more) at NLOaccuracy, but−→ not many detailled comparisons

(critical appraisals and learning curve in their phenomenological use still in infancy)

−→ no standard way of estimating uncertainties (yet?)

to improve: description of loop–induced processes−→ potentially important for new physics searches

users of codes: higher orders tricky → training needed(MC = black box attitude problematic - a new brand of pheno/experimenters needed?)

F. Krauss IPPP



a systematic uncertainty

showering a source of uncertainty−→ (N)LL only, scale variations?

(quite often just used as black box)

maybe include higher orders?

example right:

µR uncertainty in p(emit)⊥ in ggF

Dir

ePS

pp → [h → τ+τ−] @ 8TeV

Γ1 ⊕ γ1Γ1 ⊕ γ1 ⊕ Γ21/2 t < µR < 2 tΓ1 ⊕ γ1 ⊕ Γ2 ⊕ γ2Γ1 ⊕ γ1 ⊕ Γ2 ⊕ γ2 ⊕ Γ31/2 t < µR < 2 t

10−3

10−2

10−1

Differential 0 → 1 jet resolution

dσ

/d

log 10

(d01

/G

eV)

[pb]

0.5 1 1.5 2 2.5

0.8

0.9

1.0

1.1

1.2

log10(d01/GeV)

Rat

io

F. Krauss IPPP



limitations

F. Krauss IPPP



theory limitations/questions

we have constructed lots of tools for precision physics at LHC−→ but we did not cross-validate them careful enough (yet)−→ but we did not compare their theoretical foundations (yet)

will NNLO (or beyond) become as automated as NLO?−→ or more precisely: when and how?

we also need unglamorous improvements on existing tools:

systematically check advanced scale-setting schemes (MINLO)automatic (re-)weighting for PDFs & scalesscale compensation in PS is simple (implement and check)

4 vs. 5 flavour scheme −→ really?

how about αS : range from 0.113 to 0.118(yes, I know, but still - it still bugs me)

−→ is there any way to settle this once and for all (measurements?)

F. Krauss IPPP



more theory uncertainties/issues?

with NNLOPS approaching 5% accuracy or better:

non-perturbative uncertainties start to matter:−→ PDFs, MPIs, hadronization, etc.question (example): with hadronization tuned to quark jets (LEP)−→ how important is the “chemistry” of jets for JES?−→ can we fix this with measurements?example PDFs: to date based on FO vs. data−→will we have to move to resummed/parton showered?

(reminder: LO∗ was not a big hit, though)

g → qq̄ at accuracy limit of current parton showers:−→ how bad are ∼ 25% uncertainty on g → bb̄?−→ can we fix this with measurements?

F. Krauss IPPP



plan

F. Krauss IPPP



achievable goals in fixed order calculations: a roadmap (?)

practical limitations/questions to be overcome:

dealing with IR divergences at NNLO: slicing vs. subtracting(I’m not sure we have THE solution yet)

how far can we push NNLO? are NLO automated results stableenough for NNLO at higher multiplicity?matching for generic processes at NNLO?

(MINLO or UN2LOPS or something new?)

NLO for loop-induced processes:

fixed-order starting, MC@NLO tedious but straightforward

EW NLO corrections with tricky/time-consuming calculational setup

but important at large scales: effect often ∼ QCD, but opposite signneed maybe faster approximation for high-scales (EW Sudakovs)

F. Krauss IPPP



“curable” bottleneck: colours/spins in parton showers

parton shower usually is spin-averaged,leading colour, (next-to) leading log

start including next-to leading colour(first attempts by Platzer & Sjodahl; Nagy & Soper)

no big effects in e−e+ → hadrons seenmaybe more exclusive observables?

aside: can also include spin-correlationsimportant for EW emissions

(maybe relevant for ultra-high energies)

HO being implemented at nthemoment

0.001

0.01

0.1

1

average transverse momentum w.r.t. ~n3

DipoleShower + ColorFull

0.80.91

1.11.2

1 10

〈p⊥〉/GeV

fullshower

strict large-Nc

GeV

N−1dN/d

〈p⊥〉

x/full

F. Krauss IPPP



outlookwill need precision for ballistics of smoking guns

F. Krauss IPPP


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