Introduction to Event Generators 3

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Introduction to Event Generators 3

Torbj¨ orn Sj¨ ostrand

Theoretical Particle Physics

Department of Astronomy and Theoretical Physics Lund University

S¨olvegatan 14A, SE-223 62 Lund, Sweden

CTEQ/MCnet School, DESY, 12 July 2016

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Event Generators Reminder

An event consists of many different physics steps, which have to be modelled by event generators:

Torbj¨orn Sj¨ostrand Event Generators 3 slide 2/35

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Event topologies

Expect and observe high multiplicities at the LHC.

What are production mechanisms behind this?

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What is minimum bias (MB)?

MB ≈ “all events, with no bias from restricted trigger conditions”

σtot=

σ_elastic+σsingle−diffractive+σdouble−diffractive+ · · · +σnon−diffractive

Schematically:

Reality: can only observe events with particles in central detector:

no universally accepted, detector-independent definition σ_min−bias≈σnon−diffractive+σdouble−diffractive≈ 2/3 × σ_tot

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What is underlying event (UE)?

In an event containing a jet pair or another hard process, how much further activity is there, that does not have its origin in the hard process itself, but in other physics processes?

Pedestal effect: the UE contains more activity than a normal MB event does (even discarding diffractive events).

Trigger bias: a jet ”trigger” criterion E⊥jet > E⊥min is more easily fulfilled in events with upwards-fluctuating UE activity, since the UE E⊥ in the jet cone counts towards the E⊥jet. Not enough!

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What is pileup?

hni = L σ

where L is machine luminosity per bunch crossing, L ∼ n1n2/A and σ ∼ σtot≈ 100 mb.

Current LHC machine conditions ⇒ hni ∼ 10 − 20.

Pileup introduces no new physics, and is thus not further considered here, but can be a nuisance.

However, keep in mind concept of bunches of hadrons leading to multiple collisions.

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The divergence of the QCD cross section

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆσ/dp²_⊥≈ 1/p_⊥⁴ for p_⊥→ 0.

Integrate QCD 2 → 2 qq⁰ → qq⁰

qq → q⁰q⁰ qq → gg qg → qg gg → gg gg → qq

(with CTEQ 5L PDF’s)

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What is multiple partonic interactions (MPI)?

Note that σint(p⊥min), the number of (2 → 2 QCD) interactions above p⊥min, involves integral over PDFs,

σ_int(p⊥min) = Z Z Z

p⊥min

dx₁dx₂dp_⊥² f₁(x₁, p_⊥²) f₂(x₂, p_⊥²) dˆσ dp_⊥² withR dx f (x, p²_⊥) = ∞, i.e. infinitely many partons.

So half a solution to σ_int(p⊥min) > σ_tot is many interactions per event: MPI

σtot =

∞

X

n=0

σn

σ_int =

∞

X

n=0

n σ_n

σint > σtot⇐⇒ hni > 1

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Poissonian statistics

If interactions occur independently then Poissonian statistics

P_n= hniⁿ n! e^−hni

but n = 0 ⇒ no event (in many models) and energy–momentum conservation

⇒ large n suppressed so narrower than Poissonian

MPI is a logical consequence of the composite nature of protons, n_parton∼P

q,q,gR f (x) dx > 3, which allows σ_int(p⊥min) > σ_tot, but what about the limit p⊥min→ 0?

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Colour screening

Other half of solution is that perturbative QCD is not valid at small p⊥ since q, g are not asymptotic states (confinement!).

Naively breakdown at p⊥min' ~

rp

≈ 0.2 GeV · fm

0.7 fm ≈ 0.3 GeV ' Λ_QCD

. . . but better replace r_p by (unknown) colour screeninglength d in hadron:

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Regularization of low-p

_⊥

divergence

so need nonperturbative regularization for p⊥ → 0 , e.g.

dˆσ

dp_⊥² ∝ α²_s(p²_⊥)

p⁴_⊥ → α²_s(p²_⊥)

p_⊥⁴ θ (p⊥− p_⊥min) (simpler) or → α²_s(p²_⊥0+ p_⊥²)

(p_⊥0² + p_⊥²)² (more physical) where p⊥min or p⊥0 are free parameters, empirically of order 2–3 GeV.

Typical number of interactions/event is 3 at 2 TeV, 4 – 5 at 13 TeV, but may be twice that in

“interesting” high-p⊥ ones.

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Impact parameter dependence

So far assumed that all collisions have equivalent initial conditions, but hadrons are extended, so dependence on impact parameter b.

Impact parameter dependence – 2

• Events are distributed in impact parameter b

• Average activity at b proportional to O(b)

? central collisions more active) Pⁿ broader than Poissonian

? peripheral passages normally give no collisions) finite ^tot

• Also crucial for pedestal e↵ect (more later)

Torbj¨orn Sj¨ostrand PPP 6: Multiparton interactions and MB/UE slide 24/56

Overlap of protons during encounter is

O(b) = Z

d³x dt ρ1(x, t) ρ2(x, t)

where ρ is (boosted) matter distribution in p, e.g. Gaussian or electromagnetic form factor.

Average activity at b proportional to O(b):

? central collisions more active

⇒ P_n broader than Poissonian;

? peripheral passages normally give no collisions ⇒ finite σ_tot.

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Double parton scattering

Double parton scattering (DPS): two hard processes in same event.

σDPS=

( σAσB

σ_eff for A 6= B σ_Aσ_B

2 σ_eff for A = B (Poissonian ⇒ 1/2; AB + BA ⇒ 2) Note inverse relationship on σeff. Natural scale is σ_ND≈ 50 mb, but “reduced” by b dependence.

Studied by 4 jets γ+ 3 jets

4 jets, whereof two b- or c-tagged J/ψ or Υ + 2 jets (including υcc) W/Z + 2 jets

W⁻W⁻

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Double parton scattering backgrounds

Always non-DPS backgrounds, so kinematics cuts required.

Example: order 4 jets p⊥1 > p⊥2 > p⊥3 > p⊥4 and define ϕ as angle between p⊥1∓ p_⊥2 and p⊥3∓ p_⊥4 for AFS/CDF

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Experimental summary on DPS rate

Note:

big error bars, uncertain methodology, but consistent:

σeff ≈ σ_ND/3

⇒ factor ∼ 3 enhancement relative to naive expectations

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Multiplicity and MPI effects

DPS only probes high-p⊥ tail of effects.

More dramatic are effects on multiplicity distributions:

ATLAS dN/dη

• New ATLAS analysis uses

• pT> 100 MeV/c

• Nch≥ 2

• Single diffraction is inhibited, and p

_T

cut allows direct comparison with other experiments.

June 14th 2016 O. Villalobos Baillie LHCP2016

8

ArXiv:1606.01133v1

ch 2,T100 MeV/ , 0.2

dN 6.50 0.01

dη⁼ ^± _n _≥ _p_> _c_η_<

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Forward-backward correlations

Global number, such as #MPI, affects activity everywhere:

η

0 0.5 1 1.5 2 2.5

FB multiplicity correlation 0.4 0.5 0.6 0.7 0.8

0.9 Data 2010 Pythia 6 MC09

Pythia 6 DW Pythia 6 Perugia2011 Pythia 6 AMBT2B Pythia 8 4C Herwig++

ATLAS

= 7 TeV s

> 100 MeV pT

2

ch≥ n

| < 2.5 η

|

0 0.5 1 1.5 2 η 2.5

MC / data _0.8

0.9 1 1.1

(note suppressed zero on vertical axis ⇒ big effects!)

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Colour (re)connections and hp

_⊥

i(n

_ch

)

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Jet pedestal effect – 1

Events with hard scale (jet, W/Z) have more underlying activity!

Events with n interactions have n chances that one of them is hard, so “trigger bias”: hard scale ⇒ central collision

⇒ more interactions ⇒ larger underlying activity.

Studied in particular by Rick Field, with CDF/CMS data:

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Jet pedestal effect – 2

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MPI in PYTHIA

MPIs are gererated in a falling sequence of p⊥ values;

recall Sudakov factor approach to parton showers.

Energy, momentum and flavour conservedstep by step:

subtracted from proton by all “previous” collisions.

Protons modelled as extended objects, allowing both central and peripheral collisions, with more or less activity.

(Partons at small x more broadly spread than at large x .) Colour screening increases with energy, i.e. p⊥0 = p⊥0(Ecm), as more and more partons can interact.

(Rescattering: one parton can scatter several times.) Colour connections: each interaction hooks up with colours from beam remnants, but also correlations inside remnants.

Colour reconnections: many interaction “on top of” each other ⇒ tightly packed partons ⇒ colour memory loss?

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Interleaved evolution in PYTHIA

• Transverse-momentum-ordered parton showers for ISR and FSR

• MPI also ordered in p_⊥

⇒ Allows interleaved evolution for ISR, FSR and MPI:

dP dp⊥

=

dP_MPI dp⊥

+XdP_ISR dp⊥

+XdP_FSR dp⊥

× exp

−

Z p⊥max

p⊥

dP_MPI

dp⁰_⊥ +XdP_ISR

dp⁰_⊥ +XdP_FSR dp⁰_⊥

dp_⊥⁰

Ordered in decreasing p⊥ using “Sudakov” trick.

Corresponds to increasing “resolution”:

smaller p_⊥ fill in details of basic picture set at larger p_⊥. Start from fixed hard interaction ⇒ underlying event No separate hard interaction ⇒ minbias events Possible to choose two hard interactions, e.g. W⁻W⁻

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MPI in Herwig

Key point: two-component model

p⊥> p⊥min: pure perturbation theory (no modification) p⊥< p⊥min: pure nonperturbative ansatz

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MPI in Herwig – 2

Number of MPIs first picked; then generatedunordered in p⊥. Interactions uncorrelated, up until energy used up.

Force ISR to reconstruct back to gluon after first interaction.

Impact parameter byem form factor shape, but tunable width.

p⊥min scale to be tuned energy-by-energy.

Colour reconnection essential to get dn/dη correct.

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Heavy Ion Collisions

Heavy-ion physics and the QGP (P. Christiansen, Lund)

PPP 10

initial state

pre-equilibrium

QGP and hydrodynamic expansion

hadronization

hadronic phase and freeze-out

Heavy ion collisions

• The only way we can create the QGP in the laboratory!

• By colliding heavy ions it is possible to create a large (»1fm³) zone of hot and dense QCD matter

• Goal is to create and study the properties of the Quark Gluon Plasma

• Experimentally mainly the final state particles are observed, so the conclusions have to be inferred via models

6

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The three systems — understanding before 2012

Heavy-ion physics and the QGP (P. Christiansen, Lund)

PPP 10

The three systems

(understanding before 2012)

Pb-Pb

pp

p-Pb

Hot QCD matter:

This is where we expect the QGP to be created in central collisions.

QCD baseline:

This is the baseline for

“standard” QCD phenomena.

Cold QCD matter:

This is to isolate nuclear effects, e.g. nuclear pdfs.

9

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Strangeness enhancement

Multiplicity-dependent enhancement of strange and multi-strange . . . ALICE Collaboration

) c (GeV/

pT

0 2 4 6 8 10 12 14

]-1)c) [(GeV/ Tpdy/(dN2 devN1/

−7

10

6

10−

−5

10

−4

10

3

10−

−2

10

1

10−

1 10 102

103

104

105

106

107

108

109 ALICE pp s = 7 TeV

V0M multiplicity classes

(I)

(I+II)

(VII) 9)

×10

S ( K0

(VII) Λ+Λ (×10⁶)

(VII) Ξ⁻+Ξ⁺ (×10³)

(V+VI) +

+Ω Ω−

(X)

(IX+X)

Fig. 1: (color online) pT-differential yields of K⁰_S,L + L, X +X⁺andW +W⁺measured in |y| < 0.5 for a se- lection of event classes, indicated by roman numbers in brackets (see Table 1). The data are scaled by different factors to improve the visibility. The dashed curves rep- resent Tsallis-L´evy fits to each individual distribution to extract integrated yields.

|< 0.5

|η

〉 /dη Nch

〈d

10 10² 10³

)+π+−πRatio of yields to (

−3

10

2

10−

−1

10

16)

× + ( Ω

−+ Ω

×6) + ( +Ξ Ξ−

2)

× ( Λ + Λ

S 2K0

ALICE = 7 TeV s pp,

= 5.02 TeV sNN p-Pb,

= 2.76 TeV sNN Pb-Pb, PYTHIA8 DIPSY EPOS LHC

Fig. 2: (color online) pT-integrated yield ratios of strange and multi-strange hadrons to (p⁺+p ) as a function of hdNch/dhi measured in the rapidity interval

|y| < 0.5. The empty and dark-shaded boxes show the total systematic uncertainty and the contribution uncorrelated across multiplicity bins, respectively. The values are compared to calculations from MC models [39–43]

and to results obtained in Pb–Pb and p–Pb collisions at the LHC [13, 25, 27]. For Pb–Pb results the ratio 2L / (p⁺+p ) is shown.

models based on relativistic hydrodynamics. In this framework, the pTdistributions are effectively as due to particle emission from collectively expanding thermal sources [44, 45].

The blast-wave model [44] is employed to analyse the spectral shapes of K⁰_S,L and X in the common highest multiplicity class (class I). A simultaneous fit to all particles is performed following the approach discussed in [25] in the pTranges 0–1.5, 0.6–2.9 and 0.6–2.9 GeV/c, for K⁰_S,L and X, respectively.

The best-fit describes the data to better than 5% in the respective fit ranges, consistent with particle production from a thermal source at temperature Tfoexpanding with a common transverse velocity hbTi.

The resulting parameters, Tfo= 163 ± 10 MeV and hbTi = 0.49 ± 0.02, are remarkably similar to the ones obtained in p–Pb collisions for 20–40% [25], where hdNch/dhi is also comparable.

The pT-integrated yields are computed using the data in the measured ranges and extrapolations in the unmeasured regions. In order to extrapolate to the unmeasured region, the data were fitted with a Tsallis-

5

<p

_T

> vs. multiplicity

ALICE | Title of the Meeting | Date | Speaker 20

The hardening of spectra can be quantified by looking at the <p_T> as a function of multiplicity

● Rising trend of <p_T> with multiplicity for all identified particles

● Mass ordered

● Logarithmic fit to guide the eye

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Collective flow

Two-par:cle Correla:ons in 13 TeV pp

⁶

Nchrec>120 50≤Nchrec<60

Nchrec<30

near-side ridge

ATLAS, PRL 116, 172301 (2016)

Probing(novel(long,range(correla/on(phenomena(

in(pPb(collisions(with(iden/ﬁed(par/cles(at(CMS(

Zhenyu'Chen'(Rice'University)' for'the'CMS'Collabora:on'

'

Hot'Quarks'Workshop'2014' '

1'

6/14/16% Zhenyu%Chen%-%LHCP%2016,%Lund%

%

! v₂:%

"  No%energy%dependence%observed%

"  Similar%shape%as%%

%%%%%p-Pb%and%Pb-Pb%

"  Smaller%than%bigger%system%

Similar'eﬀect'involved'with'diﬀerent' magnitude?'

'

offline

Ntrk

0 100 200 300

{2}sub 2v 0.05 0.10

= 5 TeV sNN

pPb

= 2.76 TeV sNN

PbPb

= 13 TeV s pp

= 7 TeV s pp

= 5 TeV s pp Preliminary

CMS

< 3 GeV/c 0.3 < pT

| > 2 η

∆

|

offline

Ntrk

0 100 200 300

{2}

sub 3

v

0.01 0.02 0.03

< 3 GeV/c 0.3 < pT

| > 2 η

|∆

offline

Ntrk

0 100 200 300

{2}sub 2v 0.05 0.10

= 5 TeV sNN

pPb

= 2.76 TeV sNN

PbPb

= 13 TeV s pp

= 7 TeV s pp

= 5 TeV s pp Preliminary

CMS

< 3 GeV/c 0.3 < pT

| > 2 η

|∆

offline

Ntrk

0 100 200 300

{2}

sub 3

v

0.01 0.02 0.03

< 3 GeV/c 0.3 < pT

| > 2 η

|∆

7%

Increasingly blurred line between pp, pA and AA!

QGP theory wrong?

Much smaller systems enough for QGP?

Standard pp generators wrong! Need mechanism for collectivity.

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Total cross section

13. Discussion

The result for the total hadronic cross section presented here, σtot = 95.35 ± 1.36 mb, can be compared to the value measured by TOTEM in the same LHC fill using a luminosity-dependent analysis, σtot = 98.6 ± 2.2 mb [11]. Assuming the uncertainties are uncorrelated, the diﬀerence between the AT- LAS and TOTEM values corresponds to 1.3σ. The uncertainty on the TOTEM result is dominated by the luminosity uncertainty of ±4%, while the measurement reported here profits from a smaller luminosity uncertainty of only ±2.3%. In subsequent publications [16,54] TOTEM has used the same data to perform a luminosity-independent measurement of the total cross section using a simultaneous determination of elastic and inelastic event yields. In addition, TOTEM made a ρ-independent measurement without using the optical theorem by summing directly the elastic and inelastic cross sections [16]. The three TOTEM results are consistent with one another.

The results presented here are compared in Fig.19to the result of TOTEM and are also compared with results of experiments at lower energy [29] and with cosmic ray experiments [55–58]. The measured total cross section is furthermore compared to the best fit to the energy evolution of the total cross section from the COMPETE Collaboration [26] assuming an energy dependence of ln²s. The elastic measurement is in turn compared to a second order polynomial fit in ln s of the elastic cross sections. The value of σtot

reported here is two standard deviations below the COMPETE parameterization. Some other models prefer a somewhat slower increase of the total cross section with energy, predicting values below 95 mb, and thus agree slightly better with the result reported here [59–61].

[GeV]

s

10 10² 10³ 10⁴

[mb]σ

0 20 40 60 80 100 120 140

σtot

σel ATLAS TOTEM

p p Lower energy

pp Lower energy and cosmic ray Cosmic rays

COMPETE RRpl2u ) s

2( ) + 1.42ln s

13.1 - 1.88ln(

Figure 19: Comparison of total and elastic cross-section measurements presented here with other published measurements [11, 29,55–58] and model predictions as function of the centre-of-mass energy.

33

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Event-type breakdown ATLAS σ

_inel

• Cross sections obtained for ξ >

10^-6, and full kinematics.

• Quite large error for extrapolation

• Diffractive mass according to PYTHIA Donnachie- Landshoff parameterization.

June 14th 2016 O. Villalobos Baillie LHCP2016 14

σξ>10-6= 68.2±0.08±1.3 mb

σinel = 79.3±0.08±1.3 ±2.5 mb

SD DD

inel D 28%

f σ σ

σ

= + =

ArXiV:1606.0265

Phase space for diffractive masses and rapidity gaps roughly like dM²/M² = dy , i.e. flat in rapidity.

Rapidity integration means σ_sd grows faster that σtot, σ_dd even faster, etc.

⇒ Need damping.

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The Pomeron

Amplitude for (forward) elastic scattering from total cross section:

p

=⇒

p

=⇒

p p

IP

p

p p

p

IP IP

introducing the Pomeron IP as shorthand for the effective 2-gluon exchange.

Since p → p IP the Pomeron must have the quantum numbers of the vacuum:

0⁺ colour singlet.

Recall: elastic cross section requires squaring one more time:

p

=⇒

p

=⇒

p p

IP

p

IP IP

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Regge–Pomeranchuk theory of cross sections

total A

B

elastic A

B

single diffractive A

B

double diffractive A

B

central diffractive A

B

p

IP IP

IP

σ^AB_tot = βA(0) βB(0) Im GIP(s/s0, 0)

dσ^AB_el

dt = 1

16πβ²_A(t) β_B²(t) |GIP(s/s0, t)|² dσ^AB→AX_sd

dt dM² = 1

16π M²g3IPβ_A²(t)βB(0)|GIP(s/M², t)|²Im G (M²/s0, 0) dσ^AB→X_dd ¹^X²

dt dM₁²dM₂² = 1

16π M₁²M₂²g_3IP² βA(0) βB(0)|GIP(ss0/(M₁²M₂²), t)|²

× Im G (M₁²/s0, 0) Im G (M₂²/s0, 0)

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Diffraction

Ingelman-Schlein: Pomeron as hadron with partonic content Diffractive event = (Pomeron flux) × (IPp collision)

Diffraction

Ingelman-Schlein: Pomeron as hadron with partonic content Diffractive event = (Pomeron flux) × (IPp collision)

p p

IP p

Used e.g. in POMPYT POMWIG PHOJET

1) σ_SDand σ_DDtaken from existing parametrization or set by user.

2) Shape of Pomeron distribution inside a proton, f_IP/p(x_IP, t) gives diffractive mass spectrum and scattering p_⊥of proton.

3) At low masses retain old framework, with longitudinal string(s).

Above 10 GeV begin smooth transition to IPp handled with full pp machinery: multiple interactions, parton showers, beam remnants, . . . . 4) Choice between 5 Pomeron PDFs.

Free parameter σ_IPpneeded to fix #ninteractions$ = σ_jet/σ_IPp. 5) Framework needs testing and tuning, e.g. of σ_IPp.

1) σ_SD and σ_DD set by Reggeon theory.

2) f_IP/p(xIP, t) ⇒ diffractive mass spectrum, p⊥ of proton out.

3) Smooth transition from simple model at low masses to IPp with full pp machinery: multiple interactions, parton showers, etc.

4) Choice between different Pomeron PDFs.

5) Free parameter σIPp needed to fix hninteractionsi = σ_jet/σIPp.

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Gaps by subprocess

0 1 2 3 4 5 6 7 8

[mb]F η∆/dσd

1 10

102 Data L = 7.1 µb^-1

PYTHIA 8 4C Non-Diffractive Single Diffractive Double Diffractive ATLAS

= 7 TeV s

> 200 MeV pT

ηF

0 1 2 3 4 5 6 7 ∆ 8

MC/Data ₁

1.5

Non-diffractive fine, but wrong gap spectrum for diffraction.

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Multiplicity in diffractive events

0 5 10 15 20 25 30 35 40

Events

10 102

103

104

105

106

107

ATLAS < 6 ηF

∆ 4 <

= 7 TeV s

> 200 MeV pT

Data

MC PYTHIA 6 MC PYTHIA 8 MC PHOJET

NC

0 5 10 15 20 25 30 35 40

MC/Data 1

2 3

PYTHIA 6 lacks MPI, ISR, FSR in diffraction, so undershoots.