Parton Showers and theirmatching/merging
with NLO computations
Rikkert Frederix
Lund University

Iwate Collider School 2023, Feb. 27- Mar. 4, Appi, Iwate, Japan

Yesterday’s summary

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• The parton shower dresses partons with radiation. This makes
the inclusive parton-level predictions (i.e. inclusive over extra
radiation) completely exclusive• In the soft and collinear limits the partons showers areexact, but in practice they are used outside this limit as well
• Partons showers are universal (i.e. independent from theprocess)• There is a cut-off in the shower (below which we don’t trust
perturbative QCD) at which a hadronization model takes over•

Hadronization models are universal and independent fromthe energy of the collision2

Hadronisation

3FLPNNFOEFSBEGÊSHWBSJBOU

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7JUOFHBUJW• The shower stops if all partons are characterised by a scale atthe IR cut-off: Q0 ~ 1 GeV• Physically, we observe hadrons, not (coloured) partons• We need a non-perturbative model in passing from partons tocolourless hadrons• There are two models, based on physical andphenomenological considerations

3

Cluster model

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWThe structure of the perturbative evolution including angular ordering,leads naturally to the clustering in phase-space of colour-singlet parton
pairs (pre-confinement). Long-range correlations are strongly
suppressed. Hadronisation will only act locally, on low-mass colour
singlet clusters.

e-

e+

4

Stringmodel
Quark antiquark color potential and string modelė¿ėΡ

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWI>>Eƒ

From lattice
QCD one sees that the colour confinement potential of a
From lattice QCD one sees that the color confinement potential of a quark-antiquark
2 ∼ kr, with k ~quark-antiquark
linearlywith
theirdistance:
V(r)
Quark
color theirpotential
and string
growsantiquark
linearlygrows
withdistance:
V (r )model⇠ kr , withk ⇠ 0.2 GeV. This is modeled with astringwith(energy
unitpotential
length)ka quark-antiquarkthat getstension
stretched between
the qq̄
0.2 GeV,This
isuniform
modelled
a perstringwithofuniform(energyFromlattice
QCD
one seestensionthat thewith
color confinement
pair.linearly with their distance: V (r ) ⇠ kr , with k ⇠ 0.2 GeV . This is modeled with agrows
per unit
length) k that gets stretched between the qq ̄ pair.
string with uniform tension (energy per unit length) k that gets stretched between the qq̄
f&î  Ρ Ρ °Ρ LŅ  Ρ Ρ Ρ Ρ cΡ  Ρ 4  4Ρ
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Ρ 4 
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!3Ρ!
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2 ħ
H Ρ[ ΡΡ
ΡΡ ŹȟÖ­ Ρ5ΡĆ Ρ Ρ  Ρ Ρ£v}þΡ¿~þΡ¿«½ΡΡOΡ[ΡΡ5ΡfΡΡ Ρ ΡΡ² ΡΡ Ρ
ΡΡ
ΡΡ[ΡΡΡΡ4ΡΡΡ²²²Ρ ! !!Ρ4Ρ>Ρ Ρ Ρu,Ρ   Ρ! Ρ !3Ρ! ΡΡ
²! Ρ !²ΡΡ
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Ρ[ΡΡ Ρ.3Ρ[ Ρʘ  Ρ Ρ  Ρ ΡΡ[Ρ Ρ ΡͯΡ ΡΡ  -. 7KΡp ΡΡ 4Ρ ̼Ρ Ρ ȆĀ  Ρ Ρ Ρ ý Ρ[Ρ ΡΡ ΡΡΡ ΡœΡΡΡ[ΡΡ Ρ £««JΡΡ «¿þΡΡΡ  Ρ 4Ρ  Ρ   Ρ §=Ρ 4 ΡH Ρ[  Ρ ΡΡ Źȟ[Ö­ Ρ5ΡĆΡ Ρ4Ρ Ρ Ρ²²²Ρ [ΡΡHΡΡΡdΡsΡ! !!Ρ4Ρ>Ρ Ρ Ρu'K

Annu. Rev. Nucl. Part. Sci. 1986.36:253-286. Downloaded from arjournals.annualreviews.org
by Ecole Polytechnique Federal Lusanne on 12/21/09. For personal use only.

pair.

Annu. Rev. Nucl. Part. Sci. 1986.36:253-286. Downloaded from arjournals.annualreviews.org
by Ecole Polytechnique Federal Lusanne on 12/21/09. For personal use only.

Ρ Ρ Ρ Ρ[ΡΡ  Ρ.3Ρ[ Ρ -. 7K p Ρ  Ρ 4 Ρ ̼Ρ Ρ ȆĀ  Ρ Ρ Ρ ý[ Ρ  Ρ £««JΡ «¿þΡ ΡΡ  Ρ 4Ρ  Ρ   Ρ §=Ρ 4 Ρ[ΡΡHΡΡΡdΡsΡ 'K?ŜQaƄOƒ   ƒ !" ū@ĭū@ū "Y|ū@4l;4ū /@)5ū YūĮ)Õ Y45 4gū?ŜQaƄOƒ   ƒ !" ū@ĭū@ū "Y|ū@4l;4ū /@)5ū YūĮ)Õ Y45 4gūAt a certain point it becomes energetically favorable to break the string in two by
creating a new qq̄ pair in the middle of the string.

When quark-antiquarks
are too
far apart,it becomesenergeticallyAt a certain point it becomesenergeticallyfavorable
to break thestring in two by morefavourable
to breakby creatinga new qq ̄ pair in the middle.
creating
a new qq̄thepairstringin the middleof the string.
Paolo Torrielli (EPFL)

Paolo Torrielli (EPFL)

Interfacing NLO with Parton Showers

ThinkTank on Physics @ LHC

Interfacing NLO with Parton Showers

38 / 83

ThinkTank on Physics @ LHC

38 / 835

Exclusive observable

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWCharged particle multiplicity?

A parton shower program associates one of the possible histories(and pre-histories in case of pp collisions) of an hard event in an
explicit and fully detailed way, such that the sum of the probabilities ofall possible histories is unity.

6

Parton Shower MC event
generators

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWA parton shower program associates one of the possible histories(and pre-histories in case of pp) of an hard event in an explicit andfully detailed way, such that the sum of the probabilities of all
possible histories is unity.
• General-purpose tools• Always the first experimental choice• Complete exclusive description of the events: hard scattering,
showering & hadronisation (and underlying event)• Reliable and well-tuned tools• Significant and intense progress in the development of new
showering algorithms with the final aim to go at NLO in QCD
7

Pythia, Sherpa, Herwig, …

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• Significant differences between shower implementations(choice of evolution variable and kernel, momentum mappings, phasespace boundaries, massive quarks, photon emissions, etc.)• All are tuned to data, and describe it reasonably well(typically better than expected from their formal accuracy)• Some are (formally) more correct than others• However, not easy to assess accuracy for a generalobservable• Assessment (and improvement!) of formal accuracy is anactive field of research8Improving parton showers in thehard region

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• Parton shower MC programs are only correct in the softcollinear region. Hard radiation cannot be described correctly• There are two ways to improve a Parton Shower Monte Carloevent generator with matrix elements:• ME+PS merging: include matrix elements with more final
state partons to describe hard, well-separated radiation
better• NLO+PS matching: include full NLO corrections to thematrix elements to reduce theoretical uncertainties in thematrix elements. The real-emission matrix elements will
describe the hard radiation

9

An LHC collision, factorised

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

·

·

7JUOFHBUJW··Hard Interaction
Resonance Decays
MECs, Matching & Merging
FSR
ISR*
QED
Weak Showers
Hard Onium
Multiparton Interactions

dˆ0

MPI

··

Figure taken from Bierlich et al., 2022 (Pythia8.3 manual)

MPI

Meson
BaryonAntibaryon· Heavy Flavour

Beam Remnants*
Strings
Ministrings / Clusters
Colour Reconnections
String Interactions
Bose-Einstein & Fermi-Dirac
Primary Hadrons
Secondary Hadrons
Hadronic Reinteractions(*: incoming lines are crossed)

10Improving Parton Showers
LO merging

Matrix elements vs. Parton showers

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

ME

1.
Fixed order calculation
2.
Computationally expensive
3. Limited number of particles
4. Valid when partons are hard andwell separated
5. Quantum interference correct
6. Needed for multi-jet description

7JUOFHBUJWShower MC

1.
Resums logs to all orders
2.
Computationally cheap
3. No limit on particle multiplicity
4. Valid when partons are collinear
and/or soft
5. Partial interference throughangular ordering
6.
Needed for hadronisation

Approaches are complementary: merge them!

Avoid double counting, ensure smooth distributions
12

Possible double counting

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWMatrix elements

Parton shower
kT < tcut
kT < tcut
kT < tcut
kT > Qc

kT > tcut

kT > tcut
kT > tcut

...

...

kT < tcut

...

...

Possible double counting
between partons frommatrix elements and parton
shower easily avoided byapplying a cut in phase
space
13

Merging ME with PS

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• So double counting no problem, but what about getting smooth
distributions that are independent of the precise value of tcut?
• Below cutoff, distribution is given by PS- need to make ME look like PS near cutoff• Let’s take another look at the PS!

14

Merging ME with
PS
t
cut

t1

e-

t2

Q2

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW

tcut
tcut

e+
tcut

• How does the PS generate the configuration above (i.e. starting frome+e- -> qqbar events)?
• Probability for the splitting at t1 is given by2
2 ↵s (t1 )( q (Q , t1 ))Pgq (z)2⇡and for the whole tree↵s (t2 )22
2 ↵s (t1 )( q (Q , tcut )) g (t1 , t2 )( q (t2 , tcut ))Pgq (z)Pqg (z 0 )
2⇡
2⇡
15

Merging ME with
PS
t
cut

t1

e-

t2

Q2

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW

tcut
tcut

e+
tcut

(

2

q (Q , tcut ))2

g (t1 , t2 )(q (t2 , tcut ))2 ↵s (t1 )↵s (t2 )Pgq (z)Pqg (z 0 )2⇡
2⇡

Leading Logarithmic approximation of the matrix element
BUT with αs evaluated at the scale of each splitting
Sudakov suppression due to disallowing additional radiation
above the scale tcut
16

Merging ME with PS
e

e+

t1
Q2

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWt2|M|2 (ŝ, p3 , p4 , ...)

To get an equivalent treatment of the corresponding matrix element,
do as follows:
1. Cluster the event using some clustering algorithm- this gives us a corresponding “parton shower history”
2. Reweight αs in each clustering vertex with the clustering scale2
2 ↵s (t1 ) ↵s (t2 )|M| ! |M|↵s (Q2 ) ↵s (Q2 )3. Use some algorithm to apply the equivalent Sudakov
2
2
2
suppression( q (Q , tcut )) g (t1 , t2 )( q (t2 , tcut ))17

Merging ME with PS

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWCKKW (2004) and MLM (2004)• In summary:• Double counting no problem: we simply throw events away when thematrix-element partons are too soft, or when the parton shower
generates too hard radiation• Applying the matrix-element cut is easy: duringphase-space integration, we only generate eventswith partons above the matching scalekT < tcut

kT > tcut• For the cut on the shower, there are two methods. Throwing events away
after showering is not very efficient, although it is working (“MLMmethod”)• Instead we can also multiply the Born matrix elements by suitable productof Sudakov factors (i.e. the no-emission probabilities) Δ(Qmax, tcut) andstart the shower at the scale tcut (“CKKW method”).
• For a given multiplicity we have<latexit sha1_base64="C/jSNbwVVUWDAHTsvWHyI8fs69U=">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</latexit>LOn,excl = Bn ⇥(kT,ntcut )n (Q, tcut )
18

NL
dsQC

20

50

Merging results
100

200

500
d01 [GeV]

pp ! ` n̄ + 0,1,2 j @ 13 TeV

10 4

Qcut = 10 GeV
Qcut = 15 GeV
Qcut = 20 GeV

10 3
10 2

Qcut = 30 GeV
Qcut = 40 GeV
Qcut = 60 GeV
Qcut = 100 GeV
Qcut = 200 GeV
inclusive

10 1
1
10 1
10 2

dsLO ( Qcut )/dsLO (20 GeV)

10 3
10 4
1.2
1

CKKW-L
MEPS@LO

0j

1j

2j

0.8
0.6

ds/dd12 [pb/GeV]

ds/dd01 [pb/GeV]

10

0.2
10

20

50

100
3FLPNNFOEFSBEGÊSHWBSJBOU

pp ! ` n̄ + 0,1,2 j @ 13 T

10 4

4WBSU

7JUOFHBUJWQcut = 10 GeV
Qcut = 15 GeV
Qcut = 20 GeV• W+jets production: diff. jet
10 2 0➙1 transition (~ pT
rate forof hardest
jet)
10 1
10 3

1
• Small dependence
on themerging
10 1 scale for smallvalues,~10%210• When10 3 taken too large, thepartonshower cannot fill
10 4
the1.2region
all
the
way
up
0j
MEPS@LOto the1 merging scale
anymore,leading to large
0.8
deficits
0.6
dsLO ( Qcut )/dsLO (20 GeV)

NL
dsQC

0.2

0.4 Lindert,[Kallweit,
Maierhöfer,Pozzorini,
0.2
Schönherr 2016]

0.4
0.2
10

20

50

100

200

500
d01 [GeV]

10

20

50

100

19

ME+PS (at LO)

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• Merging matrix elements of various multiplicities with parton
showers improves the predictive power of the parton shower
outside the collinear/soft regions•

These merged samples give good description of the data(except for the total normalisation)• There is a dependence on the parameters responsible for the cut
in phase-space (i.e. the matching scale)• By letting the matrix elements mimic what the parton shower doesin the collinear/soft regions (PDF/alphas reweighting and including
the Sudakov suppression) the dependence is greatly reduced• In practice, one should check explicitly that this is the case byplotting differential jet-rate plots for a couple of values for thematching scale
20

Improving Parton Showers:
NLO matchingAt NLO

3FLPNNFOEFSBEGÊSHWBSJBOU

2
4WBSU

gs

7JUOFHBUJW+ ...

• We have to integrate the real emission over the complete
phase-space of the one particle that can go soft or collinear to
obtain the infra-red poles that will cancel against the virtual
corrections• Hence, we cannot introduce a "cut" that says that:• hard radiation needs to be described by
the matrix elements• and soft radiation by the parton shower• We have to invent a new procedure to match
NLO matrix elements with parton showers

22Naive (wrong) approach

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• In a fixed order calculation we have contributions with m final stateparticles
and with m+1Zfinal stateZ
Z particles
Z

NLO

⇠

d4

m B(

m) +

d4

dd l V (

m

m) +

dd

m+1 R(

m+1 )

loop

• We could try to shower them independently(k)• Let IMC (O) be the parton shower spectrum for an observable O,
showering from a k-body initial condition• We can then try to shower the m and m+1 final states
independently
d NLOwPS= ddO

m (B +Z(m)V ) IMC (O) + d

loop

(m+1)

m+1 R IMC(O)

23

NLO+PS: sources of double counting

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWParton shower
Born+Virtual:
Real emission:

...
...

• There is double counting between the real emission matrix elements and the parton
shower: the extra radiation can come from the matrix elements or the parton shower• There is also an overlap between the virtual corrections and the Sudakov
suppression in the zero-emission probability• We have to integrate the real emission over the complete phase-space of the one
particle that can go soft or collinear to obtain the infra-red poles that will cancel
against the virtual corrections• We can NOT use the same merging procedure as used at LO (MLM or CKKW):
requiring that all partons should produce separate jets is not infrared safe
24Double counting in virtual/Sudakov

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• The Sudakov factor Δ (which is responsible for the resummationof all the radiation in the shower) is the no-emission probability• It’s defined to be Δ = 1 - P, where P is the probability for abranching to occur• By using this conservation of probability in this way, Δ contains
contributions from the virtual corrections implicitly• Because at NLO the virtual corrections are alreadyincluded via explicit matrix elements, Δ is double
counting with the virtual corrections• In fact, because the shower is unitary, what we are
double counting in the real emission corrections isexactly equal to what we are double counting in thevirtual corrections (but with opposite sign)!
25

Avoiding double counting

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• There are two widely methods to circumvent this double
counting• MC@NLO (Frixione & Webber)• POWHEG (Nason)• KRKNLO (Cracow group), Vincia (Skands et al.), Geneva (Alioli et al.), …

26

MC@NLO procedure

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWFrixione & Webber (2002)• To remove the double counting, we can add and subtract thesame term to the m and m+1 body configurations
"

Z

Z

+ d

m+1 (Rd MC@NLO= d m (B +
V +
dO
loop
"

d

1 M C)##(m)
IMC (O)(m+1)

M C) )IMC(O)

Where the MC are defined to be the contributionof the parton shower to get from the m body Born
final state to the m+1 body real emission final state27

MC@NLO procedure

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWParton shower
Born+Virtual:...

Real emission:...

• Double counting is explicitly removed by including the “shower
subtraction terms”

d NLOwPS= ddO

m (B +



+ d

Z

Z
V + d

1 M C)M C)(m+1)
IMC (O)loop

m+1 (R(m)
IMC (O)28

Negative weights
d NLOwPS= ddO

m (B +



+ d

Z

4WBSU

Z
V + d

1 M C)M C)(m+1)
IMC (O)loop

m+1 (R

3FLPNNFOEFSBEGÊSHWBSJBOU

7JUOFHBUJW(m)
IMC (O)• We generate events for the two terms between the square brackets(S- and H-events) separately• There is no guarantee that these contributions are separately
positive (even though predictions for infra-red safe observables
should always be positive!)• Therefore, when we do event unweighting we can only unweight
the events up to a sign. These signs should be taken into accountwhen doing a physics analysis (i.e. making plots etc.)• The events are only physical when they are showered29

Cost of negative weights

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4WBSU

7JUOFHBUJW• The computational costs to generate events negative weights
can be enormous: for physical observables they cancel against
positive weight events, but the overall sample still carries thestatistical uncertainty of the full sample:
Correlation
C± = 0%C± = 50%C± = 100%70
50

Relative cost, c(f )

30
20
15
10
7
5
3
2
1.5
1
0

5

10

15

20

25

30

Fraction of negative weights, f [%]

35

40

45

30

NLO+PS

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7JUOFHBUJW• Advantages:• Total cross section and differential distributions related tothe hard process are NLO accurate• Reduced renormalisation and factorisation scale
uncertainties• Shower to include multiple emissions; there are models forhadronisation and underlying event• Fully exclusive description of the event• Disadvantages• Other observables (e.g., "multi-jet") are only LO accurate, oronly generated by the shower
31

Merging ME+PS at NLO accuracy

Merging LO ME with PS

3FLPNNFOEFSBEGÊSHWBSJBOU

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7JUOFHBUJWCKKW (2004) and MLM (2004)• In summary:• Double counting no problem: we simply throw events away when thematrix-element partons are too soft, or when the parton shower
generates too hard radiation
kT < Qc• Applying the matrix-element cut is easy: duringphase-space integration, we only generate eventswith partons above the matching scale

kT > Qc• For the cut on the shower, there are two methods. Throwing events away
after showering is not very efficient, although it is working (“MLMmethod”)• Instead we can also multiply the Born matrix elements by suitableproduct of Sudakov factors (i.e. the no-emission probabilities) Δ(Qmax, Qc)
and start the shower at the scale Qc (“CKKW method”).
• For a given multiplicity we haveLOn,excl = Bn ⇥(kT,n

Qc )

c
(Q
,
Q
)
n
max
33

=

Merging at NLO

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7JUOFHBUJW• To make a LO prediction exclusive in the number of jets, we need tomultiply it by a Sudakov damping factor; this is CKKW method:LOn,excl = Bn ⇥(kT,n

Qc )

c
(Q
,
Q
)
n
max

This makes the prediction exclusive at leading logarithmic accuracy• Similarly we can make an NLO prediction exclusive at leading logarithm
⇢
Z
NLO
c
c
=
B
+
V
+
d
R
⇥(k
Q
)
(Q
,
Q
)
n
n
1 n+1
T,n
n
max
n,excl, LL• We can improve here and use the real-emission matrix elements
instead of just the Sudakov:⇢

NLOn,excl, LL =Z Qc

B n + Vn +

d

0

⇢

B n + Vn +1 Rn+1Z Qc

d

1 Rn+1

0

Bn

(1)
c
(Q
,
Q
)
max
n

Bn

(1)
c
(Q
,
Q
)
max
n

⇥(kT,nQc )⇥(kT,n

Qc )

n

c
(Q
,
Q
)
n
max
34

Exclusive MC@NLO:
FxFx merging and MEPS@NLO

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• Converting the NLO exclusive predictions in the number of jets
to the MC@NLO event generation is straight-forward:
⇢

Z Qc

c
B
c
S-events:
B n + Vn +d 1 MC Bn (1)
(Q
,
Q
)
⇥(k
Q
) n (Q
max
n
T,n
⇢
Z Qc
0
c
B
c
B
c
nts:
B n + Vn +d 1 MC Bn (1)
(Q
,
Q
)
⇥(k
Q
)
(Q
,
Q
)
max
n
n
T,n
max
0⇢
R
B
R
H-events:
Rn+1 ⇥(kT,nQc ) MC ⇥(kT,nQc ) ⇥(Qc kT,n+1) n (QR
ma
⇢
R
B
R
c
-events:
Rn+1 ⇥(kT,nQc ) MC ⇥(kT,nQc ) ⇥(Qc kT,n+1) n (QR,Q)
max• But the evil is in the details…
35

FxFx merging: Higgs boson production

3FLPNNFOEFSBEGÊSHWBSJBOU

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7JUOFHBUJW[RF and Frixione]

Figure 3: As in fig. 1, with Sudakov re• Transverse momentum of the Higgs and of the 1stjet.
• Agreement with H+0j at MC@NLO
and H+1j at MC@NLO in their
the lower insets of fig. 2). On the one hand, this overestim
respective regions of phase-space;
Smoothdue
matching
in between;
contributions
to scales close
to the end-points of the mSmall dependence on matching scale(in the effective average performed by the smooth D functi

the other hand, this is not equivalent to assessing the effe
36

NLO ( Q )/ds NLO (
dsQCD
cut
QCD

0.8
0.6
0.4

100

200

Qcut = 10 GeV
Qcut = 15 GeV
Qcut = 20 GeV

10 3
10 2

1

10

2

10

3

dsLO ( Qcut )/dsLO (20 GeV)1

MEPS@LO

0j

1j

2j

0.8
0.6
0.4
0.2
10

20

50

100

200

3FLPNNFOEFSBEGÊSHWBSJBOU

0.2

10

10 4
10 3
10 2
10 1

1

4

10
1.2

0.4

20

50

100

200

500
d12 [GeV]
4WBSU

7JUOFHBUJW

Kallweit, 2016]
Lindert,[Kallweit, Lindert, Maierhöfer,ppPozzorini,
Schönherr! ` n̄ + 0,1,2 j @ 13 TeV

Qcut = 30 GeV
Qcut = 40 GeV
Qcut = 60 GeV
Qcut = 100 GeV
Qcut = 200 GeV
inclusive

10 1

10

0.6

500
d01 [GeV]

pp ! ` n̄ + 0,1,2 j @ 13 TeV

10 4

1

0.8

500
d01 [GeV]

10

1

10

2

10

3
4

10
1.2
1

0.8
0.6
0.4

pp ! ` n̄ + 0,1,2 j @ 13 TeV

10 4

Qcut = 10 GeV
Qcut Q= 10=GeV
15 GeVcut
Qcut Q=cut
15=GeV
20 GeV
Qcut = 20 GeV

10 3
10 2

Qcut = 30 GeV
QcutQ= 30=GeV
40 GeVcut
QcutQ= 40=GeV
60 GeVcut
QcutQ=cut60=GeV
100 GeV
QcutQ=cut100
GeVGeV= 200
Qcutinclusive= 200 GeV
inclusive

10 1
1

Sherpa+OpenLoops

50

ds/dd12 [pb/GeV]

20

dsLO ( Qcut )/dsLO (20 GeV)

ds/dd01 [pb/GeV]

10

Electroweak corre

Mergingsystematics: pp ! ` ⌫¯
Merging scaledependence
ds/dd01 [pb/GeV]

0.2

NLO ( Q )/ds NLO (20 GeV)
dsQCD
cut
QCD

NLO ( Q )/ds NLO (
dsQCD
cut
QCD

Next-to-leading order electroweak corrections

10 1
10 2
10 3
10 4
1.2

MEPS@LO
1MEPS@NLO QCD

0j

1j

0j

1j

2j

2j

0.8
0.6
0.4
0.2

0.2

10

10

20

20

50

50

100

100

200

200

500
500 d12 [GeV]

d01 [GeV]

25. Multijet
mergingof the1 ! higher-accurate
0 (left) and 2 ! 1 (right)
k? jet resolutions(R = 0.6)•FigureBesideshavingthesystematics
benefitsfrommatrixelements,) next-to-leading
dead zonesorderin (top)incl.multijetobs. ifmerging
Qcutintoo
in pp ! ` ⌫¯ + jets events in leading order (bottom) andthere is also a smaller merging scale dependence at NLO
the MEPS scheme. Only basic lepton acceptance cuts are applied. The contributions of the individual jet
37

FxFx
• Comparison to data
• Z+jets• Exclusive jet multiplicity
and hardest and 3rd
hardest jet pT spectra• Uncertainty band
contains ren. & fac.
scale, PDF & merging
scale dependence• Rather good agreement
between data andtheory3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJWFigure 1: Exclusive jet multiplicity. Data from ref. [28], compared to Herwig++ (leftpanel) 1:andExclusive
Pythia8jet(rightpanel) predictions.
FxFxcompared
uncertainty
envelope (“Var”)
Figuremultiplicity.
Data from The
ref. [28],to Herwig++(left
and thefully-inclusive
centralresult(“inc”) are Theshown
as green
bands andred histograms
panel)
andPythia8 (rightpanel)
predictions.
FxFx
uncertainty
envelope(“Var”)
respectively.
See the endof sect.
2 formorearedetailson as
thegreenlayoutof theandthe fully-inclusive
centralresult(“inc”)
shown
bands
andplots.
red histograms
respectively. See the end of sect. 2 for more details on the layout of the plots.
Figure 1: Exclusive jet multiplicity. Data from ref. [28], compared to Herwig++ (leftpanel) and Pythia8 (right panel) predictions. The FxFx uncertainty envelope (“Var”)
and the fully-inclusive central result (“inc”) are shown as green bands and red histograms
respectively. See the end of sect. 2 for more details on the layout of the plots.

Figure 2: As in fig. 1, for the transverse momentum of the 1st jet.
Figure 2: As in fig. 1, for the transverse momentum of the 1st jet.

Figure 2: As in fig. 1, for the transverse momentum of the 1st jet.

Figure 3: As in fig. 1, for the transverse momentum of the 3rd jet.

38

(QCD+EW)xPS
40
NLO EW
various distributions
are shown in the upper panels of each plot. The lower panels

dσ/dMT(W), pb/GeV

30

the relative di↵erence, in per cent, between the results of the new version of the30
BOX and the standard QCD release, as well as the relative e↵ect due to pure N
corrections. Therefore the comparison between the two lines in each lower panel
20
a measure of the combination of QCD and EW corrections and, more precisely, on ↵n , n
EW⌦QCD contributions at order ↵em
1 in perturbation theory.9s

25

NLO+PS matching including EW
corrections
δ(%)

20
15

3FLPNNFOEFSBEGÊSHWBSJBOU

10d1 d2d/dM (W ) (pb/GeV)2(%)
d1 + d2

1050

• In POWHEG,60two65independent
implementations
70
75
80
85
90
95
100
(W), GeV
of QCD+EW corrections tomTW-boson
production
exist [Bernaciak & Wackeroth (2012); Barzè et al.

150

-10

60

4WBSU

PWG EW w PYTHIA+PHOTOS Barzè et al. (2012)
PWG w PYTHIAEW NLO
BORN

200

100 65

70

75

80

85

90

95

7JUOFHBUJW

100mT(W), GeV

50(2012)]
0
1 , δQCD , δQCDEW for pp̄ → W + → µ+ νµ ,FIG. 3: MT (W ) distributions and relative corrections δEW-2√• MG5_aMC
and Sherpa working towards-5
S = 1.96 TeV, obtained with POWHEG-W EW, with bare cuts.
Parton showering (denoted by PS) is
-8
-11
-14
-17

1. PWG EW w shower - 2. PWG w shower
1. EW NLO - 2. BORN

50

60

70
80
M (W ) (GeV)

90

100

50 panel: the W transverse mass distribution according to the full Q
Figure 3. Upper

80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5

δEW
LOxPS
δQCD
predictions
ofthe
POWHEGBOX(denoted
as
PWG
EW
w
PYTHIA+PHOTOS),
the standard QCD
QCDxPSδQCDEW(QCD+EW)xPS
BOX (PWG w PYTHIA),
the LO and the NLO EW approximations. Lower panel: relative d40
NLO EWin per cent, between the full QCD⌦EW predictions and the pure QCD ones (red, solid
comparison with30the relative contribution due to pure NLO EW corrections (green, dot
The di↵erence between the two lines is a measure of the mixed QCD⌦EW corrections.
δ(%)

dσ/dMT(W), pb/GeV

automation. Some first results withperformed by interfacingwith Pythia.
Sherpa+OpenLoops
have beenpresented,
although they include only EW corrections ofvirtual origin [Kallweit et al. (2015)]

20

From the upper panels, one can clearly see that NLO QCD corrections in ass
10with QCD shower e↵ects are strictly needed for a correct simulation of both
9

The exact O(↵0em ↵s ) corrections to DY processes are presently unknown, albeit partial ravailable in the literature [30–33, 50] and further work is in progress along this direction.
60

65

70

75

80

mT(W), GeV

85

90

95

100

-10
60

65

70

75

80

85

90

95

100

mT(W), GeV

39

Conclusions

3FLPNNFOEFSBEGÊSHWBSJBOU

4WBSU

7JUOFHBUJW• In the last couple of years the accuracy of event generation has
greatly improved, and full automation has been achieved at NLO
accuracy• A lot of freedom in tuning has been replaced by accurate theory
descriptions:• More predictive power• Better control on uncertainties• Greater trust in the measurements• Recent developments for which I have had no time
• NLO EW corrections and the parton shower• Combining NNLO in QCD and the parton shower: MINNLO• MC@NLO-Delta: reducing negative weights in MC@NLO
40