sigma (mb)

(1)

Academic Training Lectures CERN 4, 5, 6, 7 April 2005

Monte Carlo Generators for the LHC

Torbj ¨orn Sj ¨ostrand

CERN and Lund University

1. (Monday) Introduction and Overview; Matrix Elements 2. (Tuesday) Parton Showers; Matching Issues

3. (today) Multiple Interactions and Beam Remnants

4. (Thursday) Hadronization and Decays; Summary and Outlook

(2)

Event Physics Overview

Repetition: from the “simple” to the “complex”,

or from “calculable” at large virtualities to “modelled” at small Matrix elements (ME):

1) Hard subprocess:

|M|², Breit-Wigners, parton densities.

q

q Z⁰ Z⁰

h⁰

2) Resonance decays:

includes correlations.

Z⁰

µ⁺ µ⁻

h⁰

W⁻ W⁺

ντ

τ⁻ s c

Parton Showers (PS):

3) Final-state parton showers.

q → qg g → gg g → qq q → qγ

4) Initial-state parton showers.

g q

Z⁰

(3)

5) Multiple parton–parton interactions.

6) Beam remnants, with colour connections.

p p

b b

ud ud

u u

5) + 6) = Underlying Event

7) Hadronization

c g g b

D⁻_s Λ⁰

n η

π⁺ K^∗−

φ K⁺ π⁻ B⁰

8) Ordinary decays:

hadronic, τ, charm, . . .

ρ⁺

π⁰

π⁺

γ γ

(4)

What is multiple interactions?

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dσ/dp²_⊥ ≈ 1/p⁴_⊥ for p_⊥ → 0.

integrate QCD 2 → 2

qq⁰ → qq⁰ qq → q⁰q⁰ qq → gg qg → qg gg → gg gg → qq

with CTEQ 5L PDF’s _0.01

0.1 1 10 100 1000 10000

0 5 10 15 20 25 30 35 40 45 50

sigma (mb)

pTmin (GeV)

Integrated cross section above pTmin for pp at 14 TeV jet cross section total cross section

(5)

So σ

_int

(p

_⊥min

) > σ

_tot

for p

_⊥min

∼ 5

^<

GeV

Half a solution: many interactions per event σ_tot =

∞ X

n=0

σ_n

σ_int =

∞ X

n=0

n σ_n

σ_int > σ_tot ⇐⇒ hni > 1

n P_n

hni = 2

0 1 2 3 4 5 6 7

If interactions occur independently then Poissonian statistics

P_n = hniⁿ

n! e^−hni

but energy–momentum conservation

⇒ large n suppressed

(6)

Modelling multiple interactions

T. Sj ¨ostrand, M. van Zijl, PRD36 (1987) 2019: first model(s) for event properties based on perturbative multiple interactions

(1) Simple scenario:

• Sharp cut-off at p_⊥min main free parameter

• Is only a model for nondiffractive events, i.e. for σ_nd ' (2/3)σ_tot

• Average number of interactions is hni = σ_int(p_⊥min)/σ_nd

• Interactions occur almost independently, i.e.

Poissonian statistics P_n = hniⁿe^−hni/n!

with fraction P₀ = e^−hni pure low-p_⊥ events

• Interactions generated in ordered sequence p_⊥1 > p_⊥2 > p_⊥3 > . . . by “Sudakov” trick (what happens “first”?)

dP

dp_⊥i = 1 σ_nd

dσ

dp_⊥ exp

"

−

Z _p

⊥(i−1)

p_⊥

1 σ_nd

dσ

dp⁰_⊥dp⁰_⊥

#

• Momentum conservation in PDF’s ⇒ P_n narrower than Poissonian

• Simplify after first interaction: only gg or qq outgoing, no showers, . . .

(9)

(2) More sophisticated scenario:

• Smooth turn-off at p_⊥0 scale

• Require ≥ 1 interaction in an event

• Hadrons are extended,

e.g. double Gaussian (“hot spots”):

ρ_matter(r) = N₁ exp −r² r₁²

!

+ N₂ exp −r² r₂²

!

where r₂ 6= r₁ represents “hot spots”

• Events are distributed in impact parameter b

• Overlap of hadrons during collision O(b) =

Z

d³x dt ρ^boosted_1,matter(x_{, t)ρ}^boosted_2,matter(x_{, t)}

• Average activity at b proportional to O(b)

⇒ central collisions normally more active

⇒ P_n broader than Poissonian

• More time-consuming (b, p_⊥) generation

• Need for simplifications remains

0.01 0.1 1 10

0 0.5 1 1.5 2 2.5

ρ(r) total r₁ = 1 r₂ = 0.4

p

b

b hni

1

(10)

(3) HERWIG

Soft Underlying Event (SUE), based on UA5 Monte Carlo

l

y

v v

• Distribute a (∼ negative binomial) number of clusters independently in rapidity and transverse momentum according to parametrization/extrapolation of data

• modify for overall energy/momentum/flavour conservation

• no minijets; correlations only by cluster decays (4) Jimmy (HERWIG add-on)

• similar to PYTHIA (2) above; but details different

• matter profile by electromagnetic form factor

• no p_⊥-ordering of emissions, no rescaling of PDF:

abrupt stop when (if) run out of energy (5) Phojet/DTUjet

• comes from “historical” tradition of soft physics

of “cut Pomerons” ≈ p_⊥ → 0 limit of multiple interactions

• extended also to “hard” interactions similarly to PYTHIA

(11)

without multiple interactions

(12)

with multiple interactions

(13)

Evidence for multiple interactions

• Width of multiplicity distribution: UA5, E735 (previous slides)

• Forward–backward correlations: UA5 (previous slides)

• Minijet rates: UA1

No. jets UA1 no MI simple double

(%) Gaussian

1 9.96 14.30 11.51 8.88

2 3.45 2.45 2.45 2.67

3 1.12 0.22 0.32 0.74

4 0.22 0.01 0.04 0.25

5 0.05 0.00 0.00 0.07

(14)

• Direct observation: AFS, (UA2,) CDF

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

Double Parton Scattering

1 2

3

4

|p_⊥1 + p_⊥2| ≈ 0

|p_⊥3 + p_⊥4_{| ≈ 0} dσ/dϕ flat

Double BremsStrahlung

1 2

3 4

|p_⊥1 + p_⊥2| 0

|p_⊥3 + p_⊥4_{| 0} dσ/dϕ peaked at ϕ ≈ 0 AFS 4-jet analysis (pp at 63 GeV);

double bremsstrahlung subtracted:

observed 6 in arbitrary units

no MI 0

simple MI 1

double Gaussian 3.7

(15)

CDF 3-jet + prompt photon analysis Yellow region = double parton scattering (DPS) The rest =

PYTHIA showers

σ_DPS = σ_Aσ_B

σ_eff for A 6= B =⇒ σ_eff = 14.5 ± 1.7^+1.7_−2.3 mb Strong enhancement relative to naive expectations!

(16)

• Jet pedestal effect: UA1, H1, CDF

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.

Centrality effect saturates at p_⊥hard ∼ 10 GeV.

Studied in detail by Rick Field, comparing with CDF data:

Rick Field December 1, 2004

TeV4LHC Meeting Page 4 of 27

“MAX/MIN Transverse” Densities

x Define the MAX and MIN “transverse” regions on an event-by-event basis with MAX (MIN) having the largest (smallest) density.

x The “transMIN” region is very sensitive to the “beam-beam remnant” and multiple parton interaction components of the “underlying event”.

x The difference, “transMAX” minus “transMIN”, is very sensitive to the “hard scattering” component of the “underlying event” (i.e. hard initial and final- state radiation).

Jet #1 Direction 'I

“Toward”

“TransMAX” “TransMIN”

“Away”

Jet #1 Direction

'I

“TransMAX” “TransMIN”

“Toward”

“Away”

“Toward-Side” Jet

“Away-Side” Jet Jet #3

“TransMIN” very sensitive to the “beam-beam remnants”!

(17)

Run 2 Monte-Carlo Workshop April 20, 2001

Rick Field - Florida/CDF Page 7

“Transverse” Nchg

“Transverse” Nchg versus P

versus P

_T_T

(chgjet#1) (chgjet#1)

! Plot shows the “Transverse” <Nchg> versus P_T(chgjet#1) compared to the the QCD hard scattering predictions of Herwig 5.9, Isajet 7.32, and Pythia 6.115 (default parameters with P_T(hard)>3 GeV/c).

! Only charged particles with |ηηηη| < 1 and P_T> 0.5 GeV are included and the QCD Monte- Carlo predictions have been corrected for efficiency.

Pythia 6.115

Herwig 5.9

Isajet 7.32

Charged Jet #1 Direction

∆φ

“Toward”

“Transverse” “Transverse”

“Away”

"Transverse" Nchg versus PT(charged jet#1)

0 1 2 3 4 5

0 5 10 15 20 25 30 35 40 45 50

PT(charged jet#1) (GeV/c)

"Transverse" <Nchg> in 1 GeV/c bin

Herwig Isajet Pythia 6.115 CDF Min-Bias CDF JET20

1.8 TeV |ηηηη|<1.0 PT>0.5 GeV

CDF Preliminary

data uncorrected theory corrected

(18)

MC Tools for the LHC CERN July 31, 2003

Old PYTHIA default (more initial-state radiation)

0.5 0.5

PARP(83)

0.4 0.4

PARP(84)

0.25 0.25

PARP(90)

0.95 1.0

PARP(86)

1.8 TeV 1.8 TeV

PARP(89)

4.0 0.9 2.0 GeV

4 1 Tune A

1.0 PARP(67)

1.0 PARP(85)

1.9 GeV PARP(82)

4 MSTP(82)

1 MSTP(81)

Tune B Parameter

Tuned PYTHIA 6.206 Tuned PYTHIA 6.206

¨ Plot shows the “Transverse” charged particle density versus P_T(chgjet#1) compared to the QCD hard

scattering predictions of two tuned versions of

PYTHIA 6.206 (CTEQ5L, Set B (PARP(67)=1) and Set A (PARP(67)=4)).

"Transverse" Charged Particle Density: dN/dKdI

0.00 0.25 0.50 0.75 1.00

0 5 10 15 20 25 30 35 40 45 50

"Transverse" Charged Density

1.8 TeV |K|<1.0 PT>0.5 GeV

CDF Preliminary

CTEQ5L

PYTHIA 6.206 (Set A) PARP(67)=4

PYTHIA 6.206 (Set B) PARP(67)=1

0.5 0.5

PARP(83)

0.4 0.4

PARP(84)

0.25 0.25

PARP(90)

0.95 1.0

PARP(86)

1.8 TeV 1.8 TeV

PARP(89)

4.0 0.9 2.0 GeV

4 1 Tune A

1.0 PARP(67)

1.0 PARP(85)

1.9 GeV PARP(82)

4 MSTP(82)

1 MSTP(81)

Tune B Parameter

PYTHIA 6.206 CTEQ5L

New PYTHIA default (less initial-state radiation)

Double Gaussian

Old PYTHIA default (more initial-state radiation)

Tune A CDF Run 2 Default!

(19)

MC Tools for the LHC CERN July 31, 2003

Tuned PYTHIA 6.206 Tuned PYTHIA 6.206

“Transverse” P

“Transverse” P _T _T Distribution Distribution

"Transverse" Charged Particle Density: dN/dKdI

0.00 0.25 0.50 0.75 1.00

0 5 10 15 20 25 30 35 40 45 50

"Transverse" Charged Density

1.8 TeV |K|<1.0 PT>0.5 GeV CDF Preliminary

CTEQ5L

PYTHIA 6.206 (Set A) PARP(67)=4

PYTHIA 6.206 (Set B) PARP(67)=1

PARP(67)=4.0 (old default) is favored over PARP(67)=1.0 (new default)!

P_T(charged jet#1) > 30 GeV/c

"Transverse" Charged Particle Density

1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00

0 2 4 6 8 10 12 14

PT(charged) (GeV/c) Charged Density dN/dKdIdPT (1/GeV/c)

CDF Data

1.8 TeV |K|<1 PT>0.5 GeV/c PT(chgjet#1) > 5 GeV/c

PT(chgjet#1) > 30 GeV/c

PYTHIA 6.206 Set A PARP(67)=4

PYTHIA 6.206 Set B PARP(67)=1

¨ Compares the average “transverse” charge particle density (|K|<1, P_T>0.5 GeV) versus P_T(charged jet#1) and the P_T distribution of the “transverse” density, dN_chg/dKdIdP_T with the QCD Monte-Carlo predictions of two tuned versions of PYTHIA 6.206 (P_T(hard) > 0, CTEQ5L, Set B (PARP(67)=1) and Set A (PARP(67)=4)).

(20)

Leading Jet: “MAX & MIN Transverse” Densities

PYTHIA Tune A HERWIG

"MAX/MIN Transverse" Charge Density: dN/dKdI

0.0 0.4 0.8 1.2 1.6

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" Charge Density CDF Preliminary

data uncorrected theory + CDFSIM

PYTHIA Tune A 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

"MAX/MIN Transverse" Charge Density: dN/dKdI

0.0 0.4 0.8 1.2 1.6

0 50 100 150 200 250

ET(jet#1) (GeV)

HERWIG 1.96 TeV

"MAX"

"MIN"

"AVE"

Leading Jet

"MAX/MIN Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" PTsum Density (GeV/c)

CDF Preliminary

"MAX"

"MIN"

"AVE"

Leading Jet

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

CDF Preliminary

HERWIG 1.96 TeV

"MAX"

"MIN"

"AVE"

Leading Jet

Charged particle density and PTsum density for “leading jet” events versus ET(jet#1) for PYTHIA Tune A and HERWIG.

(21)

KITP Collider Workshop February 17, 2004

“ “ Transverse” Charge Density Transverse” Charge Density

versus E

versus E _T _T (jet#1) (jet#1)

Jet #1 Direction 'I

“Toward”

“Away”

Jet #1 Direction 'I

“Toward”

“Away”

Jet #2 Direction

¨ Shows the average charged particle density, dN^chg/dKdI, in the “transverse” region (p_T

> 0.5 GeV/c, |K| < 1) versus E_T(jet#1) for “Leading Jet” and “Back-to-Back” events.

“Leading Jet”

“Back-to-Back”

"AVE Transverse" Charge Density: dN/dKdI

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" Charge Density CDF Run 2 Preliminary

data uncorrected

1.96 TeV Charged Particles (|K|<1.0, PT>0.5 GeV/c) Leading Jet

Back-to-Back

Min-Bias 0.25 per unit K-I

¨ Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM.

"AVE Transverse" Charge Density: dN/dKdI

0.0 0.2 0.4 0.6 0.8 1.0

0 50 100 150 200 250

ET(jet#1) (GeV)

1.96 TeV Charged Particles (|K|<1.0, PT>0.5 GeV/c) Leading Jet

Back-to-Back PY Tune A

HW

(22)

Back Back - - to to - - Back Back “Associated” “Associated”

Charged Particle Densities Charged Particle Densities

'I

Jet#1 Region

PTmaxT Direction

Jet#2 Region

¨ Shows the 'I dependence of the “associated” charged particle density, dNchg/dKdI, p_T > 0.5 GeV/c, |K| < 1, PTmaxT > 2.0 GeV/c (not including PTmaxT) relative to PTmaxT (rotated to 180^o) and the charged particle density, dN^chg/dKdI, p_T > 0.5 GeV/c, |K| < 1, relative to jet#1 (rotated to 270^o) for “back-to-back events” with 30 < E_T(jet#1) < 70 GeV.

Jet #1 Direction 'I

“Toward”

“Away”

Jet #2 Direction

Charged Particle Density: dN/dKdI

2

6 10

14 18

22 26

30 34

38 42

46 50

54 58

62

66

70

74

78

82

86

90

94

98

102

106

110

114

118

122

126

130

134 138 142 146 150 154 158 162 166 170 178 174 182 190 186 194 198 202 206 210 214 218 222 226 230 234 238 242 246 250 254 258 262 266 270 274 278 282 286

290 294

298 302

306 310

314 318

322 326

330 334

338 342

346 350 354 358

CDF Preliminary

data uncorrected

30 < ET(jet#1) < 70 GeV Back-to-Back

"Transverse"

Region "Transverse"

Region Jet#1

Associated Density PTmaxT > 2 GeV/c

(not included) PTmaxT

Polar Plot

“Back-to-Back”

“associated” density

“Back-to-Back”

charge density

0.5

1.0

1.5

2.0

(23)

“ “ Associated” Charge Density Associated” Charge Density PYTHIA Tune A

PYTHIA Tune A vs vs HERWIG HERWIG

Associated Particle Density: dN/dKdI

0.1 1.0 10.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Associated Particle Density

PTmaxT > 2.0 GeV/c PY Tune A

Back-to-Back 30 < ET(jet#1) < 70 GeV Charged Particles

(|K|<1.0, PT>0.5 GeV/c)

PTmaxT

CDF Preliminary

data uncorrected

theory + CDFSIM PTmaxT not included

"Jet#1"

Region

Associated Particle Density: dN/dKdI

0.1 1.0 10.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Associated Particle Density

PTmaxT > 2.0 GeV/c HERWIG

Back-to-Back 30 < ET(jet#1) < 70 GeV Charged Particles

(|K|<1.0, PT>0.5 GeV/c)

PTmaxT

CDF Preliminary

data uncorrected

theory + CDFSIM PTmaxT not included

"Jet#1"

Region

Data - Theory: Associated Particle Density dN/dKdI

-1.6 -0.8 0.0 0.8 1.6

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Data - Theory

CDF Preliminary

Back-to-Back 30 < ET(jet#1) < 70 GeV PYTHIA Tune A

PTmaxT "Jet#1"

Region PTmaxT > 2.0 GeV/c (not included)

Data - Theory: Associated Particle Density dN/dKdI

-1.0 -0.5 0.0 0.5 1.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Data - Theory

CDF Preliminary

Back-to-Back 30 < ET(jet#1) < 70 GeV HERWIG

PTmaxT "Jet#1"

Region PTmaxT > 2.0 GeV/c (not included)

For PTmaxT > 2.0 GeV both PYTHIA and HERWIG produce

slightly too many “associated”

particles in the direction of PTmaxT!

But HERWIG (without multiple parton interactions) produces

too few particles in the direction opposite of PTmaxT!

PTmaxT > 2 GeV/c

(24)

“ “ Transverse 1” Region Transverse 1” Region vs vs

“Transverse 2” Region

"Transverse 1" vs "Transverse 2"

0.5 1.0 1.5 2.0 2.5 3.0 3.5

0 2 4 6 8 10 12 14

"Transverse 1" Nchg

"Transverse 2" Nchg

CDF Run 2 Preliminary

Charged Particles (|K|<1.0, PT>0.5 GeV/c) 1.96 TeV

Leading Jet 30 < ET(jet#1) < 70 GeV

HW PY Tune A

0.8 1.0 1.2 1.4 1.6 1.8

0 2 4 6 8 10 12 14

"Transverse 1" Nchg

"Transverse 2" <PT> (GeV/c)

1.96 TeV ^{PY Tune A}

HW

0.5 1.0 1.5 2.0 2.5 3.0

0 2 4 6 8 10 12

"Transverse 1" Nchg

"Transverse 2" Nchg

Charged Particles (|K|<1.0, PT>0.5 GeV/c) Back-to-Back

30 < ET(jet#1) < 70 GeV PY Tune A

HW

0.50 0.75 1.00 1.25 1.50

0 2 4 6 8 10 12

"Transverse 1" Nchg

"Transverse 2" <PT> (GeV/c)

Back-to-Back 30 < ET(jet#1) < 70 GeV

PY Tune A

HW

(25)

PYTHIA Tune A vs JIMMY: “Transverse Region”

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

CDF Preliminary

"MAX"

"MIN"

"AVE"

Leading Jet

"Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0 50 100 150 200 250 300 350 400 450 500

PT(jet#1) (GeV/c)

"Transverse" PTsum Density

RDF Preliminary

generator level

Charged Particles (|K|<1.0, PT>0.5 GeV/c) Max Transverse

Min Transverse

Average Transverse 1.96 TeV

PYA = dashed JM = solid

x (left) Run 2 data for charged scalar PTsum density (|K|<1, pT>0.5 GeV/c) in the MAX/MIN/AVE “transverse” region versus P_T(jet#1) compared with PYTHIA Tune A (after CDFSIM).

x (right) Shows the generator level predictions of PYTHIA Tune A (dashed) and JIMMY (P_Tmin=1.8 GeV/c) for charged scalar PTsum density (|K|<1, pT>0.5 GeV/c) in the MAX/MIN/AVE “transverse” region versus P_T(jet#1).

x The tuned JIMMY now agrees with PYTHIA for PT(jet#1) < 100 GeV but produces much more activity than PYTHIA Tune A (and the data?) in the

“transverse” region for P_T(jet#1) > 100 GeV!

(26)

Colour correlations

hp_⊥i(n_ch) is very sensitive to colour flow

p p

long strings to remnants ⇒ much n_ch/interaction ⇒ hp_⊥i(n_ch) ∼ flat

p p

short strings (more central) ⇒ less n_ch/interaction ⇒ hp_⊥i(n_ch) rising

(27)

“ “ Transverse” < Transverse” < p p _T _T > versus > versus

“Transverse”

“Transverse” N N chg chg

Jet #1 Direction 'I

“Toward”

“Away”

Jet #1 Direction 'I

“Toward”

“Away”

Jet #2 Direction

¨ Shows <p_T> versus N^chg in the “transverse” region (p_T > 0.5 GeV/c, |K| < 1) for

“Leading Jet” and “Back-to-Back” events with 30 < E_T(jet#1) < 70 GeV compared with

“min-bias” collisions.

“Leading Jet”

“Back-to-Back”

¨ Look at the <p_T> of particles in the “transverse” region (p_T > 0.5 GeV/c, |K| < 1) versus the number of particles in the “transverse” region: <p_T> vs Nchg.

Min-Bias

"Transverse" Average PT versus Nchg

0.5 1.0 1.5 2.0

0 2 4 6 8 10 12 14 16 18 20 22

Number of Charged Particles

Average PT (GeV/c)

Charged Particles (|K|<1.0, PT>0.5 GeV/c) PYTHIA Tune A 1.96 TeV

Min-Bias

Back-to-Back 30 < ET(jet#1) < 70 GeV

(28)

Energy dependence of p _⊥min and p _⊥0

Larger collision energy

⇒ probe parton (≈ gluon) density at smaller x

⇒ smaller colour screening length d

⇒ larger p_⊥min or p_⊥0

Post-HERA PDF fits steeper at small x

⇒ stronger energy dependence

Current PYTHIA default (Tune A, old model), tied to CTEQ 5L, is

p_⊥min(s) = 2.0 GeV s

(1.8 TeV)²

!_0.08

(29)

paul.szczypka@cern.ch 9

Extrapolation of P _T _min I

P

_{T Min}

= 3.34 ± 0.13 İ = 0.079 ± 0.006

LHC Fitting to:

These values give:

<dN_ch/dȘ>^LHC_Ș=0 = 6.45 ± 0.25

Compared to the phenomenological extrapolation of:

<dN_ch/dȘ>^LHC_Ș=0 = 6.27 ± 0.50

ĺ Compatible

in Single-Diffractive Events

(30)

Run 2 Monte-Carlo Workshop April 20, 2001

DiJet vs

DiJet vs Z Z - - Jet Jet

“Transverse” Nchg

! Comparison of the dijet and the Z-boson data on the average number of charged particles (P_T> 0.5 GeV, |ηηηη| <1) for the “transverse” region.

! The plot shows the QCD Monte-Carlo predictions of PYTHIA 6.115 (default

parameters with P_T(hard)>3 GeV/c)for dijet (dashed) and “Z-jet” (solid) production.

DiJet

Z-boson

PYTHIA

"Transverse" Nchg vs PT(charged jet#1 or Z-boson)

0 1 2 3 4 5

0 5 10 15 20 25 30 35 40 45 50

PT(charged jet#1 or Z-boson) (GeV)

Pythia Z-jet Pythia DiJet CDF Z-boson CDF Min-Bias CDF JET20

<Nchg>

1.8 TeV |eta|<1.0 PT>0.5 GeV

CDF Preliminary

data uncorrected data corrected

Charged Jet #1 Z-bosonor Direction

∆φ

“Toward”

“Away”

(31)

Initiators and Remnants

p

g u s s u d

initiators:

in to hard interaction

beam remnants

Need to assign:

• correlated flavours

• correlated x_i = p_zi/p_ztot

• correlated primordial k_⊥i

• correlated colours

• correlated showers

• PDF after preceding MI/ISR activity:

0) Squeeze range 0 < x < 1 into 0 < x < 1 − ^P x_i (ISR: i 6= i_current) 1) Valence quarks: scale down by number already kicked out

2) Introduce companion quark q/q to each kicked-out sea quark q/q, with x based on assumed g → qq splitting

3) Gluon and other sea: rescale for total momentum conservation

(32)

Beam remnant physics

Colour flow connects hard scattering to beam remnants.

Can have consequences, e.g. in π⁻p

A(x_F) = #D⁻ − #D⁺

#D⁻ + #D⁺

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 A(xF)

x_F Pair production (a)

All channels WA92, 350 GeV WA82, 340 GeV E791, 500 GeV E769, 250 GeV

(also B asymmetries at LHC, but small)

p⁺ π⁻

u u

c c

ud d

If low-mass string e.g.:

cd: D⁻, D^∗−

cud: Λ⁺_c , Σ⁺_c , Σ^∗+_c

⇒ flavour asymmetries

d cs

ssssssssss sssssssssss ssssss sssssssssssssss ssssssssssssssss

sssssssssssss ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

D

Can give D ‘drag’ to larger x_F than c quark for any string mass

(33)

Interleaved Multiple Interactions

interaction number

p_⊥

hard int.

1

mult. int.

2

mult. int.

3

mult int.

4 p_⊥max

p_⊥min p_⊥1

p_⊥2

p_⊥3

p_⊥4 p_⊥23

ISR

ISR p⁰_⊥1

(34)

Competition

“Evolution” equation, only Multiple Interactions:

dP

dp_⊥ = dP_MI

dp_⊥ exp −

Z _p_⊥i−1 p_⊥

dP_MI

dp⁰_⊥ dp⁰_⊥

!

Evolution equation, only Initial State Radiation:

dP

dp_⊥ = dP_ISR

dp_⊥ exp −

Z _p_⊥i−1 p_⊥

dP_ISR

dp⁰_⊥ dp⁰_⊥

!

Evolution equation, MI + ISR, with competition for PDF and phase space:

dP

dp_⊥ = dP_MI

dp_⊥ + ^X dP_ISR dp_⊥

!

exp −

Z _p_⊥i−1 p_⊥

dP_MI

dp⁰_⊥ + ^X dP_ISR dp⁰_⊥

!

dp⁰_⊥

!

with ISR sum running over all previous MI

⇒ one interleaved sequence of MI and ISR

FSR: no competition so not required (but nice for ME merging)

(35)

Other issues

• Regularization procedure:

αs(p²_⊥)dp²_⊥

p²_⊥ → αs(p²_⊥0 + p²_⊥) dp²_⊥ p²_⊥0 + p²_⊥

common for MI (quadratically) and ISR by colour neutralization p_⊥0 ≈ 2–3 GeV energy-dependent

• Intertwined interactions:

hard interactions

Not (yet) explicitly included, but estimated; shown not to be critical

• Where does the baryon number go?

Junction “carries” baryon number!

Motion determined by colour flow attached to it.

Messy hadronization (but handled with model)

q q

q

junction

(36)

Data comparisons

usually comparable with Tune A (for better or worse), but still in need of good tuning and detailed tests, and . . . . . .hp_⊥i(n_ch) problematical (need very short string!)

0.3 0.4 0.5 0.6

50 100 150

n_ch

<p ⊥>

Tevatron Run II: <p_⊥>(n_ch) Tune A

Rap

Sharp ISR Low FSR High FSR

colour correlations not yet understood!

(37)

A. M. Moraes Tunings for min-bias and the UE ATLAS-SW, 18^thFebruary 2004 PARP(67) = 4

MSTP(2) = 1 MSTP(33) = 0 PARP(85) = 0.9 PARP(86) = 0.95 40% of the hadron radius

(PARP(84) = 0.4) PARP(82) = 2.0 PARP(89) = 1.8 TeV

PARP(90) = 0.25 MSTP(81) = 1 MSTP(82) = 4

CTEQ 5L (MSTP(51)=7) Non-diffractive inelastic +

double diffraction (MSEL=0, ISUB 94

and 95)

CDF – Tune A (PYTHIA6.206)

Regulating initial state radiation

sand K-factors Gluon production

mechanism Core radius

pT min

Multiple interactions models

p.d.f.

Generated processes (QCD + low-pT)

Comments

PARP(67) = 1

PARP(67) = 4 PARP(67) = 1

MSTP(2) = 1 MSTP(33) = 0

MSTP(2) = 2 MSTP(33) = 3 MSTP(2) = 1

MSTP(33) = 0

PARP(85) = 0.33 PARP(86) = 0.66

PARP(85) = 0.33 PARP(86) = 0.66 PARP(85) = 0.33

PARP(86) = 0.66

50% of the hadron radius (PARP(84) = 0.5)

20% of the hadron radius (PARP(84) = 0.2) 20% of the hadron radius

(PARP(84) = 0.2)

PARP(82) = 1.8 PARP(89) = 1 TeV

PARP(90) = 0.16

PARP(82) = 1.55 no energy depend.

PARP(82) = 1.9 PARP(89) = 1 TeV

PARP(90) = 0.16

MSTP(81) = 1 MSTP(82) = 4

MSTP(81) = 1 MSTP(82) = 4 MSTP(81) = 1

MSTP(82) = 1

CTEQ 5L (MSTP(51)=7)

CTEQ 2L (MSTP(51)=9) CTEQ 5L

(MSTP(51)=7)

Non-diffractive + double diffraction (MSEL=0, ISUB 94

and 95)

Non-diffractive inelastic (MSEL=1) Non-diffractive inelastic

(MSEL=1)

PYTHIA6.214 - Tuned

ATLAS – TDR (PYTHIA5.7) PYTHIA6.2 -

Default

(38)

5^thNovember 2004 Minimum-bias and the Underlying Event at the LHC

A. M. Moraes

LHC predictions: pp collisions at ¥s = 14 TeV

0 2 4 6 8 10

10² 10³ 10⁴ 10⁵

PYTHIA6.214 - tuned PYTHIA6.214 - default PHOJET1.12

pp interactions-

UA5 and CDF data

dN chg/dȘatȘ=0

¥s (GeV)

•PYTHIAmodels favour ln²(s);

•PHOJETsuggests a ln(s)dependence.

LHC

2 4 6 8 10 12

0 10 20 30 40 50

CDF data

PYTHIA6.214 - tuned

PHOJET1.12 LHC

Tevatron

x1.5 x 3

dN_chg/dȘ ~ 30

dN_chg/dȘ ~ 15

Central Region

(min-bias dN_chg/dȘ ~ 7)

Transverse < N chg>

P_t(leading jet in GeV)

(39)

5^thNovember 2004 Minimum-bias and the Underlying Event at the LHC

A. M. Moraes

LHC predictions: JIMMY4.1 Tunings A and B vs.

PYTHIA6.214 – ATLAS Tuning (DC2)

5 10 15 20

0 10 20 30 40 50

CDF data

JIMMY4.1 - Tuning A JIMMY4.1 - Tuning B

PYTHIA6.214 - ATLAS Tuning

Transverse < N chg>

P_t (leading jet in GeV) Tevatron LHC

x 4

x 5

x 3

(40)

Multiple Interactions Outlook

• Multiple interactions concept compelling; it has to exist at some level. •

? By now, strong direct evidence, overwhelming indirect evidence ?

• Understanding of multiple interactions crucial for LHC precision physics •

• Many details uncertain •

? p_⊥min/p_⊥0 cut-off ?

? impact parameter picture ?

? energy dependence ?

? multiparton densities in incoming hadron ?

? colour correlations between scatterings ?

? interferences between showers ?

? . . .?

• Above physics aspects must all be present, and more? • If a model is simple, it is wrong!

• So stay tuned for even more complicated models in the future. . . . •

sigma (mb)

Monte Carlo Generators for the LHC

Torbj ¨orn Sj ¨ostrand

Event Physics Overview

What is multiple interactions?

So σ

(p

) > σ

for p

∼ 5

GeV

Modelling multiple interactions

Evidence for multiple interactions

• Direct observation: AFS, (UA2,) CDF

• Jet pedestal effect: UA1, H1, CDF

“MAX/MIN Transverse” Densities

“Transverse” Nchg

“Transverse” Nchg versus P

versus P

(chgjet#1) (chgjet#1)

Tuned PYTHIA 6.206 Tuned PYTHIA 6.206

Tuned PYTHIA 6.206 Tuned PYTHIA 6.206

“Transverse” P

“Transverse” P T T Distribution Distribution

Leading Jet: “MAX & MIN Transverse” Densities

“ “ Transverse” Charge Density Transverse” Charge Density

versus E

versus E T T (jet#1) (jet#1)

Back Back - - to to - - Back Back “Associated” “Associated”

Charged Particle Densities Charged Particle Densities

“ “ Associated” Charge Density Associated” Charge Density PYTHIA Tune A

PYTHIA Tune A vs vs HERWIG HERWIG

“ “ Transverse 1” Region Transverse 1” Region vs vs

“Transverse 2” Region

“Transverse 2” Region

PYTHIA Tune A vs JIMMY: “Transverse Region”

Colour correlations

“ “ Transverse” < Transverse” < p p T T > versus > versus

“Transverse”

“Transverse” N N chg chg

Energy dependence of p ⊥min and p ⊥0

Extrapolation of P T _min I

P

= 3.34 ± 0.13 İ = 0.079 ± 0.006

These values give:

Compared to the phenomenological extrapolation of:

ĺ Compatible

DiJet vs

DiJet vs Z Z - - Jet Jet

“Transverse” Nchg

“Transverse” Nchg

Initiators and Remnants

Beam remnant physics

Interleaved Multiple Interactions

Competition

Other issues

Data comparisons

LHC predictions: pp collisions at ¥s = 14 TeV

LHC predictions: JIMMY4.1 Tunings A and B vs.

PYTHIA6.214 – ATLAS Tuning (DC2)

x 4

x 5

x 3

Multiple Interactions Outlook

“Transverse” P _T _T Distribution Distribution

versus E _T _T (jet#1) (jet#1)

“ “ Transverse” < Transverse” < p p _T _T > versus > versus

Energy dependence of p _⊥min and p _⊥0

Extrapolation of P _T _min I