sigma (mb)

(1)

Joint Belgian Dutch German Graduate School Texel, The Netherlands 15 – 26 September 2008

Event Generators

Torbj ¨orn Sj ¨ostrand

Lund University

1. (yesterday) Introduction and Overview; Final-State Parton Showers 2. (yesterday) Initial-State Parton Showers; Matching Issues

3. (today) Multiple Interactions

4. (today) Hadronization; Generator News & Conclusions

(2)

What is minimum bias?

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

σ

_tot

= σ

_elastic

+ σ

single−diffractive

+ σ

double−diffractive

+. . .+σ

non−diffractive

y dn/dy

reality: σ

_min−bias

≈ σ

non−diffractive

+ σ

double−diffractive

≈ 2/3 × σ

_tot

What is underlying event?

y dn/dy

underlying event jet

pedestal height

(3)

What is multiple interactions?

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆ σ/dp

²_⊥

≈ 1/p

⁴_⊥

for p

_⊥

→ 0.

integrate QCD 2 → 2 qq

^′

→ qq

^′

qq → q

^′

q

^′

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

(4)

σ

_int

(p

_⊥min

) =

ZZZ

p_⊥min

dx

₁

dx

₂

dp

²_⊥

f

₁

(x

₁

, p

²_⊥

) f

₂

(x

₂

, p

²_⊥

) dˆ σ

dp

²_⊥

Half a solution to σ

_int

(p

_⊥min

) > σ

_tot

: 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

= hni

ⁿ

n! e

^−hni

but energy–momentum conservation

⇒ large n suppressed

(5)

perturbative QCD not valid at small p

_⊥

since q, g not asymptotic states (confinement!).

Naively breakdown at p

_⊥min

≃ ¯ h

r

p

≈ 0.2 GeV · fm

0.7 fm ≈ 0.3 GeV ≃ Λ

_QCD

. . . but better replace r

p

by (unknown) colour screening length d in hadron

r r

d resolved

r r

d

screened

λ ∼ 1/p

_⊥

(6)

so modify dˆ σ

dp

²_⊥

∝ α

²_s

(p

²_⊥

)

p

⁴_⊥

→ α

²_s

(p

²_⊥

)

p

⁴_⊥

θ (p

_⊥

− p

_⊥min

) (simpler) or → α

²_s

(p

²_⊥0

+ p

²_⊥

)

(p

²_⊥0

+ p

²_⊥

)

²

(more physical)

p

²_⊥

dˆ σ/dp

²_⊥

0 where p

_⊥min

or p

_⊥0

are free parameters, empirically of order 2 GeV

Typically 2 – 3 interactions/event at the Tevatron, 4 – 5 at the LHC, but may be more

in “interesting” high-p

_⊥

ones.

(7)

Basic generation of multiple interactions

• For now exclude diffractive (and elastic) topologies,

i.e. only model nondiffractive events, with σ

_nd

≃ 0.6 × σ

_tot

• Differential probability for interaction at p

_⊥

is dP

dp

_⊥

= 1 σ

_nd

dσ dp

_⊥

• Average number of interactions naively hni = 1

σ

_nd

Z _E_cm_/2 0

dσ

dp

_⊥

dp

_⊥

• Require ≥ 1 interaction in an event

or else pass through without anything happening

P

_≥1

= 1 − P

₀

= 1 − exp(−hni)

(Alternatively: allow soft nonperturbative interactions

even if no perturbative ones.)

(8)

Can pick n from Poissonian and then generate n independent interactions according to dσ/dp

_⊥

(so long as energy left), or better. . .

. . . generate interactions in ordered sequence p

_⊥1

> p

_⊥2

> p

_⊥3

> . . .

• recall “Sudakov” trick used e.g. for parton showers:

if probability for something to happen at “time” t is P (t)

and happenings are uncorrelated in time (Poissonian statistics) then the probability for a first happening after 0 at t

₁

is

P(t

₁

) = P (t

₁

) exp

−

Z _t₁

0

P (t) dt

and for an i’th at t

_i

is

P(t

_i

) = P (t

_i

) exp −

Z _t_i

t_i−1

P (t) dt

!

• Apply to ordered sequence of decreasing p

_⊥

, starting from E

cm

/2 P(p

_⊥

= p

_⊥i

) = 1

σ

_nd

dσ

dp

_⊥

exp

"

−

Z _p

⊥(i−1)

p_⊥

1 σ

_nd

dσ

dp

^′_⊥

dp

^′_⊥

#

• Use rescaled PDF’s taking into account already used momentum

=⇒ n

_int

narrower than Poissonian

(9)

Impact parameter dependence

So far assumed that all collisions have equivalent initial conditions, but hadrons are extended,

e.g. empirical double Gaussian:

ρ

_matter

(r) = N

₁

exp − r

²

r

²₁

!

+ N

₂

exp − r

²

r

²₂

!

where r

₂

6= r

₁

represents “hot spots”, and overlap of hadrons during collision is

O(b) =

Z

d

³

x dt ρ

^boosted_1,matter

( x , t)ρ

^boosted_2,matter

( x , t)

or electromagnetic form factor:

S

p

( b ) =

Z

d

²

k 2π

exp(i k · b ) (1 + k

²

/µ

²

)

²

where µ = 0.71 GeV → free parameter, which gives

O(b) = µ

²

96π (µb)

³

K

₃

(µb)

(10)

1e-05 0.0001 0.001 0.01 0.1 1

0 1 2 3 4 5 6 7 8

O(b)

b

Tune A double Gaussian old double Gaussian Gaussian ExpOfPow(d=1.35) exponential EM form factor

p p

b

b hni

1

all

n ≥ 1

• Events are distributed in impact parameter b

• Average activity at b proportional to O(b)

⋆ central collisions more active ⇒ P

_n

broader than Poissonian

⋆ peripheral passages normally give no collisions at all ⇒ finite σ

_tot

• Also crucial for pedestal effect (more later)

(11)

PYTHIA implementation

(1) Simple scenario (1985):

first model for event properties based on perturbative multiple interactions no longer used (no impact-parameter dependence)

(2) Impact-parameter-dependence (1987):

still in frequent use (Tune A, Tune DWT, ATLAS tune, . . . )

• double Gaussian matter distribution,

• interactions ordered in decreasing p

_⊥

,

• PDF’s rescaled for momentum conservation,

• but no showers for subsequent interactions and simplified flavours (3) Improved handling of PDFs and beam remnants (2004)

• Trace flavour content of remnant, including baryon number (junction)

u u

d

• Study colour (re)arrangement

among outgoing partons (ongoing!)

• Allow radiation for all interactions

(12)

(4) Evolution interleaved with ISR (2004)

• Transverse-momentum-ordered showers dP

dp

_⊥

= dP

_MI

dp

_⊥

+

^X

dP

_ISR

dp

_⊥

!

exp −

Z _p_⊥i−1

p_⊥

dP

_MI

dp

^′_⊥

+

^X

dP

_ISR

dp

^′_⊥

!

dp

^′_⊥

!

with ISR sum over all previous MI

interaction number

p

_⊥

p_⊥max

p_⊥min

hard int.

1

p_⊥1

mult. int.

2

mult. int.

3 p_⊥2

p_⊥3

ISR

p^′_⊥1

(5) Rescattering (in progress)

is 3 → 3 instead of 4 → 4:

(13)

HERWIG implementation

(1) Soft Underlying Event (1988), based on UA5 Monte Carlo

´ H µ C¶ ·N <= < U º Ö QN K FIWV ? KN < F= B R Q IJ S I ;< W Q AM= K

ZX ç ` ì _ ] _ ê a` Yjk i ^` mn flop t Z[ s

[ Z\ w v^] ] q

y

Ü = O ; FI

P = S IJ A Q I ;K M I< F

B IS

N FI AJ < ; Q >K

= M @ AB _ `a

xK

N < F= B < O

= J= B ; F= M N J FIK >B= <= K= ? F= M _ ` a I< B= ; ?: = M

• 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

(2) Jimmy (1995; HERWIG add-on; part of HERWIG++)

• only model of underlying event, not of minimum bias

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

• matter profile by electromagnetic form factor (with tuned size)

• no p

_⊥

-ordering of emissions, no rescaling of PDF:

abrupt stop when (if) run out of energy (3) Ivan (2002, code not public; in progress)

• also handles minimum bias

• soft and hard multiple interactions together fill whole p

_⊥

range

(14)

PhoJet (& relatives) implementation

(1) Cut Pomeron (1982)

• Pomeron predates QCD; nowadays ∼ glueball tower

• Optical theorem relates σ

_total

and σ

_elastic

∝

2 ⇒

• Unified framework of nondiffractive and diffractive interactions

• Purely low-p

_⊥

: only primordial k

_⊥

fluctuations

• Usually simple Gaussian matter distribution (2) Extension to large p

_⊥

(1990)

• distinguish soft and hard Pomerons (cf. Ivan):

soft = nonperturbative, low-p

_⊥

, as above hard = perturbative, “high”-p

_⊥

• hard based on PYTHIA code, with lower cutoff in p

_⊥

(15)

without multiple interactions

(16)

with multiple interactions

(17)

Direct observation of multiple interactions

Four studies: AFS (1987), UA2 (1991), CDF (1993, 1997) 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 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/π for AFS/CDF

AFS 4-jet analysis (pp at 63 GeV): observe 6 times Poissonian prediction, with impact parameter expect 3.7 times Poissonian,

but big errors ⇒ low acceptance, also UA2

(18)

Figure 1: S distribution for 1VTX data (points). The DP component to the data, determined by the two-dataset method to be 52.6% of the sample, is shown as the shaded region (the shape is taken from MIXDP). Also shown is the admixture 52.6% MIXDP + 47.4% PYTHIA, normalized to the data (line).

16

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

PYTHIA showers

σ

_DPS

= σ

_A

σ

_B

σ

_eff

for A 6= B =⇒ σ

_eff

= 14.5 ± 1.7

^+1.7_−2.3

mb

Strong enhancement relative to naive expectations!

(19)

Same study also planned for LHC Selection for DPS delicate balance:

showers dominate at large p

_⊥

⇒ too large background

multiple interactions dominate at small p

_⊥

, but there jet

identification difficult

.

(jet 3) (GeV/c) p

T

10 20 30 40 50

(nb / GeV/c)

T

/dp σ d

^-2

10

-1

1

ISR/FSR off

MI off

Pythia 8.108

+ X @ 14 TeV γ

→ pp

(R = 0.4), CDF selections

k

T

(20)

Jet pedestal effect

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:

“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 x

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”!

(21)

(22)

MC Tools for the LHC CERN July 31, 2003

Rick Field - Florida/CDF Page 28

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

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

"Transverse" Charged Density

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

data uncorrected theory corrected

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

data uncorrected theory corrected

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)).

(23)

Rick Field December 1, 2004

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)

"Transverse" Charge Density CDF Preliminary

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.

(24)

KITP Collider Workshop February 17, 2004

“ “ 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 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 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 2" <PT> (GeV/c)

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

PY Tune A

HW

(25)

Rick Field December 1, 2004

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, p

T

>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

_T

min=1.8 GeV/c) for charged scalar PTsum density (|K|<1, p

_T

>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 P

T

(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)

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, dN^chg/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, dNchg/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.

“Toward”

“Transverse” “Transverse”

“Away”

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

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

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

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

"Transverse"

Region "Transverse"

Region Jet#1

Associated Density PTmaxT > 2 GeV/c

(not included) PTmaxT

Polar Plot

“Back-to-Back”

“associated” density

charge density

0.5

1.0

1.5

2.0

(27)

“ “ 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

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

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

(28)

(29)

(30)

(31)

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

(32)

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

“Transverse”

“Transverse” N N chg chg

“Toward”

“Away”

“Toward”

“Away”

¨

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”

¨

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 N^chg.

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

(33)

(34)

Extrapolation to LHC

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 8 default, tied to CTEQ 5L, is p

_⊥0

(s) = 2.15 GeV s

(1.8 TeV)

²

!_0.08

(35)

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);

•PHOJET suggests 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 < Nchg>

P_t(leading jet in GeV)

(36)

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

(37)

18 PTJIM=4.9

PTJIM=4.9

= 2.8

= 2.8 x (14 / 1.8)x (14 / 1.8)^0.27^0.27

x3

x2.7 LHC

Tevatron

•energy dependent PTJIM •energy dependent PTJIM generates UE predictions generates UE predictions similar to the ones

similar to the ones generated by PYTHIA6.2 generated by PYTHIA6.2 –– ATLAS.

ATLAS.

UE tunings: Pythia vs. Jimmy

(38)

Multiple Interactions Outlook

Issues requiring further thought and study:

• Multi-parton PDF’s f

_a₁_a₂_a₃_···

(x

₁

, Q

²₁

, x

₂

, Q

²₂

, x

₃

, Q

²₃

, . . .)

• Close-packing in initial state, especially small x

• Impact-parameter picture and (x, b) correlations

e.g. large-x partons more central!, valence quarks more central?

• Details of colour-screening mechanism

• Rescattering: one parton scattering several times

• Intertwining: one parton splits in two that scatter separately

• Colour sharing: two FS–IS dipoles become one FS–FS one

• Colour reconnection: required for hp

_⊥

i(n

_charged

)

• Collective effects (e.g. QGP, cf. Hadronization above)

• Relation to diffraction: eikonalization, multi-gap topologies, . . . Action items:

• Vigorous experimental program at LHC

• Study energy dependence: RHIC (pp) → Tevatron → LHC

• Develop new frameworks and refine existing ones

Much work ahead!

(39)

Hadronization/Fragmentation models

Perturbative → nonperturbative =⇒ not calculable from first principles!

Model building = ideology + “cookbook”

Common approaches:

1) String Fragmentation (most ideological)

2) Cluster Fragmentation (simplest?)

3) Independent Fragmentation (most cookbook)

4) Local Parton–Hadron Duality (limited applicability)

Best studied in

e

⁺

e

⁻

→ γ

^∗

/Z

⁰

→ qq

DELPHI Interactive Analysis

Run: 39265 Evt: 4479

Beam: 45.6 GeV Proc: 4-May-1994

DAS : 5-Jul-1993 14:16:48 Scan: 3-Jun-1994

TD TE TS TK TV ST PA

Act

Deact 95 (145)

0 ( 0)

173 (204)

0 ( 20)

0 ( 0)

38 ( 38)

0 ( 42)

0 ( 0)

X Y Z

(40)

The Lund String Model

In QED, field lines go all the way to infinity

+

... ... ... ...

...

.. ...

...

... ...

...

....

...

....

...

....

...

.... ...

...

... ...

...

. ... ... ...

... ...

...

... ...

...

... ...

...

....

...

. ...

...

− +

since photons cannot interact with each other.

Potential is simply additive:

V ( x ) ∝

^X

i

1 | x − x

_i

|

(41)

In QCD, for large charge separation, field lines seem to be compressed to tubelike region(s) ⇒ string(s)

r r

... ... ... ... ... ... ... ...

...

... ... ... ...

... ...

...

... ... ... ... ...

... .... ... ... ...^...^{.... ...}...^{.... ...}.... ..............................................

...... ...... .... .................

...

......

.......

......

...

.... ...

...

............................................

. ...

...

......

.......

...

.............

...

.................

... ... ... ... ... ... ...

...

... ...

...

... ... ... ... ... ... ... ...

by self-interactions among soft gluons in the “vacuum”.

(Non-trivial ground state with quark and gluon “condensates”.

Analogy: vortex lines in type II superconductor) Gives linear confinement with string tension:

F (r) ≈ const = κ ≈ 1 GeV/fm ⇐⇒ V (r) ≈ κr Separation of transverse and longitudinal degrees of freedom

⇒ simple description as 1+1-dimensional object – string –

with Lorentz invariant formalism

(42)

Linear confimenent confirmed e.g. by quenched lattice QCD

String tension

V (r)

r linear part

Coulomb part

total

V (r) ≈ − 4 3

α

_s

r + κr ≈ − 0.13

r + r (for α

_s

≈ 0.5, r in fm and V in GeV)

V (0.4 fm) ≈ 0: Coulomb important for internal structure of hadrons,

not for particle production (?)

(43)

Real world (??, or at least unquenched lattice QCD)

=⇒ nonperturbative string breakings gg . . . → qq V (r)

r quenched QCD

full QCD

Coulomb part

simplified colour representation:

r r

... ... ...

⇓ r r

... ... ...

r r

⇓ r r

. ...

... ... ...

... ... ... ...

r r

... ... ...

(44)

Repeat for large system ⇒ Lund model which neglects Coulomb part:

dE dz

=

dp

_z

dz

=

dE dt

=

dp

_z

dt

= κ

Motion of quarks and antiquarks in a qq system:

z q t

q

gives simple but powerful picture of hadron production

(with extensions to massive quarks, baryons, . . . )

(45)

How does the string break?

q q

^′

q

^′

q

m

_⊥q′

= 0

q q

^′

q

^′

q

d = m

_⊥q

/κ m

_⊥q′

> 0

String breaking modelled by tunneling:

P ∝ exp





− πm

²_⊥q

κ





= exp





− πp

²_⊥q

κ





exp − πm

²_q

κ

!

1) common Gaussian p

_⊥

spectrum

2) suppression of heavy quarks uu : dd : ss : cc ≈ 1 : 1 : 0.3 : 10

⁻¹¹

3) diquark ∼ antiquark ⇒ simple model for baryon production

Hadron composition also depends on spin probabilities, hadronic wave functions, phase space, more complicated baryon production, . . .

⇒ “moderate” predictivity (many parameters!)

(46)

Fragmentation starts in the middle and spreads outwards:

z q t

q m

²_⊥

m

²_⊥

2 1

but breakup vertices causally disconnected

⇒ can proceed in arbitrary order

⇒ left–right symmetry

P(1, 2) = P(1) × P(1 → 2)

= P(2) × P(2 → 1)

⇒ Lund symmetric fragmentation function

f (z) ∝ (1 − z)

^a

exp(−bm

²_⊥

/z)/z

₀

0.5 1 1.5 2 2.5 3

0 0.2 0.4 0.6 0.8 1 f(z), a = 0.5, b= 0.7

m_T² = 0.25 m_T² = 1 m_T² = 4

sigma (mb)

Event Generators

Torbj ¨orn Sj ¨ostrand

Lund University

1. (yesterday) Introduction and Overview; Final-State Parton Showers 2. (yesterday) Initial-State Parton Showers; Matching Issues

3. (today) Multiple Interactions

4. (today) Hadronization; Generator News & Conclusions

What is minimum bias?

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

σ

= σ

+ σ

+ σ

+. . .+σ

y dn/dy

reality: σ

≈ σ

+ σ

≈ 2/3 × σ

What is underlying event?

y dn/dy

underlying event jet

pedestal height

What is multiple interactions?

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆ σ/dp

≈ 1/p

for p

→ 0.

integrate QCD 2 → 2 qq

→ qq

qq → q

q

qq → gg qg → qg gg → gg gg → qq

with CTEQ 5L PDF’s

σ

(p

) =

dx

dx

dp

f

(x

, p

) f

(x

, p

) dˆ σ

dp

Half a solution to σ

(p

) > σ

: many interactions per event

σ

=

σ

σ

=

n σ

σ

> σ

⇐⇒ hni > 1

n P

hni = 2

0 1 2 3 4 5 6 7

If interactions occur independently then Poissonian statistics

P

= hni

n! e

but energy–momentum conservation

⇒ large n suppressed

Other half of solution:

perturbative QCD not valid at small p

since q, g not asymptotic states (confinement!).

Naively breakdown at p

≃ ¯ h

r

≈ 0.2 GeV · fm

0.7 fm ≈ 0.3 GeV ≃ Λ

. . . but better replace r

by (unknown) colour screening length d in hadron