Pythia Overview : 2013–2016skands.physics.monash.edu/slides/files/16-MCnet-Pythia.pdf · 2013: Freezing of the Fortran Pythia 2 December 2012 Dear Pythia Users and Supporters, …

Pythia Overview : 2013–2016P e t e r S k a n d s ( M o n a s h U n i v e r s i t y )

MCnet Network Meeting CERN, November 2016

On behalf of: TS Torbjörn SjöstrandND Nishita DesaiNF Nadine FischerIH Ilkka HeleniusPI Philip IltenLL Leif LönnbladSM Stephen MrennaSP Stefan PrestelCR Christine RasmussenPS Peter Skands+SA Spyros ArgyropoulosJC Jesper Roy ChristiansenRC Richard Corke

See T. Sjöstrand et al., CPC 191 (2015) 159

2013: Freezing of the Fortran Pythia

2

December 2012

Dear Pythia Users and Supporters,

…

A key request of the LHC community has been for us to transition from Fortran to C++. We have been manpower-limited, so that project has taken much longer than it ought to have. However, since some time now, the new Pythia 8 code should be able to do just about everything the old Pythia 6 code could, and then some more.

…

Development of Pythia 6 now stops. We will still provide support and urgent fixes to the code, if necessary, until 1 March 2013. At this point, the Pythia 6 code will be frozen, and a final legacy version will be released later in 2013. We will then continue to answer questions regarding the behaviour of Pythia 6 until 1 July 2013, after which only Pythia 8 will be actively developed and supported.

๏Beginning of 2013: •Pythia 8 (C++) ~ similar level of capabilities as Pythia 6 (F77)

•(Too) Demanding to develop & support two separate large codes.

๏Decision to freeze PYTHIA 6. ๏Staggered → September 2013 ๏First development stopped, then support

๏By now, usage (slowly) declining •Pythia 6.4 remains widely used

๏Despite lack of support •Pythia 8 usage is increasing

๏But does not appear to have overtaken Pythia 6 yet …

TS=Sjöstrand ND=Desai NF=Fischer IH=Helenius PI=Ilten LL=Lönnblad SM=Mrenna SP=Prestel CR=Rasmussen PS=Skands SA=Argyropoulos JC=Christiansen RC=Corke

TS, SM, PS

2014: Release of Pythia 8.2

3

๏CPC writeup (on arXiv: Oct 2014) •First attempt to provide more than “coversheet” for Pythia 8 release → arXiv paper expanded by ~ factor 2 (to 45 pages)

•Still nowhere close to Pythia 6 manual (576p) but supplemented by extensive HTML manual


TS et al., CPC 191 (2015) 159

Computer Physics Communications 191 (2015) 159–177

Contents lists available at ScienceDirect

Computer Physics Communications

journal homepage: www.elsevier.com/locate/cpc

An introduction to PYTHIA 8.2I

Torbjörn Sjöstranda,⇤, Stefan Askb,1, Jesper R. Christiansena, Richard Corke a,2,Nishita Desai c, Philip Iltend, Stephen Mrennae, Stefan Prestel f,g,Christine O. Rasmussena, Peter Z. Skandsh,i

a Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Swedenb Department of Physics, University of Cambridge, Cambridge, UKc Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germanyd Massachusetts Institute of Technology, Cambridge, MA 02139, USAe Fermi National Accelerator Laboratory, Batavia, IL 60510, USAf Theory Group, DESY, Notkestrasse 85, D-22607 Hamburg, Germanyg SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USAh CERN/PH, CH-1211 Geneva 23, Switzerlandi School of Physics, Monash University, PO Box 27, 3800 Melbourne, Australia

a r t i c l e i n f o

Article history:Received 14 October 2014Accepted 26 January 2015Available online 11 February 2015

Keywords:Event generatorsMultiparticle productionMatrix elementsParton showersMatching and mergingMultiparton interactionsHadronisation

a b s t r a c t

The Pythia program is a standard tool for the generation of events in high-energy collisions, comprising acoherent set of physics models for the evolution from a few-body hard process to a complexmultiparticlefinal state. It contains a library of hard processes, models for initial- and final-state parton showers,matching and merging methods between hard processes and parton showers, multiparton interactions,beam remnants, string fragmentation and particle decays. It also has a set of utilities and several interfacesto external programs. Pythia 8.2 is the second main release after the complete rewrite from Fortran toC++, and now has reached such a maturity that it offers a complete replacement for most applications,notably for LHC physics studies. The many new features should allow an improved description of data.

New version program summary

Program title: Pythia 8.2Catalogue identifier: ACTU_v4_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ACTU_v4_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public Licence, version 2No. of lines in distributed program, including test data, etc.: 478360No. of bytes in distributed program, including test data, etc.: 14131810Distribution format: tar.gzProgramming language: C++.Computer: Commodity PCs, Macs.Operating system: Linux, OS X; should also work on other systems.RAM: ⇠10 megabytesClassification: 11.2.

I This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).⇤ Corresponding author.

E-mail address: [email protected] (T. Sjöstrand).1 Now at Winton Capital Management, Zurich, Switzerland.2 Now at Nordea Bank, Copenhagen, Denmark.

http://dx.doi.org/10.1016/j.cpc.2015.01.0240010-4655/© 2015 Elsevier B.V. All rights reserved.

https://arxiv.org/abs/1410.3012

2014: Release of Pythia 8.2

4

๏Code & Build Restructuring •Revamped configure+make (+simplify linking of external libs); Auxiliary files moved to share/Pythia; Dynamical loading of LHAPDF interface when requested (v5 or v6)

๏Significant News (continued on next slides) •Weak Showers (since 8.176): W/Z emissions from q, ℓ, ν •Improved handling of (helicity-dependent) tau decays (since 8.150)

๏All decays with BR > 0.1% fully modelled with MEs and Form Factors ๏Extended to correlations between known resonances in LHEF input (since 8.200) ๏Extended to set up tau spin information in W’ and Z’ decays (since 8.209)

•Significant extensions to colour-octet cc & bb onium states (since 8.185) •Several New Models for Colour Reconnections •Comprehensive update of baseline tune

๏From 4C to Monash 2013 (still default) ๏Including new ee tune to (revised) LEP/SLD data & new internal NNPDF 2.3 implementation

๏+ Several further options from ATLAS and CMS (A14 + MonashStar added in 8.205)


PI, TS, …

RC,TS JHEP 1103 (2011) 032 PS et al., EPJ C74 (2014) 3024

JC,TS JHEP 1404 (2014) 115

JC,PS JHEP 1508 (2015) 003 SA,TS JHEP 1411 (2014) 043

PI

PI

+implementation of SK models for ee (since 8.209)

๏(since 8.170)

News cont’d: ME Matching & Merging

5

๏No internal ME generator → rely on (LHEF) interfaces •8.2: aMC@NLO matching added to the list of implemented schemes

๏With Torielli, Frixione; required addition of “global recoil” option

•→ A comprehensive suite of approaches (+ examples & tutorial) ๏aMC@NLO Matching ๏POWHEG Merging ๏CKKW-L Merging ๏NL3 Merging (~ CKKW-L @ NLO) ๏UMEPS Merging ๏UNLOPS Merging (~ UMEPS @ NLO) ๏FxFx ๏Jet Matching (aka MLM)

๏+ MECs (matrix-element corrections) •Often forgotten that standalone Pythia includes LO MECs for the 1st emission in all SM (and many BSM) decay processes (e.g., t→bW+g)

•+ a few production processes (Drell-Yan & Higgs production)


Stefan Prestel, with Leif Lönnblad, Steve Mrenna

+ 2014: LHEF v3

Mos

t of t

his

wor

k do

ne b

y SP

ove

r th

e la

st 4

yea

rs …

Les Houches arXiv:1405.1067,

Lönnblad & Prestel, JHEP 1302 (2013) 094, Lönnblad & Prestel, JHEP 1303 (2013) 166

See e.g., Frederix, Frixione, Papaefstathiou, Prestel, Torrielli: JHEP 1602 (2016) 131


Unitarised Matching & Merging

6TS=Sjöstrand ND=Desai NF=Fischer IH=Helenius PI=Ilten LL=Lönnblad SM=Mrenna SP=Prestel CR=Rasmussen PS=Skands SA=Argyropoulos JC=Christiansen RC=Corke

Slides adapted from Stefan Prestel

-30 -20 -10

0 10 20 30 40 50

1 2 3 4 5 6 7 8 9 10

Dev

iatio

n [%

]

p⊥ w [GeV]

(CKKW-L tMS=0.5 GeV) / (Pythia8)(CKKW-L tMS=1 GeV ) / (Pythia8)(CKKW-L tMS=2 GeV ) / (Pythia8)

2.0⋅10-8

4.0⋅10-8

6.0⋅10-8

8.0⋅10-8

1.0⋅10-7

1.2⋅10-7

1.4⋅10-7

dσ/d

p⊥

w [

mb/

GeV

]

Pythia8CKKW-L tMS=0.5 GeVCKKW-L tMS=1 GeV CKKW-L tMS=2 GeV

-30 -20 -10

0 10 20 30 40 50

1 2 3 4 5 6 7 8 9 10D

evia

tion

[%]

p⊥ w [GeV]

(UMEPS tMS=0.5 GeV) / (Pythia8)(UMEPS tMS=1 GeV ) / (Pythia8)(UMEPS tMS=2 GeV ) / (Pythia8)

2.0⋅10-8

4.0⋅10-8

6.0⋅10-8

8.0⋅10-8

1.0⋅10-7

1.2⋅10-7

1.4⋅10-7

dσ/d

p⊥

w [

mb/

GeV

]

Pythia8UMEPS tMS=0.5 GeVUMEPS tMS=1 GeV UMEPS tMS=2 GeV

p⊥ ECM = 7

⇒⇒

CKKW-L (non-unitarised)UMEPS (unitarised)

Matrix Elements contain singularities beyond LL; not canceled by pure shower Sudakov. Imposing detailed balance (unitarity) restores explicit real-virtual cancellation Extreme example: choosing very low matching scales (~ in Sudakov peak region)

Preserves Sudakov Peak StructureTotal Cross Section Grows + Sudakov Peak Modified

-30 -20 -10

0 10 20 30 40 50

1 2 3 4 5 6 7 8 9 10

Dev

iatio

n [%

]

p⊥ w [GeV]

(CKKW-L tMS=0.5 GeV) / (Pythia8)(CKKW-L tMS=1 GeV ) / (Pythia8)(CKKW-L tMS=2 GeV ) / (Pythia8)

2.0⋅10-8

4.0⋅10-8

6.0⋅10-8

8.0⋅10-8

1.0⋅10-7

1.2⋅10-7

1.4⋅10-7

dσ/d

p⊥

w [

mb/

GeV

]

Pythia8CKKW-L tMS=0.5 GeVCKKW-L tMS=1 GeV CKKW-L tMS=2 GeV

-30 -20 -10

0 10 20 30 40 50

1 2 3 4 5 6 7 8 9 10

Dev

iatio

n [%

]

p⊥ w [GeV]

(UMEPS tMS=0.5 GeV) / (Pythia8)(UMEPS tMS=1 GeV ) / (Pythia8)(UMEPS tMS=2 GeV ) / (Pythia8)

2.0⋅10-8

4.0⋅10-8

6.0⋅10-8

8.0⋅10-8

1.0⋅10-7

1.2⋅10-7

1.4⋅10-7

dσ/d

p⊥

w [

mb/

GeV

]

Pythia8UMEPS tMS=0.5 GeVUMEPS tMS=1 GeV UMEPS tMS=2 GeV

p⊥ ECM = 7

⇒⇒

see main86.ccexample program

http://main86.cc

Unitarised Merging @ NLO



0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

15 20 25 30 35 40 45

!m

erg

ed / !

incl

usi

ve

tMS [GeV]

NL3 (no K-factor)

NL3 (0-jet K-factor)

15 20 25 30 35 40 45

0.99

0.995

1

1.005

1.01

tMS [GeV]

UNLOPS (no K-factor)

UNLOPS (0-jet K-factor)

→

⇒ 3

NLO merged results for H + jets (based on LHEF input files generated in the POWHEG framework)

NL3 (non-unitarised)

“Undercompensation" Cross section grows

“Overcompensation” Cross section diminishes

UNLOPS (unitarised)

Improved stability


Lonnblad & Prestel, JHEP 1303 (2013) 166

Note change of scale!!

http://main88.cc

Unitarised Merging @ NLO



p⊥,H ∆φ12 →

⇒


Lonnblad & Prestel, JHEP 1303 (2013) 166

NLO merged results for H + jets (based on LHEF input files generated in the POWHEG framework)

http://main88.cc

Weak

Strong

Strong

Weak

Strong

Strong

Weak

Strong

Weak

Weak

Strong

Strong

Strong

Strong

Drell-Yan + QCD correction Dijet + EW correction

Further Matching & Merging Aspects



๏Combining resonant “signals” and non-resonant “backgrounds”

๏Electroweak Merging

Wbj

⋄⋄⇒ b − jet

Recent exploration for single-top production

Introducing “resonance histories” (from kinematical considerations, or from partial amplitudes)

(a.k.a. “resonance-aware” matching)

Weak

Strong

Strong

Weak

Strong

Strong

Weak

Strong

Weak

Weak

Strong

Strong

Strong

Strong


Weak

Strong

Strong

Weak

Strong

Strong

Weak

Strong

Weak

Weak

Strong

Strong

Strong

Strong


Weak

Strong

Strong

Weak

Strong

Strong

Weak

Strong

Weak

Weak

Strong

Strong

Strong

Strong

Drell-Yan + QCD correction Dijet + EW correctionQCD correction Weak correction

Drell-Yan DijetDataDefault schemeEW-improved

10−4

10−3

10−2

10−1

1

W → eν (MC) vs W → ℓν (data), dressed level

dσ

W+≥

2j/

dH

T

200 400 600 800 1000 1200 1400 1600 1800 20000.60.70.80.91.01.11.21.31.4

HT [GeV]

MC

/D

ata

JC & SP

DataDefault schemeEW-improved

10−4

10−3

10−2

10−1

1

W → eν (MC) vs W → ℓν (data), dressed level

dσ

W+≥

2j/

dH

T

200 400 600 800 1000 1200 1400 1600 1800 20000.60.70.80.91.01.11.21.31.4

HT [GeV]

MC

/D

ata

Weak Showers JC,TS JHEP 1404

(2014) 115


New Colour-Reconnection Models

10

๏1980’ies: MPI + CR : rise of <pT> vs Nch ๏(+ not mentioned here: rapidity gaps, onium production, …)

๏1990’ies: CR at LEP2: string drag effect on mW ๏2000’s: Tevatron “Tune A”: needed ~ 100% colour correlations

๏+ O(0.5 GeV) CR uncertainty on Tevatron top quark mass ๏Best LEP2 fit (2013) excluded no-CR at 99.5% CL


TS, v Zijl Phys.Rev. D36 (1987) 2019

The new QCD-based CR model (1)

J. Christiansen & P. Skands, JHEP 1508 (2015) 003:New model relies on two main principles? SU(3) colour rules give allowed reconnections

Possible reconnections

Ordinary string reconnection

(qq: 1/9, gg: 1/8, model: 1/9)

Triple junction reconnection

(qq: 1/27, gg: 5/256, model: 2/81)

Double junction reconnection

(qq: 1/3, gg: 10/64, model: 2/9)

Zipping reconnection

(Depends on number of gluons)

Jesper Roy Christiansen (Lund) Non pertubative colours November 3, MPI@LHC 10 / 15

? minimal � measure gives preferred reconnections

Torbjorn Sjostrand Colour Reconnection slide 14/24

SA,TS JHEP 1411 (2014) 043

+ “Gluon-Move Model” (and a few variants) mainly intended for conservative (maximal) effect on top quark mass:

+ Superconductor-inspired SK-I and SK-II models re-implemented in Pythia 8

Bri

ef H

isto

ry

Still ⇒ Δmt ~ 500 MeV

ATLAS & CMS : ~ 100 MeV ?

(Since 8.209)


2015-2016: Further Recent News

11

๏Runtime interface to POWHEG BOX (PI)

๏Can run MadGraph5_aMC@NLO from within Pythia (PI)

๏New machinery for hard diffraction + physics studies •Partonic substructure of Pomeron: diffractive jets •MPI-based gap survival probability

๏Extended options for damped ISR/FSR above hard scale

๏Reweighting machinery for ISR/FSR branchings (SP)

๏Interface to the Python programming language (PI)

๏Various PDF upgrades (TS) & SUSY/SLHA updates (ND)

๏Thermal Hadronisation, Close-Packing Effects, and Hadron Rescattering Options


See talk by Nadine FischerNF & TS arXiv:1610.09818

CR & TS JHEP 1602 (2016) 142


0 0.1 0.2 0.3 0.4 0.5

/d(1

-T)

σ d

σ1/

4−10

3−10

2−10

1−10

1

10

210

3101-Thrust (udsc)

Pythia 8.215Data from Phys.Rept. 399 (2004) 71

L3 MECs OFF: muRMECs OFF: P(z)

V I N

C I

A R

O O

T

hadrons→ee 91.2 GeV

1-T (udsc)0 0.1 0.2 0.3 0.4 0.5

Theo

ry/D

ata

0.5

1

1.5

0 0.1 0.2 0.3 0.4 0.5

/d(1

-T)

σ d

σ1/

4−10

3−10

2−10

1−10

1

10

210

3101-Thrust (udsc)


L3 MECs ON: muRMECs ON: P(z)

V I N

C I

A R

O O

T


1-T (udsc)0 0.1 0.2 0.3 0.4 0.5

Theo

ry/D

ata

0.5

1

1.5

Figure 3: Illustration of the default nonsingular variations for FSR splitting kernels, corresponding to cNS =

±2 (shown in red with \\\ hashing), compared with the default renormalisation-scale variations by a factorof 2 with the NLO compensation term switched on (shown in blue with /// hashing). Left: matrix-elementcorrections OFF. Right: matrix-element corrections ON. Note that the range of the ratio plot is greater than infig. 1 Distribution of 1-Thrust for e+e� ! hadrons at the Z pole, excluding b-tagged events; ISR switched off;data from the L3 experiment [26].

m2

b

= 2pb

· pg

[29], with pb

the 4-momentum of the massive quark and pg

that of the emitted gluon.(For spacelike virtual massive quarks, the mass correction has the opposite sign [8].) Thus,

P 0(t, z) =

↵s

2⇡C P (z) + cNS Q

2/m2

dip

t

!, (38)

where C is the colour factor. The variation can therefore be obtained by introducing a spurious termproportional to Q2/m2

dip

in the splitting kernel used to compute the accept probability, hence

R0acc

=

P 0acc

Pacc

= 1 +

cNS Q2/m2

dip

P (z), (39)

from which we also immediately confirm that the relative variation explicitly vanishes when Q2 ! 0

or P (z) ! 1.To motivate a reasonable range of variations, we take the nonsingular terms that different physical

matrix elements exhibit as a first indicator, and supplement that by considering the terms that areinduced by PYTHIA’s matrix-element corrections (MECs) for Z boson decays [30]. In particular,the study in [28] found order-unity differences (in dimensionless units) between different physicalprocesses and three different antenna-shower formalisms: Lund dipoles a la ARIADNE [31,32], GGGantennae a la VINCIA [7, 33, 34], and Sector antennae a la Kosower [28, 35]. Therefore, here we alsotake variations of order unity as the baseline for our recommendations.

In fig. 3, we illustrate the splitting-kernel variation taking cNS = ±2 as a first guess at a reasonablerange of variation. As can be observed by comparing the left- and right-hand panes of the figure,where PYTHIA’s MECs are switched off and on respectively, this variation, labeled P (z) and shown

13

New: Automated Shower Uncertainties

12

๏Based on original proposal for VINCIA: •Pythia 8 implementation (+ All-orders proof)

๏(~ Simultaneously with same principle in Herwig++, Sherpa)

๏For each trial branching, with splitting variables, {t}:

•If accepted, compute alternative weight for different αs or splitting kernel:

•If rejected, compute alternative no-emission weight:


S. Mrenna, P. Skands, S. Prestel

Giele, Kosower, PS PRD84 (2011) 054003

SM, PS Phys.Rev. D94 (2016) no.7, 074005

The proposal to compute the probability of an event generated by P 0 based on an event generatedusing P is as following [7] (suppressing again the z dependence for clarity):

1. Start the event evolution by setting all weights (nominal and uncertainty-variation ones) equal tothe input weight of the event, w0

= w.

2. If the trial branching is accepted, multiply the alternative weight w0 by the relative ratio of acceptprobabilities,

R0acc

(t) =

P 0acc

(t)

Pacc

(t)=

P 0(t)

P (t). (16)

3. If the trial branching is rejected, multiply the alternative weight w0 by the relative ratio of reject-probabilities,

R0rej

(t) =

P 0rej

(t)

Prej

(t)=

1� P 0acc

(t)

1� Pacc

(t)=

ˆP (t)� P 0(t)

ˆP (t)� P (t). (17)

4. If desired, the detailed balance between the accept and reject probabilities could optionally beallowed to be broken by up to a non-singular term, P 0

acc

6= 1�P 0rej

, to represent uncertainties dueto genuine (non-canceling) higher-order corrections, which would modify the total cross sections.For the current implementation in PYTHIA, however, we do not consider this possibility further.

Step 2 is responsible for adjusting the naive splitting probabilities, while Step 3 is responsible for ad-justing the no-splitting Sudakov factors. The result is that the set of weights w0 represents a separatelyunitary event sample, with hw0i = hwi; i.e., the samples integrate to the same total cross section. Wealready know that the probability distribution of the generated event sample, when applying the nom-inal set of weights, w, is the distribution defined by eq. (4). We shall now prove that the probabilitydistribution obtained from the same generated event sample, when applying the set of weights w0, isthe correct resummed distribution for the P 0 radiation kernels,

dP 0

dt dz= P 0

(t, z) �0(t

0

, t) , (18)

where the apostrophes on both P 0 and �

0 emphasize that the modified radiation probability enters inboth places.

For zero rejected trials, the modified weight distribution is:

dP 00

dt= R0

acc

(t)| {z }reweight

Pacc

(t)| {z }accept trial

ˆP (t) ˆ

�(t0

, t)| {z }generate trial

= P 0(t) ˆ

�(t0

, t) , (19)

for one rejected trial,

dP 01

dt= R0

acc

(t)| {z }reweight

Pacc


ˆP (t) ˆ�(t0

, t)

Zt

0

t

dt1

R0rej

(t)| {z }reweighting

⇣ˆP (t

1

)� P (t1

)

⌘

| {z }reject trial

(20)

= P 0(t) ˆ

�(t0

, t)

Zt

0

t

dt1

⇣ˆP (t

1

)� P 0(t

1

)

⌘, (21)

and for two rejected trials,

dP 02

dt= P 0

(t) ˆ

�(t0

, t)

Zt

0

t

dt1

⇣ˆP (t

1

)� P 0(t

1

)

⌘Zt

1

t

dt2

⇣ˆP (t

2

)� P 0(t

2

)

⌘, (22)

hence exactly the same structure emerges for the reweighted sample as for the underlying veto al-gorithm above, just with P replaced by P 0. The proof that eq. (18) results from the sum over allpossibilities is therefore identical to the proof of the original (unweighted) veto algorithm above.

6

The proposal to compute the probability of an event generated by P 0 based on an event generatedusing P is as following [7] (suppressing again the z dependence for clarity):

1. Start the event evolution by setting all weights (nominal and uncertainty-variation ones) equal tothe input weight of the event, w0

= w.

2. If the trial branching is accepted, multiply the alternative weight w0 by the relative ratio of acceptprobabilities,

R0acc

(t) =

P 0acc

(t)

Pacc

(t)=

P 0(t)

P (t). (16)

3. If the trial branching is rejected, multiply the alternative weight w0 by the relative ratio of reject-probabilities,

R0rej

(t) =

P 0rej

(t)

Prej

(t)=

1� P 0acc

(t)

1� Pacc

(t)=

ˆP (t)� P 0(t)

ˆP (t)� P (t). (17)

4. If desired, the detailed balance between the accept and reject probabilities could optionally beallowed to be broken by up to a non-singular term, P 0

acc

6= 1�P 0rej

, to represent uncertainties dueto genuine (non-canceling) higher-order corrections, which would modify the total cross sections.For the current implementation in PYTHIA, however, we do not consider this possibility further.

Step 2 is responsible for adjusting the naive splitting probabilities, while Step 3 is responsible for ad-justing the no-splitting Sudakov factors. The result is that the set of weights w0 represents a separatelyunitary event sample, with hw0i = hwi; i.e., the samples integrate to the same total cross section. Wealready know that the probability distribution of the generated event sample, when applying the nom-inal set of weights, w, is the distribution defined by eq. (4). We shall now prove that the probabilitydistribution obtained from the same generated event sample, when applying the set of weights w0, isthe correct resummed distribution for the P 0 radiation kernels,

dP 0

dt dz= P 0

(t, z) �0(t

0

, t) , (18)

where the apostrophes on both P 0 and �

0 emphasize that the modified radiation probability enters inboth places.

For zero rejected trials, the modified weight distribution is:

dP 00

dt= R0

acc

(t)| {z }reweight

Pacc


ˆP (t) ˆ

�(t0

, t)| {z }generate trial

= P 0(t) ˆ

�(t0

, t) , (19)

for one rejected trial,

dP 01

dt= R0

acc

(t)| {z }reweight

Pacc


ˆP (t) ˆ�(t0

, t)

Zt

0

t

dt1

R0rej

(t)| {z }reweighting

⇣ˆP (t

1

)� P (t1

)

⌘

| {z }reject trial

(20)

= P 0(t) ˆ

�(t0

, t)

Zt

0

t

dt1

⇣ˆP (t

1

)� P 0(t

1

)

⌘, (21)

and for two rejected trials,

dP 02

dt= P 0

(t) ˆ

�(t0

, t)

Zt

0

t

dt1

⇣ˆP (t

1

)� P 0(t

1

)

⌘Zt

1

t

dt2

⇣ˆP (t

2

)� P 0(t

2

)

⌘, (22)

hence exactly the same structure emerges for the reweighted sample as for the underlying veto al-gorithm above, just with P replaced by P 0. The proof that eq. (18) results from the sum over allpossibilities is therefore identical to the proof of the original (unweighted) veto algorithm above.

6

0 0.1 0.2 0.3 0.4 0.5

/d(1

-T)

σ d

σ1/

4−10

3−10

2−10

1−10

1

10

210

3101-Thrust (udsc)


L3 MECs OFF: muRMECs OFF: P(z)

V I N

C I

A R

O O

T


1-T (udsc)0 0.1 0.2 0.3 0.4 0.5

Theo

ry/D

ata

0.5

1

1.5

0 0.1 0.2 0.3 0.4 0.5

/d(1

-T)

σ d

σ1/

4−10

3−10

2−10

1−10

1

10

210

3101-Thrust (udsc)


L3 MECs ON: muRMECs ON: P(z)

V I N

C I

A R

O O

T


1-T (udsc)0 0.1 0.2 0.3 0.4 0.5

Theo

ry/D

ata

0.5

1

1.5

Figure 3: Illustration of the default nonsingular variations for FSR splitting kernels, corresponding to cNS =

±2 (shown in red with \\\ hashing), compared with the default renormalisation-scale variations by a factorof 2 with the NLO compensation term switched on (shown in blue with /// hashing). Left: matrix-elementcorrections OFF. Right: matrix-element corrections ON. Note that the range of the ratio plot is greater than infig. 1 Distribution of 1-Thrust for e+e� ! hadrons at the Z pole, excluding b-tagged events; ISR switched off;data from the L3 experiment [26].

m2

b

= 2pb

· pg

[29], with pb

the 4-momentum of the massive quark and pg

that of the emitted gluon.(For spacelike virtual massive quarks, the mass correction has the opposite sign [8].) Thus,

P 0(t, z) =

↵s

2⇡C P (z) + cNS Q

2/m2

dip

t

!, (38)

where C is the colour factor. The variation can therefore be obtained by introducing a spurious termproportional to Q2/m2

dip

in the splitting kernel used to compute the accept probability, hence

R0acc

=

P 0acc

Pacc

= 1 +

cNS Q2/m2

dip

P (z), (39)

from which we also immediately confirm that the relative variation explicitly vanishes when Q2 ! 0

or P (z) ! 1.To motivate a reasonable range of variations, we take the nonsingular terms that different physical

matrix elements exhibit as a first indicator, and supplement that by considering the terms that areinduced by PYTHIA’s matrix-element corrections (MECs) for Z boson decays [30]. In particular,the study in [28] found order-unity differences (in dimensionless units) between different physicalprocesses and three different antenna-shower formalisms: Lund dipoles a la ARIADNE [31,32], GGGantennae a la VINCIA [7, 33, 34], and Sector antennae a la Kosower [28, 35]. Therefore, here we alsotake variations of order unity as the baseline for our recommendations.

In fig. 3, we illustrate the splitting-kernel variation taking cNS = ±2 as a first guess at a reasonablerange of variation. As can be observed by comparing the left- and right-hand panes of the figure,where PYTHIA’s MECs are switched off and on respectively, this variation, labeled P (z) and shown

13


d02 × 2

d23 × 10−1

d34 × 10−2

d45 × 10−3

Dir

eP

S

e−q→ e−q @ 300 GeV

Q2> 100 GeV2

Sherpa

Pythia

10−6

10−5

10−4

10−3

10−2

10−1

1

10 1Differential kT-jet resolution at parton level (Breit frame)

dσ

/d

log

10(d

nm

/G

eV)

[pb

]

d02

-2 σ

0 σ

2 σ

Dev

iati

on

d23

-2 σ

0 σ

2 σ

Dev

iati

on

d34

-2 σ

0 σ

2 σ

Dev

iati

on

d45

0.5 1 1.5 2

-2 σ

0 σ

2 σ

log10(dnm/GeV)

Dev

iati

on

New Shower Plug-Ins: DIRE & VINCIA


p⊥ 1/p2⊥

⇒ 1/p2⊥

→


Dire

10−1

H1 data, 20 < Q < 30 GeV, Eur.Phys.J.C46:343-356,2006

1/σd

σ/dB

0 0.1 0.2 0.3 0.4 0.5

0.6

0.8

1

1.2

1.4

B

MC/Data

Dire

10−2

10−1

H1 data, 20 < Q < 30 GeV, Eur.Phys.J.C46:343-356,2006

1/σd

σ/d(1

−T)

0 0.2 0.4 0.6 0.8 1

0.6

0.8

1

1.2

1.4

1− T

MC/Data

S Höche, SP Eur.Phys.J. C75 (2015) no.9, 461


P e t e r S k a n d s

VINCIA is an Antenna Shower

14M o n a s h U n i v e r s i t y

P. S k a n d s

Our Research

๏Parton Showers are based on 1→2 splittings •I.e., each parton undergoes a sequence of splittings

๏Multi-parton coherence effects can be included via “angular ordering” ๏Or via “dipole radiation functions”

๏(~ partitions dipole radiation pattern into 2 monopole terms) ๏Recoil effects needed to impose (E,p) conservation (“local” or “global”)

๏At Monash, we develop an Antenna Shower, in which splittings are fundamentally 2→3

•Each colour dipole/antenna undergoes a sequence of splittings ๏+ Intrinsically includes dipole coherence (leading NC) ๏+ Lorentz invariance and explicit local (E,p) conservation ๏+ The non-perturbative limit of a colour dipole is a string piece

๏Roots in Lund ~ mid-80ies: Gustafson & Petterson, Nucl.Phys. B306 (1988) 746

•What’s new in our approach? ๏Higher-order perturbative effects can be introduced via calculable corrections in an elegant and very efficient way ๏+ Writing a genuine antenna shower also for the initial state evolution

13

E.g., PYTHIA (also HERWIG, SHERPA)

E.g., VINCIA (also ARIADNE)

Cf a lattice and its dual lattice Can either perceive of lattice sites

or lattice links. Equivalent (dual) representations.

๏ Splittings are fundamentally 2→3 Each colour antenna undergoes a sequence of splittings

Proof of concept for one-loop corrections

+ Framework for 2nd-order kernels, implementation of 2→4

Antenna radiation functions & phase-space factorisations Collinear Limits → DGLAP kernels (→ collinear factorisation) Soft Limits → Eikonal factors (→ Leading-Colour coherence)

2→3 phase-space maps = exact, on-shell factorisations of the (n+1)/n-parton phase spaces (→ Lorentz invariant, pμ conserving, and valid over all of phase space - not just in limits)

• + Non-perturbative limit of colour dipoles/antennae → string pieces → natural matching onto (string) hadronisation models

๏What’s new in our approach? (e.g., not in ARIADNE) •+ Iterated (tree-level) MECs: matrix-element corrections (since v1.x) •+ Backwards antenna evolution for ISR (new in v2.0) •+ Automated uncertainty bands/weights (& runtime ROOT displays)

Virtual Numerical Collider with Interleaved Antennae (For FSR, identical to CDM: colour dipole model)

vincia.hepforge.org

Giele, Kosower, PS PRD84 (2011) 054003 (same principle as now in Herwig++, Pythia 8, Sherpa)

N Fischer, Ritzmann, SP, PS arXiv:1605.06142

Li & PS, arXiv:1611.00013

See talk by Hai Tao Li

Hartgring, Laenen, PS JHEP 1310 (2013) 127

http://vincia.hepforge.org





p0 5 10 15 20

rate

0

0.01

0.02

0.03

Pythia

Vincia (default)

Vincia (enh. antennae)

20 40 60 80 100 120

-410

-310

-210

20 40 60 80 100 120

-410

-310

-210

Figure 2: The Drell-Yan pT spectrum. The dashed red curveshows the value computed using Vincia with default antennæfunctions, while the dotted green curve shows the Vincia pre-dicted with an enhanced antenna function. The solid bluecurve gives the Pythia 8 prediction. The inset shows the high-pT tail.

certainty due to the shower function and in particu-lar higher-order terms in the shower. The di↵er-ence shown here is illustrative only; a more ex-tensive exploration of possible antenna variationswould be required before taking the spread as aquantitative estimate of the uncertainty. We maynonetheless observe that the Pythia 8 referencecalculation di↵ers from the Vincia one (with de-fault antenna) by roughly the same amount in thepeak region as does the enhanced Vincia predic-tion. This illustrates a tradeo↵ between a more ac-tive recoil strategy (Pythia) and a more active radi-ation pattern (enhanced Vincia), which will be in-teresting to study more closely. At large pT , allthree curves are close to each other; the transversemomentum here is dominated by the recoil againsthard lone-gluon emission. This region would bedescribed well by fixed-order calculations.

For initial–final configurations, coherence is par-ticularly important, and can lead to sizable asym-metries (see, e.g., [26]). An illustration of the e↵ectis given in fig. 3, which shows qq ! qq scatter-ing with two di↵erent color-flow assignments: for-ward (left) and backward (right). In both cases,the starting scale of the shower evolution wouldbe pT , the transverse-momentum scale character-izing the hard scattering. Coherence, however, im-

Figure 3: Di↵erent color flows and corresponding emissionpatterns in qq ! qq scattering. The straight (black) lines arequarks with arrows denoting the direction of motion in the ini-tial or final states, and the curved (colored) lines indicating thecolor flow. The beam axis is horizontal, and the vertical axisis transverse to the beam. The initial-state momenta would bereversed in a Feynman diagram, so that the gluon emissionssymbolically indicated by curly lines would be inside the cor-responding color antennæ. Forward flow is shown on the left,and backward flow on the right.

0° 45° 90° 135° 180°

1180°

2180°

q Hgluon, beamLr e

mit

Figure 4: Angular distribution of the first gluon emission inqq ! qq scattering at 45�, for the two di↵erent color flows.The light (red) histogram shows the emission density for theforward flow, and the dark (blue) histogram shows the emis-sion density for the backward flow.

plies that radiation should be directed primarily in-side the color antenna, so that in the forward flowit would be directed towards large rapidity, andstrongly suppressed at right angles to the beam di-rection. In the backward flow, conversely, radiationat right angles to the beam should be unsuppressed.The two radiation patterns are illustrated schemat-ically by the gluons in fig. 3. The intrinsic coher-ence of the antenna formalism accounts for this ef-fect automatically. That Vincia reproduces this fea-ture is demonstrated in fig. 4, which shows the an-gular distribution of the first emitted gluon for theforward and backward color flows, respectively, fora scattering angle of 45� and pT = 100 GeV. Thedistributions clearly show that the backward color

7

P e t e r S k a n d sp0 5 10 15 20

rate

0

0.01

0.02

0.03

Pythia

Vincia (default)


20 40 60 80 100 120

-410

-310

-210

20 40 60 80 100 120

-410

-310

-210





0° 45° 90° 135° 180°

1180°

2180°

q Hgluon, beamL

r emit



7

p0 5 10 15 20

rate

0

0.01

0.02

0.03

Pythia

Vincia (default)


20 40 60 80 100 120

-410

-310

-210

20 40 60 80 100 120

-410

-310

-210





0° 45° 90° 135° 180°

1180°

2180°

q Hgluon, beamL

r emit



7

New: Hadron Collisions

15

๏Example: quark-quark scattering in hadron collisions •Consider one specific phase-space point (eg scattering at 45o) •2 possible colour flows: A and B

M o n a s h U n i v e r s i t y

A) “forward” colour flow

B) “backward” colour flow

Example taken from: Ritzmann, Kosower, PS, PLB718 (2013) 1345

PS: coherence also influences the Tevatron top-quark forward-backward asymmetry: see PS, Webber, Winter, JHEP 1207(2012)151

Antenna Patterns

Kinematics (e.g., Mandelstam variables) are identical. The only difference is the colour-flow assignment.

A

B

http://arxiv.org/abs/arXiv:1210.6345

(New: Photon-Photon Interactions)

16

๏Currently included (version 8.219): •Hard processes in resolved photon-photon collisions of real photons : γγ→X; with parton showers and beam remnants

๏Hard processes in resolved γγ interactions can also be generated in e+e- collisions by convolution of EPA and photon PDFs

•One set of PDFs for resolved photons (CJKL)

๏Will be included soon (next version): •Further kinematic cuts (e.g. on mγγ) •Direct (unresolved) processes with scattered leptons •Soft processes and MPIs for resolved photon-photon collisions including also these processes in e+e- collisions


Ilkka Helenius

See talk by Ilkka Helenius

d�ch/d

p T[pb/G

eV]

OPAL Pythia 8Res-ResDir-DirDir-RestotalMPI o↵

|⌘| < 1.5Q2

� < 1.0GeV2

10 < W�� < 125GeVe+e�,

ps = 166GeV

Ratio

toMPIo↵

pT

charged-particle pT spectrum

Summary


Documents

Pythia Overview : 2013–2016skands.physics.monash.edu/slides/files/16-MCnet-Pythia.pdf · 2013: Freezing of the Fortran Pythia 2 December 2012 Dear Pythia Users and Supporters, …