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
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
motivation & introduction
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
need more precise & accurate tools for more precise physics
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
matching @ (N)NLO
and
merging @ (N)LO
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
illustration: pH⊥ in 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 byMC@NLO , restrict toQn+1 < Qcut
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
including EW corrections
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 1j inclusive
LONLO QCD
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 1j inclusive
LONLO QCDNLO QCD+EW
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 1j inclusive
LONLO QCDNLO QCD+EWNLO QCD+EW+subLO
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 1j exclusive
LONLO QCDNLO QCD+EWNLO QCD+EW+subLO
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 2j 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) ≈ πNLO 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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 2j inclusive
LONLO QCD
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 2j inclusive
LONLO QCDNLO QCD+EW
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 2j inclusive
LONLO QCDNLO QCD+EWNLO QCD+EW+subLO
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
Sher
pa+O
pen
Lo
ops
LHC 8 TeVpp → µν + 2j inclusive
LONLO QCDNLO QCD+EWNLO QCD+EW+subLONLO QCD+EW+subLO+sub2LO
0
0.05
0.1
0.15
0.2
0.25Angular separtion of leading jet and muon
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
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)
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
0.25Angular separtion of leading jet and muon
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
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
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)R
) [fb]
∆/d
(σ
d
20
40
60
80
100
1201 = 8 TeV, 20.3 fbs
Data
ALPGEN+PYTHIA6 W+jets
PYTHIA8 W+j & jj+weak shower
SHERPA+OpenLoops W+j & W+jj
< 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
, 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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
NLO EW predictions for ∆R(µ, j1)R
) [fb]
∆/d
(σ
d
5
10
15
20
25
30
35
40
45
501 = 8 TeV, 20.3 fbs
Data
ALPGEN+PYTHIA6 W+jets
PYTHIA8 W+j & jj+weak shower
SHERPA+OpenLoops W+j & W+jj
> 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
, 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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
improving parton showers
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
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
0.8 ≤ |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
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
1.6 < |yZ|
10−3 10−2 10−1 1
0.80.91.01.11.2
→ | | ≥
φ∗η
MC
/Dat
a
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
including NLO splitting kernels
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
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Introduction fixed-order inprovements Parton Showers future directions
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
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Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
validation of 1→ 3 splittings
(Hoeche & Prestel, 1705.00742)
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
impact of 1→ 3 splittings
(Hoeche & Prestel, 1705.00742)
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
b DataNLO1/4 t ≤ µ2
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
physical results: e−e+ → hadrons
(Hoeche, FK & Prestel, 1705.00982)
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
b DataNLO1/4 t ≤ µ2
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
b DataNLO1/4 t ≤ µ2
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
physical results: DY at LHC
(Hoeche, FK & Prestel, 1705.00982)
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
b DataNLO1/4 t ≤ µ2
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 ]
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 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
b DataNLO1/4 t ≤ µ2
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 ]
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 5 10 15 20 25 300.80.91.01.11.21.31.4
Z pT [GeV]
MC
/Dat
a
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
physical results: diff. jet rates at LHC
(Hoeche, FK & Prestel, 1705.00982)
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
limitations
and
future challenges
F. Krauss IPPP
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
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
Quest for Precision in Simulations for the LHC
Introduction fixed-order inprovements Parton Showers future directions
F. Krauss IPPP
Quest for Precision in Simulations for the LHC