Bryan Webber Cavendish Laboratory University of Cambridge

QCD and Monte Carlo Tools

Bryan Webber 1 CERN-Fermilab HCP School 2017 Monte Carlo Event Generation

• Aim is to produce simulated (particle-level) datasets like those from real collider events ✤ i.e. lists of particle identities, momenta, ... ✤ simulate quantum effects by (pseudo)random numbers • Essential for: ✤ Designing new experiments and data analyses ✤ Correcting for detector and selection effects ✤ Testing the SM and measuring its parameters ✤ Estimating new signals and their backgrounds

Bryan Webber 2 CERN-Fermilab HCP School 2017 Monte Carlo Basics

Bryan Webber 3 CERN-Fermilab HCP School 2017 Monte Carlo Integration • Basis of all Monte Carlo methods: b 1 N I = f(x) dx (b a)f(x ) I ⇡ N i ⌘ N Za i=1 X weight wi

where x i are randomly (uniformly) distributed on [a,b].

Then I =limIN = E[w] ,I = Var[w]/N • N !1 p where Var[w]=E[(w E[w])2]=E[w2] (E[w])2 b b 2 2 =(b a) f(x) dx f(x) dx V ⌘ Za Za ⇥ ⇤ ⇥ Central limit⇤ theorem: I = I V/N N ± P (< 1) = 68% p Bryan Webber 4 CERN-Fermilab HCP School 2017 Convergence • Monte Carlo integrals governed by Central Limit Theorem: error c.f. trapezium rule only if derivatives exist and are ﬁnite, e.g. Simpson’s rule

1 ⇡ I = 1 x2 dx = =0.785 0 4 Z p 2 ⇡2 pV = =0.223 r3 16 0.223 I =0.785 ± pN

Bryan Webber 5 CERN-Fermilab HCP School 2017 Importance Sampling • Convergence is improved by putting more points in regions where integrand is largest • Corresponds to a Jacobian transformation • Variance is reduced (weights “ﬂattened”)

2/3 x3 ⇢ = x 3 0 2 1 4 ⇡ 2 ⇡2 Bryan Webber r 6 CERN-Fermilab HCP School 2017 Hit-and-Miss

• Accept points with probability = wi/wmax (provided all wi > 0) • Accepted points are distributed like real events

• MC efﬁciency eMC = E[w]/wmax improved by importance sampling

1 2 "MC =1/I =2/⇡ = 64% " = dx(1 x )/I =3/⇡ = 95% MC Z0 " (1 " ) 0.48 " (1 " ) 0.21 = MC MC = = MC MC = r N pN r N pN

Bryan Webber 7 CERN-Fermilab HCP School 2017 Multi-dimensional Integration

• Formalism extends trivially to many dimensions • Particle physics: very many dimensions, e.g. phase space = 3 dimensions per particles, LHC event ~ 250 hadrons. • Monte Carlo error remains • Trapezium rule • Simpson's rule

Bryan Webber 8 CERN-Fermilab HCP School 2017 Monte Carlo: Summary

Disadvantages of Monte Carlo: • Slow convergence in few dimensions. Advantages of Monte Carlo: • Fast convergence in many dimensions. • Arbitrarily complex integration regions (ﬁnite discontinuities not a problem). • Few points needed to get ﬁrst estimate (“feasibility limit”). • Every additional point improves accuracy (“growth rate”). • Easy error estimate. • Hit-and-miss allows unweighted event generation, i.e. points distributed in phase space just like real events.

Bryan Webber 9 CERN-Fermilab HCP School 2017 Phase Space Generation

Phase space:

Two-body easy:

Bryan Webber 10 CERN-Fermilab HCP School 2017 Phase Space Generation

Other cases by recursive subdivision:

Or by ‘democratic’ algorithms: RAMBO, MAMBO Can be better, but matrix elements rarely flat.

Bryan Webber 11 CERN-Fermilab HCP School 2017 Particle Decays ` Simplest example W t ⌫ e.g. top quark decay: b p p p p t · ⇥ b ·

Breit-Wigner peak of W very strong - but can be removed by importance sampling: m2 M 2 m2 arctan W W (prove it!) W ⇥ M W W ⇥ Bryan Webber 12 CERN-Fermilab HCP School 2017 Associated Distributions

e.g. lepton momentum in top decays: Big advantage of Monte Carlo integration: Simply histogram any ` associated quantities. Almost any other technique requires new ⌫ integration for each observable. Can apply arbitrary cuts/ smearing.

Bryan Webber 13 CERN-Fermilab HCP School 2017 Hadron-Hadron Cross Sections

`+ pp p pq¯ = x2pp¯ Z _ p pq = x1pp p p¯

` 2 s = Ecm =4pppp¯ sˆ =4pqpq¯ = x1x2s

0 + Consider e.g. pp¯ Z ` ` • ! ! • Integrations over incoming parton momentum distributions: 1 1 (s)= dx1f(x1) dx2f(x2)ˆ(x1x2s) Z0 Z0 • Hard process cross section ˆ (ˆ s ) has strong peak, due to Z 0 resonance: needs importance sampling (like W in top decay)

Bryan Webber 14 CERN-Fermilab HCP School 2017 Drell-Yan production • Large number of measurements o Total and differential cross-sections in boson * (lepton) kinematics (y, pT, " ,…) o Cross-section ratios (W+/W-, W/Z, …) o Jet distributions • ATLAS/CMS and LHC-b complementary • Low & high x accessed by off-shell data • Large statistics, clean signature, excellent detector calibration à typical experimental systematics +~1% • ppLuminosity ` systematics ` cross (2-3%) andsection also other contributions! cancel in ratios

9 orders in cross-section • Understand proton structure: constrain PDFs • Probe higher-order pQCD

Full spin correlations calculations • Study non-perturbative efffects, soft gluon resummation, parton shower modelling • Test Monte Carlo tools M=psˆ [GeV/c2] 2 CMS-PAS-SMP-16-009 M=psˆ [GeV/c ] • Essential for precision physics at LHC G. Pásztor: Hard QCD @ LHC, LP2017 27 4⇡sˆ `q ˆqq¯ Z0 `+` = ! ! 3M 2 (ˆs M 2 )2 +2 M 2 Z Z Z Z + “Background” is qq¯ ⇤ ` ` • ! !

Bryan Webber 15 CERN-Fermilab HCP School 2017 Parton-Level Monte Carlo Calculations

Now we have everything we need to make parton-level cross section calculations and distributions Can be largely automated… • MADGRAPH • GRACE • COMPHEP • AMEGIC++ • ALPGEN But… • Fixed parton/jet multiplicity • No control of large higher-order corrections • Parton level Need hadron level event generators Bryan Webber 16 CERN-Fermilab HCP School 2017 Monte Carlo Event Generation

Bryan Webber 17 CERN-Fermilab HCP School 2017 Monte Carlo Event Generation

• Monte Carlo event generation: ✤ theoretical status and limitations • Recent improvements: ✤ perturbative and non-perturbative • Overview of results: ✤ W, Z, top, Higgs, BSM (+jets)

Bryan Webber 18 CERN-Fermilab HCP School 2017 4 4 Limits

0.0045 Quark-Quark Quark-Gluon 0.004 Gluon-Gluon

0.0035 CMS Simulation Preliminary

0.003 s = 8 TeV, WideJets |η| < 2.5 & |∆η | < 1.3 jj 0.0025

Normalized yield/GeV 0.002

0.0015

0.001

0.0005

0 1000 2000 3000 4000 5000 6000 Dijet Mass (GeV)

Figure 2: The reconstructed resonance mass spectrum generated with the PYTHIA MC simulation and Tune D6T for qq G qq, qg q qg, gg G gg for resonance masses of ⇥ ⇥ ⇥ ⇥ ⇥ ⇥ 1.0, 2.0, 3.0, 4.0, and 5.0 TeV. A high-mass dijet event

Figure 3: The event with the highest invariant mass: 3D view (left) and 2D view (right). The invariant massM of the= two 5.15 wide TeV jets is 5.15 TeV. • jj CMS PAS EXO-12-059

Bryan Webber 19 CERN-Fermilab HCP School 2017 LHC dijet

p Hard process

Bryan Webber 20 CERN-Fermilab HCP School 2017 LHC dijet

p Hard process Parton showers

Bryan Webber 21 CERN-Fermilab HCP School 2017 LHC dijet

p Hard process Parton showers Underlying event

Bryan Webber 22 CERN-Fermilab HCP School 2017 LHC dijet

p Hard process Parton showers Underlying event Conﬁnement

Bryan Webber 23 CERN-Fermilab HCP School 2017 quark jet LHC dijet )

p beam ) jet beam p jet ) Hard process Parton showers Underlying event

Conﬁnement ) Hadronization quark jet Bryan Webber 24 CERN-Fermilab HCP School 2017 Theoretical Status Exact ﬁxed-order perturbation theory

p Hard process

Bryan Webber 25 CERN-Fermilab HCP School 2017 Theoretical Status Exact ﬁxed-order perturbation theory Approximate all-order perturbation theory

p Hard process Parton showers

Bryan Webber 26 CERN-Fermilab HCP School 2017 quark jet Theoretical Status) Exact ﬁxed-order perturbation theory Approximate all-order perturbation theory Semi-empirical local models only p beam ) jet beam p jet ) Hard process Parton showers Underlying event

Conﬁnement ) Hadronization quark jet Bryan Webber 27 CERN-Fermilab HCP School 2017 QCD Factorization

1 2 2 2 2 2 pp X (Epp)= dx1 dx2 fi(x1,µ ) fj(x2,µ )ˆij X (x1x2Epp,µ ) ! ! Z0 ( ( momentum parton hard process fractions distributions cross section at scale µ2

• Jet formation and underlying event take place over a much longer time scale, with unit probability • Hence they cannot affect the cross section • Scale dependences of parton distributions and hard process cross section are perturbatively calculable, and cancel order by order

Bryan Webber 28 CERN-Fermilab HCP School 2017 Parton Shower Approximation

• Keep only most singular parts of QCD matrix elements: ↵S d⇠i di Collinear dn+1 Pii(zi,i) dzi dn ⇠i =1 cos ✓i • ⇡ 2⇡ ⇠i 2⇡ i ↵ X p p d Soft d S ( T T ) i · j !d!d⇠ i d • n+1 ⇡ 2⇡ i · j p kp k i 2⇡ n i,j i j X · · ↵ ⇠ d! d = S ( T T ) ij d⇠ i d 2⇡ i · j ⇠ ⇠ ! i 2⇡ n i,j i j X ↵ d! d⇠ S ( T T )⇥(⇠ ⇠ ) i d ⇡ 2⇡ i · j ij i ! ⇠ n i,j i X j

✓ij >✓i ! =(1 z )E i i i ✓i ziEi Angular-ordered parton shower (or dipoles)

Bryan Webber 29 CERN-Fermilab HCP School 2017 Parton Shower Evolution

✓ ✓ Ei+1 hard 0 1 ✓3 z = ✓ ✓4 E process E0 E1 2E2 E3 E4 i ✓ 0 2 H 4 1+z A Pq q(z)= D ! 3 1 z R (E ,✓ ) O 1 1 N I Z (E2,✓2) A T (E ,✓ ) I 3 3 (E4,✓4) O N

E✓< Qmin

E0 Bryan Webber 30 CERN-Fermilab HCP School 2017 Parton Shower Evolution

✓ ✓ Ei+1 hard 0 1 ✓3 z = ✓ ✓4 E process E0 E1 2E2 E3 E4 i ✓ 0 2 H 4 1+z A Pq q(z)= D ! 3 1 z R (E E ,✓ ) (E1,✓1) O 0 1 1 N Pg g(z)= ! I 1+z4 +(1 z)4 ✓ Z (E2,✓2) 3 A z(1 z) T (E ,✓ ) I 3 3 (E4,✓4) 1 2 2 O Pg q = z +(1 z) N ! 2 ⇥ ⇤ E✓< Qmin

E E0 Bryan Webber 31 CERN-Fermilab HCP School 2017 Sudakov Factor

• Di(Q,Qmin) = probability for parton i to evolve from Q to Qmin without any resolvable emissions: ↵ E0 d! ✓0 d✓ (Q ,Q ) 1 C S 2 ⇥(!✓ Q )+... i 0 min ⇡ i ⇡ ! ✓ min Z Z ↵ Q 1 C S ln2 0 + ... ⇡ i ⇡ Q ✓ min ◆ ↵ Q exp C S ln2 0 ⇡ i ⇡ Q  ✓ min ◆ • Cq = CF = 4/3, Cg = CA =3 • Then probability to evolve from Q1 to Q2 without resolvable emissions is Di(Q1,Qmin)/Di(Q2,Qmin)

• Given Q1, ﬁnd Q2 by solving • Di(Q1,Qmin)/Di(Q2,Qmin) = Random #

Bryan Webber 32 CERN-Fermilab HCP School 2017 Hadronization Models

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory breaks Preconfinementdown and hadrons are formed

Planar approximation:• Before gluon that, at = scalescolour—anticolour ~ few x LQCD, there pair .is universal preconfinement of colour Follow colour structure of parton shower: colour-singlet pairs • Colour, flavour and momentum flows are only locally end up close inredistributed phase space by hadronization

Mass spectrumBryan Webber of colour-singlet pairs asymptotically33 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber Hadronization Models

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory breaks Preconfinementdown and hadrons are formed

Planar approximation:• Before gluon that, at = scalescolour—anticolour ~ few x LQCD, there pair. is universal preconfinement of colour Follow colour structure• Colour, of flavour parton and shower: momentum colour-singlet flows are only pairs locally end up close inredistributed phase space by hadronization

Mass spectrumBryan Webber of colour-singlet pairs asymptotically34 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber String Hadronization Model

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory breaks Preconfinementdown and hadrons are formed

Planar approximation:• Before gluon that, at = scalescolour—anticolour ~ few x LQCD, there pair. is universal preconﬁnement of colour Follow colour structure• Colour of ﬂow parton dictates shower: how to colour-singlet connect hadronic pairs string end up close in(width phase ~ spacefew x LQCD) with shower

Mass spectrumBryan Webber of colour-singlet pairs asymptotically35 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber String Hadronization Model

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory breaks Preconfinementdown and hadrons are formed

Mass spectrumBryan Webber of colour-singlet pairs asymptotically36 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber String Hadronization Model

• At short distances (large Q), QCD is like QED: colour field lines spread out (1/r potential) • At long distances, gluon self-attraction gives rise to colour string (linear potential, quark confinement) • Intense colour field induces quark-antiquark pair creation: hadronization

++ –

Bryan Webber 37 CERN-Fermilab HCP School 2017 Cluster Hadronization Model

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory Preconfinementbreaks down and hadrons are formed

Planar approximation:• Before gluon that, at = scalescolour—anticolour ~ few x LQCD, there pair. is universal preconﬁnement of colour Follow colour structure• Decay of preconﬁnedparton shower: clusters colour-singlet provides a direct pairs basis end up close infor phase hadronization space

Mass spectrumBryan Webber of colour-singlet pairs asymptotically38 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber Cluster Hadronization Model

• In parton shower, relative transverse momenta evolve from a high scale Q towards lower values

• At a scale near LQCD~200 MeV, perturbation theory Preconfinementbreaks down and hadrons are formed

Mass spectrumBryan Webber of colour-singlet pairs asymptotically39 CERN-Fermilab HCP School 2017 independent of energy, production mechanism, … Peaked at low mass

LHC Simulations 2 Bryan Webber Cluster Hadronization Model

• Mass distribution of preconﬁned clusters is universal • Phase-space decay model for most clusters • High-mass tail decays anisotropically (string-like)

Bryan Webber 40 CERN-Fermilab HCP School 2017 Hadronization Status

• No fundamental progress since 1980s ✤ Available non-perturbative methods (lattice, AdS/ QCD, ...) are not applicable • Less important in some respects in LHC era ✤ Jets, leptons and photons are observed objects, not hadrons • But still important for detector effects ✤ Jet response, heavy-ﬂavour tagging, lepton and photon isolation, ...

Bryan Webber 41 CERN-Fermilab HCP School 2017 Multiparton Interaction Model (PYTHIA/JIMMY)

For small pt min and high energy inclusive parton—parton cross section is larger than total proton—proton cross section. Underlying! More than one parton—parton Event scatter per proton—proton(MPI)

NeedMultiple a model parton of spatial interactions distribution within in same proton collision • ! Perturbation theory gives n-scatter distributions LHC✤ SimulationsDepends 3 on density proﬁle of proton Bryan Webber • Assume QCD 2-to-2 secondary collisions

✤ Need cutoff at low pT • Need to model colour ﬂow ✤ Colour reconnections are necessary

Bryan Webber 42 CERN-Fermilab HCP School 2017 Underlying Event

〉 1.6 1.6

φ δ

Trans-min region ATLAS Trans-min region ATLAS η

1.4 [GeV] 1.4 δ -1 〉 -1

/ p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb T φ T ch δ 1.2 plead > 1 GeV 1.2 plead > 1 GeV η N

〈 T T δ / 1 T 1 p Σ

leading charged particle 0.8 〈 0.8

0.6 0.6

0.4 Data PYTHIA 8 Monash 0.4 Data PYTHIA 8 Monash PYTHIA 8 A14 Herwig7 PYTHIA 8 A14 Herwig7 0.2 PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos

towards 1 1 < 60 | | Model / Data 0.8 Model / Data 0.8

transverse (min) transverse (max) 5 10 15 20 25 30 5 10 15 20 25 30 plead [GeV] plead [GeV] 60 < < 120 60 < < 120 T T

| | 〉 1.6 | | 1.6

〉 2.4 3

φ φ δ

Trans-min region ATLAS δ Trans-min region ATLAS

η 2.2 Trans-max region ATLAS Trans-max region ATLAS 1.4 [GeV] 1.4 η δ 〉

-1 -1 [GeV]

δ away -1 〉 -1 / p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb

φ 2 2.5 T / pT > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb φ ch δ T T

lead ch lead δ

1.2 p> > 1 GeV 1.2 plead > 1 GeV lead 120 η

〈 T 1.8 pT > 1 GeV p > 1 GeV η N δ

〈 T T

| | δ / T 1.6 / 2 1 1 T p p Σ

1.4 Σ 〈

0.8 0.81.2 〈 1.5 0.6 0.61 0.8 1 0.4 0.4 Data PYTHIA 8 Monash 0.6 Data PYTHIA 8 Monash Data PYTHIA 8 Monash PYTHIA 8 A14 Herwig7 PYTHIA 8 A14 Herwig7 0.4 PYTHIA 8 A14 Herwig7 0.5 PYTHIA 8 A14 Herwig7 0.2 PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos PYTHIA 8 A2 Epos Figure 1: Deﬁnition of regions in the azimuthal angle with respect to the leading (highest-pT) charged particle, with arrows representing particles associated with the hard scattering process and the leading charged particle 1 1 highlighted in red. Conceptually, the presence of a hard-scatter particle on the right-hand side of the1 transverse 1 region, increasing its p , typically leads to thatModel / Data 0.8 side being identiﬁed as the “trans-max” and henceModel / Data the0.8 left-hand T Model / Data 0.8 Model / Data 0.8 side as the “trans-min”, with maximumATLAS sensitivity, JHEP to the 03(2017)157 UE. 5 10 15 20 25 30 5 10 15 20 25 30 P 5 10 15 20 25 30 5 10 15 20 25 30 lead lead p [GeV] plead [GeV] lead T pT [GeV] p [GeV] T T

〉 2.4 3

〉 1.6 φ Bryan Webber 43 CERN-Fermilab HCP School 2017 δ φ

2.2 ↵ Trans-max region ATLAS δ 0.8 Trans-max region ATLAS illustrated in Figure 1, the azimuthal angularη di erence with respect to the leading (highest-pT) chargedTrans-diff region ATLAS Trans-diff region ATLAS [GeV] δ η -1 〉 -1 [GeV]

1.4 δ 2 2.5 〉 / p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb-1 -1 φ T T / p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb ch

δ particle, = lead , is used to deﬁne the regions: T φ T lead 0.7 lead ch 1.8 p > 1 GeV p > 1 GeV δ η

| | | | N lead lead 〈 T T

δ p > 1 GeV 1.2 p > 1 GeV η N

〈 T T δ 1.6 / 2 T < 0.6 / 60, the “towards region”; T p 1 p • | | 1.4 Σ

Σ 〈

1.2 1.50.5 〈 60 < < 120, the “transverse region”; and 0.8 • | | 1 0.4 0.6 > 120, the “away region”. 0.8 1 • | | 0.6 Data PYTHIA 8 Monash 0.3 Data PYTHIA 8 Monash Data PYTHIA 8 Monash 0.4 Data PYTHIA 8 Monash PYTHIA 8 A14 Herwig7 PYTHIA 8 A14 Herwig7 As the scale of the hard scattering increases,0.4 the leading charged particle acts as a convenient0.5 indic- PYTHIA 8 A14 Herwig7 PYTHIA 8 A14 Herwig7 PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos ator of the main ﬂow of hard-process energy.0.2 The towards and away regions are dominated by particle PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos production from the hard process and are hence relatively insensitive to the softer UE. In contrast,1.2 the 1 1 transverse region is more sensitive to the UE, and observables deﬁned inside it are the primary1.1 focus of 1 1

UE measurements. Model / Data 0.8 Model / Data 0.8 Model / Data 0.9 Model / Data 0.8 0.8 A further reﬁnement is to distinguish on a per-event basis5 between10 15 the more20 and25 the less30 active sides of5 the 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 transverse region [15, 16], deﬁned in terms of their relative scalar sums of primaryplead charged-particle [GeV] p and plead [GeV] T T pTlead [GeV] plead [GeV] T T termed “trans-max” and “trans-min” respectively.〉 The trans-min region is relatively insensitive1.6 to wide-

δ 0.8 Trans-diff region ATLASFigure 5: MeanTrans-diff densities region of charged-particle multiplicityATLAS Nch (left) and pT (right) as a function of leading charged- angle emissions from the hard process, andη the di↵erence between trans-max and trans-min observables [GeV] 1.4 δ -1 〉 -1

/ p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb p > 0.5 GeV, |η| < 2.5 s = 13 TeV, 1.6 nb 0.7 T particle φ pT, in theT trans-min (top), trans-max (middle) and trans-di↵ (bottom) azimuthal regions. The error bars on ch (termed the “trans-di↵”) hence represents the e↵ects of hard-process contamination. In thisδ analysis, an plead > 1 GeV 1.2 plead > 1 GeV P η N

〈 T T

data pointsδ represent statistical uncertainty and the blue band the total combined statistical and systematic uncer- event must have a non-zero primary charged-particle0.6 multiplicity in the trans-min region in/ order to be tainty. T 1 p included in either the trans-min, -max, or -di↵ observables. Σ

0.5 〈 0.8 16 0.4 0.6

0.3 Data PYTHIA 8 Monash 0.4 Data PYTHIA 8 Monash 3 PYTHIA 8 A14 Herwig7 PYTHIA 8 A14 Herwig7 0.2 PYTHIA 8 A2 Epos 0.2 PYTHIA 8 A2 Epos

1.2

1.1 1 1

Model / Data 0.9 Model / Data 0.8 0.8 5 10 15 20 25 30 5 10 15 20 25 30 plead [GeV] plead [GeV] T T

Figure 5: Mean densities of charged-particle multiplicity Nch (left) and pT (right) as a function of leading charged- particle pT, in the trans-min (top), trans-max (middle) and trans-di↵ (bottom) azimuthal regions. The error bars on data points represent statistical uncertainty and the blue band the totalP combined statistical and systematic uncertainty.

16 4

A C Fig. 4 Formation of clusters, which we represent by ovals here. Colour lines are dashed. The left D diagram shows colour-singlet clusters formed according to the dom- inating colour structure in the 1/Nc expansion. The right diagram shows a possible colour- B reconnected state: the partons of the clusters A and B are arranged in new clusters, C and D.

– C and D are no colour octets. p 4. If at least one reconnection possibility could be found in step 3, select the one which results in the v v smallest sum of cluster masses, mC + mD. Accept v s s¯ this colour reconnection with an adjustable probability preco. In this case replace the clusters A and v g s¯ s B by the newly formed clusters C and D. 5. Continue with the next quark in step 2. Fig. 3 For the hard subprocess a valence quark v is extracted from the proton. Since the valence quark parton distribu- The parameter preco steers the amount of colour recon- 7 tion functions dominate at large momentum fractions x and nection in the PCR model. Because of the selection rule small scales Q2,theinitial-stateshower,whichisgenerated to remark that the fraction of WW events with non- 1.0 in step 4, the PCR model tends to replace the heaviest vanishingbackwards colour length drop starting is slightly from higher the than partonic for scatter,n-type commonly ter- i-type the dijet case. Nevertheless, the vast majority of WW 0.8 minates on a valence quark. This situationh-type is shown in the clusters by lighter ones. A priori the model is not guar- events is not a↵ectedColour by colour reconnection, too. Reconnection leftmost ﬁgure. If the perturbative evolution0.6 still terminates anteed to be generally valid because of the following i

on a sea (anti)quark or a gluon, asf indicated in the other 8 reasons: The random ordering in the first step makes 3.2 Classificationfigures, of clustersone or two additional non-perturbative0.4 splittings are 8 performed to force the evolution to end with a valence quark. this algorithm non-deterministic since a di↵erent or- 0.2 1 1 The grey-shaded area indicates this non-perturbative0 region, 1 der of the initial clusters, generally speaking,1 0 leads to 10 10 0.0 whereas the perturbative parton shower happens0 in the1 region 2 0di.35↵erent3 reconnectiondefault possibilities clusters being tested.1 More- default clusters 10 10 10 10 10 0.35 1 GeV h-type clusters GeV below. 10 mcut/GeV / / 2 GeV GeV h-type clusters cl 0over,.30 apparently quarksi-type clustersand antiquarks arecl 10 treated dif- / / n type Fig. 8 Cluster fraction2 functions, defined in Eq.M (6), for LHC M 3 d n-type clusters d cl cl 10 0.30 i-type clusterscluster dijet events10 at 7 TeV. 0ferently.25 in the algorithm described above. n/ n/ 4 d d M M after reconnection 10 2.1 Plain colour reconnection 3 0.20 d n-type clusters d 10 h-type clusters 5 0.25 First we use this classification to analyse/n hadron /n 10 1 1 n/ n/ 0.15 i-type clusters h type collision events4 as they are immediately before colour 6 d d 10 afterA first reconnection modelcluster for colour reconnection10 has been imple- 2.2 Statistical colourn-type reconnection clusters 0.20 rearrangement. For that purpose, we define0 the.10 cluster 7 h-type clusters fraction functions5 10 /n mented in Herwig astype cluster of version 2.5/n 10 [39]. We refer to it 8 1 i 1 0.05 10 0.15 i-type clusters N (m ) as the plain colour reconnection model6 (PCR) in this aThecut other colour reconnection implementation9 studied fa(mcut) Na(mcut) Nb(mcut)= 0.00 , 10 10⌘ Ncl 0 1 2 3 4 n-type clusters b=h,i,n 0 2 4 6 8 10 10 10 10 10 10 paper. The following steps describe the full procedure:. X in this paper overcomes the conceptual drawbacks of 0.10 7 (6) Mcluster [GeV] Mcluster [GeV] 10 the PCR model. We refer to this model as statistical 1. Create a list of all quarks in the event, in random (a) (b) 0.05 Fig. 7 Classification of colour clusters in a hadron collision where Na(mcut8) is the number of a-type clusterscolour (a = reconnection (SCR) throughout this work. In the event, which, in this example, consists of the primary subpro- h, i, n)with10m mcut, counted in a suFig.ciently 9 Primary large cluster mass spectrum in LHC dijet events at 7 TeV. Figure (a) compares the mass distribution in the order. Perform the subsequent steps exactly once fortrk1 cess (left)Charged and particle one additional at 900 GeV, parton track interaction.p > 500 MeV, The for N grey-ch 6 Transverse1 Nchg density vs. p ,pre-colour-reconnection⌅s = 7 TeV stage to the distribution after colour reconnection. The contributions of the three cluster classes are ⇥ number of events . For instance, fi(100 GeV)first = 0. place,15 the algorithm aims at finding a cluster con-

⇤ 9 shaded area denotes non-perturbative parts of the simula- every quark in this list. says 15 10 % of all clusters with a massstacked. larger The than histograms in (b) merely di↵er from the ones in (a) in their binning. 0.00 d /d tion.2.6 The three clusters represent the cluster classes deﬁned 1.4

No recon ⇥ 0 1 2 3 4 0 2 ch in4 Sec. 3.2: n-type6 (blue), i-type8 (red) and h-type10 clusters 100 GeV are subprocess-interconnecting10 10 clusters.ﬁguration By 10 with a preferably10 small10 colour length, deﬁned N 2.4 /d d (orange). 2. The current quark is part of a cluster.1.2 Label this

construction,chg fa(mcut) is a number between 0 and 1 for ev as N

N 2.2 Mcluster [GeV] every2 class1a. Moreover, the cluster fractionbelow functions 6 GeV, as perturbative hM-typecluster and [GeV]i-type clus- 4 Tuning and comparison of the model results

cluster A. d 1/ 2 Col recon satisfy ⇥ ters do. In theN high-mass tail, however, n-type clusters with data (a)These3. resultsConsider generically raise a colour the question reconnection which with0.8 all other clus- (b) cl 1.8 clearly dominate, as2 already indicated by the cluster mechanism in the hadron event generation is respon- fa(0m.6 cut)=1. “Colour length” ATLAS data m i ,reduced by reconnectionIn this section we address(2) the question of whether the sible1.6 for theseters overly heavythat(min clusters. bias) exist To at gain that access time. to Label the potential re- fraction functions discussed above. Both their minor Fig. 9 Primary cluster mass spectrumATLAS data in LHC dijet events ata=h,i,n 7 TeV. Figure (a) comparesUE-EE-⌘3-CTEQ the6L1 mass distribution in the 2 min X 0.4 contributioni=1 at low masses and their large contribution MPI model in Herwig,equippedwiththenewCR this1.4 issue, weHw++ classifyconnection2.4, µ all= clusters1.0, p partner= by3.0 their ancestorsB. For in the possible new clusters UE-EE-SCR-CTEQ6L1 pre-colour-reconnection stage to theHw++ distribution2.5,MB900-CTEQ⇥ 6L1 after colour reconnection.Figure 8 shows the The cluster contributions fraction functions for of LHCX the three cluster classes are model, can improve the description of the ATLAS MB the1.2 event history. A sketch of the three types of clusters 0.2 at highUE7-2 masses do not change after colour reconnection. dijet eventsMassive at ps = 7 TeV. leading The fraction clusters of non- reduced stacked. The histograms inin (b) shown merely in Fig.C 7.and di↵erD from, which the would ones emergein (a) in when theirA binning.and B are re- In total,where however,Ncl theis mass the distribution number of is more clusters peaked in theand UEevent data, and see Fig.mi 2. To that end we need to find 1 perturbative0 clusters increases with m and exceeds 1.4 1.4 aftercut colour reconnection and the high-mass tail is sup- values of free parameters (tune parameters) of the MPI – The first classconnected are the clusters (cf. consisting Fig. of 4), partons the following0.5 at m conditions70 GeV. So for must an increasingis threshold the invariant mass of cluster i. In the definition of the 1.2 cut1.2 ⇡ model with CR that allow to get the best possible emitted perturbatively in the same partonic subpro- m up to values well beyond physicallypressed reasonable by a factor larger than 10. 1 be satisfied: cut 1 Similar need in string model cess. We call them h-type (hard) clusters. cluster masses of a few GeV, the contributioncolour of n-type length we opt for squared massesdescription to give of cluster the experimental data. Since both CR

MC/data 0.8 MC/data 0.8 below 6 GeV, as perturbative– The secondh-type– classThe of clustersand newi are-type clusters the subprocesses- clus- are lighter,clusters4 Tuning becomes more and and more comparison dominant. of the model results models can be regarded as an extension of the cluster 0 6 0 6 conﬁgurations with similarly heavy clusters precedence .interconnecting clusters, which combine par- A bin-by-bin. breakdown to the contributions of the model [36], which is used for hadronization in Herwig, ters do. In the high-mass tail,tons generated-2 however,-1 perturbativelyn-type0 in clusters di1 ↵erent par-2 variouswith cluster data2 types4 to the6 total8 cluster10 mass12 over distribu-14 16 conﬁgurations18 20 with less equally distributedthe tune of Herwig clusterwith CR models may require a tonic subprocesses.mC They+ m areD labelled

HERWIG http://projects.hepforge.org/herwig/ Angular-ordered parton shower, cluster hadronization

v6 Fortran; Herwig++

PYTHIA http://www.thep.lu.se/∼torbjorn/Pythia.html Dipole-type parton shower, string hadronization v6 Fortran; v8 C++

SHERPA http://projects.hepforge.org/sherpa/ Dipole-type parton shower, cluster hadronization

C++ “General-purpose event generators for LHC physics”, A Buckley et al., arXiv:1101.2599, Phys. Rept. 504(2011)145

Bryan Webber 45 CERN-Fermilab HCP School 2017 Generator Citations

• Most-cited article only for each version • 2017 is extrapolation (Jan to July x12/7)

Bryan Webber 46 CERN-Fermilab HCP School 2017

OtherOther Relevant Software relevant software (with apologies for omissions) Some examples (with apologies for many omissions): Other event/shower generators: PhoJet, Ariadne, Dipsy, Cascade, Vincia Matrix-element generators: MadGraph/MadEvent, CompHep, CalcHep, Helac, Whizard, Sherpa, GoSam, aMC@NLO Matrix element libraries: AlpGen, POWHEG BOX, MCFM, NLOjet++, VBFNLO, BlackHat, Rocket Special BSM scenarios: Prospino, Charybdis, TrueNoir Mass spectra and decays: SOFTSUSY, SPHENO, HDecay, SDecay Feynman rule generators: FeynRules PDF libraries: LHAPDF Resummed (p ) spectra: ResBos ? Approximate loops: LoopSim Jet ﬁnders: anti-k and FastJet ? Analysis packages: Rivet, Professor, MCPLOTS Detector simulation: GEANT, Delphes Constraints (from cosmology etc): DarkSUSY, MicrOmegas Standards: PDF identity codes, LHA, LHEF, SLHA, Binoth LHA, HepMC Can be meaningfully combined andSjöstrand, used for LHC Nobel physics! Symposium, May 2013

BryanTorbj¨orn Webber Sj¨ostrand Challenges for47 QCD TheoryCERN-Fermilab slide HCP 21/24 School 2017 Parton Shower Monte Carlo

0 http://mcplots.cern.ch/ Hard subprocess: qq¯ Z /W ± • !

• Leading-order (LO) normalization need next-to-LO (NLO) • Worse for high pT and/or extra jets need multijet merging Bryan Webber 48 CERN-Fermilab HCP School 2017 Summary on Event Generators

• Fairly good overall description of data, but… • Hard subprocess: LO no longer adequate • Parton showers: need matching to NLO ✤ Also multijet merging ✤ NLO showering? • Hadronization: string and cluster models ✤ Need new ideas/methods • Underlying event due to multiple interactions ✤ Colour reconnection necessary

Bryan Webber 49 CERN-Fermilab HCP School 2017