the quest for precision in simulations for the lhc · birmingham seminar, 11.10.2017 f. krauss ippp...

Introduction fixed-order inprovements Parton Showers future directions

The Quest for Precision inSimulations for the LHC

Frank Krauss

Institute for Particle Physics PhenomenologyDurham University

Birmingham Seminar, 11.10.2017

F. Krauss IPPP

Quest for Precision in Simulations for the LHC


what the talk is about

fixed order & matching & merging with parton showers

revisiting 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)

F. Krauss IPPP



need more precise & accurate tools for more precise physics

F. Krauss IPPP



matching @ (N)NLO

and

merging @ (N)LO

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 automated 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



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/W /VH 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



Z+jets at 13 Tev: comparison with ATLAS datavarious merging codes at LO and NLO

jetsN

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

) [p

b]je

ts*+

Nγ

(Z/

σ

-210

-110

1

10

210

310

410

510

610ATLAS Preliminary

1−13 TeV, 3.16 fb

jets, R = 0.4tanti-k

< 2.5jet

y > 30 GeV, jet

Tp

) + jets−l+ l→*(γZ/

Data

HERPAS + ATHLACK B

2.1HERPA S

6YP + LPGEN A

8 CKKWLYP + MG5_aMC

8 FxFxYP + MG5_aMC

jetsN

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pre

d./D

ata

0.5

1

1.5

jetsN

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pre

d./D

ata

0.5

1

1.5

jetsN

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

Pre

d./D

ata

0.5

1

1.5

[GeV]TH

200 400 600 800 1000 1200 1400

[pb/

GeV

]T

/dH

σd

-410

-310

-210

-110

1

10

210

310ATLAS Preliminary

1−13 TeV, 3.16 fb

jets, R = 0.4tanti-k

< 2.5jet

y > 30 GeV, jet

Tp

1 jet≥) + −l+ l→*(γZ/ Data

NNLOjetti

1 jet N≥ Z + HERPAS + ATHLACK B

2.1HERPA S6YP + LPGEN A

8 CKKWLYP + MG5_aMC8 FxFxYP + MG5_aMC

[GeV]T

H

200 400 600 800 1000 1200 1400

Pre

d./D

ata

0.5

1

1.5

[GeV]T

H

200 400 600 800 1000 1200 1400P

red.

/Dat

a 0.5

1

1.5

[GeV]TH

200 400 600 800 1000 1200 1400

Pre

d./D

ata

0.5

1

1.5

F. Krauss IPPP



including EW corrections

F. Krauss IPPP



EW corrections

EW corrections sizeable O(10%) at large scales: must include them!

but: more painful to calculate

need EW showering & possibly corresponding PDFs(somewhat in its infancy: chiral couplings)

example: Zγ vs. pT (right plot)(handle on pZ⊥ in Z → νν)

(Kallweit, Lindert, Pozzorini, Schoenherr for LH’15)

difference due to EW charge of Z

no real correction (real V emission)

improved description of Z → ``

bb

b

bbb

b bb

bb b

bb

b

b

b

b

bb

b

b

bb

bb

bb

bb

bb

b b b b

bb

b

b

bb

bb

bb

bb

b b b b b b

Sher

pa+O

pen

Lo

ops

b NLO QCDb NLO QCD+EW

b CMS dataJHEP10(2015)128

0

0.01

0.02

0.03

0.04

0.05Z/γ ratio for events with njets ≥ 1

dσ

/dpZ T

/d

σ/d

pγ T

b

b

b b

b

b

b

b b

b bb

b

b

b

b

b

b

b

b

b b

b

b

b

b b

b bb

b

b

b

b

b

b

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

100 200 300 400 500 600 700 800

0.8

0.9

1.0

1.1

1.2

pZ/γT [GeV]

MC

/Dat

a

F. Krauss IPPP



inclusion of electroweak corrections in simulation

incorporate approximate electroweak corrections in MEPS@NLO

1 using electroweak Sudakov factors

Bn(Φn) ≈ Bn(Φn) ∆EW(Φn)

2 using virtual corrections and approx. integrated real corrections

Bn(Φn) ≈ Bn(Φn) + Vn,EW(Φn) + In,EW(Φn) + Bn,mix(Φn)

real QED radiation can be recovered through standard tools(parton shower, YFS resummation)

simple stand-in for proper QCD⊕EW matching and merging→ validated at fixed order, found to be reliable,→ difference . 5% for observables not driven by real radiation

F. Krauss IPPP



results: pp → `−ν + jets(Kallweit, Lindert, Maierhofer, Pozzorini, Schoenherr JHEP04(2016)021)

Sher

pa+O

pen

Lo

ops

Qcut = 20 GeV

MEPS@LOMEPS@NLO QCDMEPS@NLO QCD+EWvirtMEPS@NLO QCD+EWvirt w.o. LO mix

100

10–3

10–6

10–9

pp → ℓ−ν + 0,1,2 j @ 13 TeV

dσ

/dp T

,V[p

b/G

eV]

50 100 200 500 1000 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

pT,V [GeV]

dσ

/dσ

NL

OQ

CD

Sher

pa+O

pen

Lo

ops

Qcut = 20 GeV

MEPS@LOMEPS@NLO QCDMEPS@NLO QCD+EWvirtMEPS@NLO QCD+EWvirt w.o. LO mix

100

10–3

10–6

10–9

pp → ℓ−ν + 0,1,2 j @ 13 TeV

dσ

/dp T

,j 1[p

b/G

eV]

50 100 200 500 1000 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

pT,j1 [GeV]

dσ

/dσ

NL

OQ

CD

⇒ particle level events including dominant EW corrections

F. Krauss IPPP



NLO EW predictions for ∆R(µ, j1)

Sher

pa+O

pen

Lo

ops

LHC 8 TeVpp → µν + 1j inclusive

LO

0 1 2 3 4 50

0.05

0.1

0.15

0.2

0.25Angular separtion of leading jet and muon

∆R(µ, j)

dσ

/d∆

R[p

b] measure collinear W emission?LHC@8TeV, pj1⊥ > 500GeV, central µ and jet

LO pp →Wj with ∆φ(µ, j) ≈ π

NLO corrections neg. in peaklarge pp →Wjj component opening PS

sub-leading Born (γPDF) at large ∆R

restrict to exactly 1j , no pj2⊥ > 100 GeV

describe pp →Wjj @ NLO, pj2⊥ > 100 GeV

pos. NLO QCD,

neg. NLO EW,

∼ flat

sub-leading Born contribs positive

sub2leading Born (diboson etc) conts. pos.→ possible double counting with BG

merge using exclusive sums

F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCD

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D

measure collinear W emission?LHC@8TeV, pj1⊥ > 500GeV, central µ and jet

LO pp →Wj with ∆φ(µ, j) ≈ πNLO corrections neg. in peaklarge pp →Wjj component opening PS




pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCDNLO QCD+EW

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D






pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCDNLO QCD+EWNLO QCD+EW+subLO

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D






pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops

LHC 8 TeVpp → µν + 1j exclusive


0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D






pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LO

0 1 2 3 4 50

0.05

0.1

0.15

0.2


∆R(µ, j)

dσ

/d∆

R[p

b] measure collinear W emission?LHC@8TeV, pj1⊥ > 500GeV, central µ and jet





pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCD

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D






pos. NLO QCD,

neg. NLO EW,

∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCDNLO QCD+EW

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D






pos. NLO QCD, neg. NLO EW, ∼ flat




F. Krauss IPPP




Sher

pa+O

pen

Lo

ops



0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D










F. Krauss IPPP




Sher

pa+O

pen

Lo

ops


LONLO QCDNLO QCD+EWNLO QCD+EW+subLONLO QCD+EW+subLO+sub2LO

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D










F. Krauss IPPP




Sher

pa+O

pen

Lo

ops

LHC 8 TeVpp → µν + 1j exclusive+pp → µν + 2j inclusive

LONLO QCDNLO QCD+EWNLO QCD+EW+subLONLO QCD+EW+subLO+sub2LO

0

0.05

0.1

0.15

0.2


dσ

/d∆

R[p

b]

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0.5

1

1.5

Rat

iow

rt.N

LO

QC

D

0 1 2 3 4 5

0.5

1

1.5

∆R(µ, j)

Rat

iow

rt.N

LO

QC

D










F. Krauss IPPP



NLO EW predictions for ∆R(µ, j1)R

) [fb]

∆/d

(σ

d

20

40

60

80

100

120

140

160

180 1 = 8 TeV, 20.3 fbs

Data

ALPGEN+PYTHIA6 W+jets

PYTHIA8 W+j & jj+weak shower

SHERPA+OpenLoops W+j & W+jj

NNLOjetti

1 jet N≥W +

> 500 GeVT

Leading Jet p

ATLAS

0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2

, closest jet)µR(∆

0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2

Data comparison(M. Wu ICHEP’16, ATLAS arXiv:1609.07045)

ALPGEN+PYTHIA

pp →W + jets MLM merged(Mangano et.al., JHEP07(2003)001)

PYTHIA 8pp →Wj + QCD showerpp → jj + QCD+EW shower

(Christiansen, Prestel, EPJC76(2016)39)

SHERPA+OPENLOOPS

NLO QCD+EW+subLOpp →Wj/Wjj excl. sum

(Kallweit, Lindert, Maierhofer,)

(Pozzorini, Schoenherr, JHEP04(2016)021)

NNLO QCD pp →Wj(Boughezal, Liu, Petriello, arXiv:1602.06965)

F. Krauss IPPP




) [fb]

∆/d

(σ

d

20

40

60

80

100

1201 = 8 TeV, 20.3 fbs

Data




< 600 GeVT

500 GeV < Leading Jet p

ATLAS

0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2


0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2


ALPGEN+PYTHIA




SHERPA+OPENLOOPS





F. Krauss IPPP




) [fb]

∆/d

(σ

d

5

10

15

20

25

30

35

40

45

501 = 8 TeV, 20.3 fbs

Data




> 650 GeVT

Leading Jet p

ATLAS

0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2


0 0.5 1 1.5 2 2.5 3 3.5 4

Pre

d./

Da

ta

0.5

1

1.5

2


ALPGEN+PYTHIA




SHERPA+OPENLOOPS





F. Krauss IPPP



improving parton showers

F. Krauss IPPP



motivation: why care?

QCD radiation omnipresent at the LHC

enters as signal (and background) in high-p⊥ analyses

multi-jet signatures

−→ multijet merging & higher-order matching (not the topic today)

inner-jet structures e.g. from “fat jets”

−→ parton shower algorithms

begs the question:can we improve on parton showers and increase their precision?

(keep in mind: accuracy vs. precision)

F. Krauss IPPP



another systematic uncertainty

parton showers are approximations, based on

leading colour, leading logarithmic accuracy, spin-average

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⊥)

QT resummation includes A1,2,3 and B1,2

(transverse momentum of Higgs boson etc.)

showers usually include terms A1,2 and B1

A = cusp terms (“soft emissions”), B ∼ anomalous dimensions γ

F. Krauss IPPP



connection to fragmentation functions

DGLAP for FFs:

d xDa(x , t)

d log t=∑b=q,g

1∫0

dτ

1∫0

dz δ(x − τz)αS

2π[zPab(z)]+ τDb(τ, t) .

rewrite for definition of “+”-function, [zPab(z)]+ = limε→0

zPab(z , ε):

Pab (z, ε) = Pab (z) Θ(1 − z − ε) − δab

∑c=q,g

Θ(1 − z − ε)

ε

1∫0

dξ ξPac (ξ)

d log Da(x , t)

d log t= −

∑c=q,g

1−ε∫0

dξαS

2πξPac (ξ)

︸︷︷︸derivative of Sudakov

+∑b=q,g

1−ε∫x

dz

z

αS

2πPac (z)

Db( xz, t)

Da(x , t)

F. Krauss IPPP



re-introduce Sudakov form factor

∆a(t, t0) = exp

−t∫

t0

dt ′

t ′

∑c=q,g

1−ε∫0

dξαS

2πξPac(ξ)

to express equation above through generating functionalDa(x , t, µ2) = Da(x , t)∆a(µ2, t):

d logDa(x , t, µ2)

d log t=∑b=q,g

1−ε∫x

dz

z

αS

2πPac(z)

Db( xz , t)

Da(x , t)

add initial states (PDFs) & arrive at argument(s) for Sudakov formfactors when jets not measured

∑i∈IS

∑b=q,g

1−ε∫xi

dz

z

αS

2πPbai (z)

fb( xiz , t)

fai (x , t)+∑j∈FS

∑b=q,g

1−ε∫xi

dz zαS

2πPajb(z) .

F. Krauss IPPP



subtle symmetry factors

observations for LO PS in final state:

only P(0)qq used but not P

(0)qg

P(0)gg comes with “symmetry factor” 1/2

challenge this way of implementing symmetry through:(Jadach & Skrzypek, hep-ph/0312355)

∑i=q,g

1−ε∫0

dz z P(0)qi (z) =

1−ε∫ε

dz P(0)qq (z) +O(ε)

∑i=q,g

1−ε∫0

dz z P(0)gi (z) =

1−ε∫ε

dz

[1

2P

(0)gg (z) + nf P

(0)gq (z)

]+O(ε)

net effect: replace symmetry factors by parton marker z

F. Krauss IPPP



implementation in DIRE

evolution and splitting parameter ((ij) + k → i + j + k):

κ2j,ik =

4(pi pj )(pj pk )

Q4and zj =

2(pj pk )

Q2.

splitting functions including IR regularisation(a la Curci, Furmanski & Petronzio, Nucl.Phys. B175 (1980) 27-92)

P(0)qq (z, κ2) = 2CF

[1 − z

(1 − z)2 + κ2−

1 + z

2

],

P(0)qg (z, κ2) = 2CF

[z

z2 + κ2−

2 − z

2

],

Ps(0)gg (z, κ2) = 2CA

[1 − z

(1 − z)2 + κ2− 1 +

z(1 − z)

2

],

P(0)gq (z, κ2) = TR

[z2 + (1 − z)2

]

renormalisation/factorisation scale given by µ = κ2Q2

combine gluon splitting from two splitting functions with differentspectators k → accounts for different colour flows

F. Krauss IPPP



LO results for Drell-Yan(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


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



including NLO splitting kernels

F. Krauss IPPP



including NLO splitting kernels

( Hoeche, FK & Prestel, 1705.00982, and Hoeche & Prestel, 1705.00742)

expand splitting kernels as

P(z , κ2) = P(0)(z , κ2) +αS

2πP(1)(z , κ2)

aim: reproduce DGLAP evolution at NLOinclude all NLO splitting kernels

three categories of terms in P(1):

cusp (universal soft-enhanced correction) (already included in original showers)

corrections to 1→ 2new flavour structures (e.g. q → q′), identified as 1→ 3

new paradigm: two independent implementations

F. Krauss IPPP



implementation details: 1→ 2 splittings

problem: new pole structure 1/z appears

in final-state shower: symmetrisation yields extra factor z(such a factor is present in IS shower)

this factor accounts for 1/2 typically applied to g → gg

include also q → gq splitting

physical interpretation:

“unconstrained” (without) vs. “constrained” evolution(DGLAP evolution for fragmentation functions)

factor z explicitly guarantees (momentum) sum rulesit also identifies final state particle

F. Krauss IPPP



symmetry factors not so clear at NLO −→ more care needed

∑b=q,g ,b 6=a

1−ε∫0

dz1

1−ε∫0

dz2z1z2

1− z1Θ(1− z1 − z2)

×

Pa→bab(z1, z2, . . . ) + Pa→bba(z1, z2, . . . )

=

∑b=q,g ,b 6=a

1−ε∫0

dz1

1−z1∫0

dz21∏

i=q,g

ni !Pa→bab(z1, z2, . . . ) +O(ε)

F. Krauss IPPP



1→ 3 flavour changing kernels

(Hoeche & Prestel, 1705.00742)

start with triple-collinear splitting functions(Campbell & Glover, hep-ph/9710255 & Catani & Grazzini, hepph/9908523)

re-interpret splitting as sequential:(aij) + k → (ai) + j + k ⊗ (ai) + k → a+ i + k

kinematic mappings from CDST(Catani, Dittmaier, Seymour & Trocsanyi, hep-ph/0201036)

evolution and splitting parameters:

t =4(pjpai )(paipk)

q2 −m2aij −m2

k

, za =2papk

q2 −m2aij −m2

k

sai = 2papi + m2a + m2

i , xa =papkpaipk

pa

pi

pj

pk

q

paij

↓pa

pi

pjpk

q

paij

pai

F. Krauss IPPP



phase space factorised by successive s-channels:(Dittmaier, hep-ph/9904440)

dΦ+2 =

[1

4(2π)3

dt

tdzadφjJ

(1)FF

] [1

4(2π)3dsai

dxaxa

dφiJ(2)FF (2paipj)

]combine with ME in coll. limit −→ diff. branching probability:

d log ∆1→3(aij)a

d log t=

∫dza

∫dsai

∫dxa

xa

∫dφ

2π

(αS

2π

)2 zazi

1− za

P(aij)a(pa, pi , pj )

s2aij/(2papj )

with P(aij)a = triple-collinear splitting function

F. Krauss IPPP



subtractions

must subtract spin-correlated iterated 1→ 2 splittings

d log ∆(1→2)2

(aij)a

d log t=

∫dza

∫dsai

sai

∫dξ

ξ

(αS

2π

)2 zazi

1− za

P(0)(aij)(ai)

(ξ)P(0)(ai)a

( zaξ

)

saij/(2papj )

must subtract convolution of one-loop matching coefficient withfixed-order renormalisation of fragmentation function, I

Iqq′(z) = 2CF

∫z

dx

x

(1 + (1− x)2

xlog[x(1− x)] + x

)P

(0)gq′(

z

x)

(this is the finite part of convoluting 1 → 2 in D dimensions with another 1 → 2 in 4 dimensions)

F. Krauss IPPP



final result

arrive at final expression, ready for MC implementation

Pqq′(z) =

(I +

1

εP − I

)qq′

(z) +

∫dΦ+1

(R − S

)qq′

(z ,Φ+1) ,

where (I +

1

εP)

qq′(z) =

∫dΦ+1 Sqq′ (z,Φ+1)

finite

Rqq′ (z,Φ+1) = P1→3qq′ (z,Φ+1)

Sqq′ (z,Φ+1) =saij

sai

(P

(0)qg ⊗ P

(0)gq′

)(z,Φ+1)

this looks like MC@NLO inside the Sudakov exponent

F. Krauss IPPP



validation of 1→ 3 splittings


y23

y34 × 10

Dir

ePS

e+e−→ qq @ 91.2 GeV

Sherpa

Pythia

-400

-300

-200

-100

0

100

200

300

400Jet resolution at parton level (Durham algorithm)

dσ

/d

log 10

y nn+

1[p

b]

y23

-2 σ

0 σ

2 σ

Dev

iati

on

y34

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5

-2 σ

0 σ

2 σ

log10 yn n+1

Dev

iati

on

d01

d12

Dir

ePS

pp → e+νe @ 8 TeV

Sherpa

Pythia-250

-200

-150

-100

-50

0

50

Jet resolution at parton level (kT algorithm)

dσ

/d

log 10

(dn

n+1/

GeV

)[p

b]

d01

-2 σ

0 σ

2 σ

Dev

iati

ond12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-2 σ

0 σ

2 σ

log10(dn n+1/GeV)

Dev

iati

on

F. Krauss IPPP



impact of 1→ 3 splittings


y23

Dir

ePS

e+e−→ qq @ 91.2 GeV

0.9850.99

0.9951.0

1.0051.01

1.0151.02

1.025

LOLO + 1 → 3

Jet resolution at parton level (Durham algorithm)

Rat

ioto

LO

PS

y34

one 1 → 3all 1 → 3

05

1015202530

dσ

/d

log 10

y 34

[pb]

y45 one 1 → 3all 1 → 3

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5

-0.10

0.10.20.30.40.5

log10 yn n+1

dσ

/d

log 10

y 45

[pb]

d01

Dir

ePS

pp → e+νe @ 8 TeV

0.98

0.99

1.0

1.01

1.02

1.03

1.04LOLO + 1 → 3

Jet resolution at parton level (kT algorithm)

Rat

ioto

LO

PS

d12one 1 → 3all 1 → 3

-60

-40

-20

0

20

dσ

/d

log 10

(d12

/G

eV)

[pb]

d23

one 1 → 3all 1 → 3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

01234567

log10(dn n+1/GeV)

dσ

/d

log 10

(d23

/G

eV)

[pb]

F. Krauss IPPP



physical results: e−e+ → hadrons

(Hoeche, FK & Prestel, 1705.00982)

b bb

b

b

b

b

bb

b b b b bb

bb

bb

bb

bb

bb

bb

b

b

b

b

b

Dir

ePS

b DataNLO1/4 t ≤ µ2

R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t10−1

1

10 1

10 2

Differential 2-jet rate with Durham algorithm (91.2 GeV)

dσ

/d

y 23

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

10−4 10−3 10−2 10−1

0.6

0.8

1

1.2

1.4

yDurham23

MC

/Dat

a

bb

b

b

b

b

bb

b b b b bb

bb

b

b

b

b

b

b

b

b

b

b

b

b

b

Dir

ePS


R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t10−2

10−1

1

10 1

10 2

10 3Differential 3-jet rate with Durham algorithm (91.2 GeV)

dσ

/d

y 34

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

10−4 10−3 10−2 10−1

0.6

0.8

1

1.2

1.4

yDurham34

MC

/Dat

a

F. Krauss IPPP



physical results: e−e+ → hadrons


b

bb

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

bbbbbbbb

b

Dir

ePS


R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

10−3

10−2

10−1

1

10 1

Thrust (ECMS = 91.2 GeV)

1/σ

dσ

/d

T

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 b b b b b b b b

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

0.6

0.8

1

1.2

1.4

T

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 b b b b bbbbbb

b

b

bb

b

b

Dir

ePS


R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

10−3

10−2

10−1

1

C-Parameter (ECMS = 91.2 GeV)

1/σ

dσ

/d

Cb 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 b b b b b b b b b b b b b b b

0 0.2 0.4 0.6 0.8 1

0.6

0.8

1

1.2

1.4

C

MC

/Dat

a

F. Krauss IPPP



physical results: DY at LHC


b

b b

b

b

b

b

b

b

b

bb

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

Dir

ePS


R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Z → ee ”dressed”, Inclusive

1σ

fidd

σfid

dp T

[GeV

−1 ]


0 5 10 15 20 25 300.80.91.01.11.21.31.4

Z pT [GeV]

MC

/Dat

a

b

b b

b

b

b

b

b

b

b

bb

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

Dir

ePS


R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.080.0 < |yZ| < 1.0, ”dressed”

1σ

fidd

σfid

dp T

[GeV

−1 ]


0 5 10 15 20 25 300.80.91.01.11.21.31.4

Z pT [GeV]

MC

/Dat

a

F. Krauss IPPP



physical results: diff. jet rates at LHC


Dir

ePS

pp → e+e− @ 7 TeV

NLO1/4 t ≤ µ2

R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

10 3

dσ

/d

log 10

(d01

/G

eV)

[pb]

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.70.80.91.01.11.21.3

log10(d01/GeV)

Rat

ioto

LO

Dir

ePS

pp → h @ 8 TeV

NLO1/4 t ≤ µ2

R ≤ 4 tLO1/4 t ≤ µ2

R ≤ 4 t

10−3

10−2

dσ

/d

log 10

(d01

/G

eV)

[pb]

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80.70.80.91.01.11.21.3

log10(d01/GeV)

Rat

ioto

LO

F. Krauss IPPP



limitations

and

future challenges

F. Krauss IPPP



limitation: computing short-distance cross sections – LO(Childers, Uram, LeCompte, Benjamin, Hoeche, CHEP 2016)

challenge of efficiency on tomorrow’s (& today’s) computers

2000’s paradigm: memory free, flops expensive(example: 16-core Xeon, 20MB L2 Cache, 64GB RAM)

2020’s paradigm: flops free, memory expensive & must be managed(example: 68-core Xeon KNL, 34MB L2 Cache, 16GB HBM, 96GB RAM)

may trigger rewrites of code to account for changing paradigm

CHEP San Francisco J. Taylor Childers October 2016

Code improvements enable scaling on KNL

31

9hr run-time

matrix element contributions

New results from two days ago… next test on Mira to see if we see similar improvements (figures stolen from Taylor-Childers’ talk at CHEP)

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)

we also need unglamorous improvements on existing tools:

account for new computer architectures and HPC paradigmssystematically 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 bugs me)

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

F. Krauss IPPP



achievable goals (I believe we know how to do this)

NLO for loop-induced processes:

MC@NLO tedious but straightforward → around the corner

EW NLO corrections with tricky/time-consuming calculation setup

but important at large scales: effect often ∼ QCD, but opposite signneed maybe faster approximation for high-scales (EW Sudakovs)work out full matching/merging instead of approximations

improve parton shower:

beyond (next-to) leading log, leading colour, spin-averagedHO effects in shower and scale uncertainties

→ NLO DGLAP nearly done, now soft?

start including next-to leading colourinclude spin-correlations → important for EW emissions

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

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)

tt (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;1605.08011)

Vγ (1504.01330)

γγ (1110.2375; 1603.02663)

Vj (1507.02850; 1512.01291; 1602.06965; 1605.04295; 1610.07922)

Hj (1408.5325; 1504.07922; 1505.03893; 1508.02684; 1607.08817)

jj (1310.3993; 1611.01460)

NLO corrections to gg → VV (1605.04610)

WBF at NNLO (1506.02660) and N3LO (1606.00840)

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

F. Krauss IPPP



living with the revolution

we will include them into full simulations(I am willing to place a bet: 5 years at most!)

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?)

more scales (internal or external) complicated – need integrals

philosophical questions:

going to higher power of N often driven by need to include larger FSmultiplicity – maybe not the most efficient methodlimitations of perturbative expansion:−→ breakdown of factorisation at HO (Seymour et al.)−→ higher-twist: compare (αS/π)n with ΛQCD/MZ

F. Krauss IPPP



F. Krauss IPPP


the quest for precision in simulations for the lhc · birmingham seminar, 11.10.2017 f. krauss ippp...

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