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Nordic LHC Physics Workshop Uppsala, 12 November 2002

LHC Physics

Event Generators

Torbj ¨orn Sj ¨ostrand

Department of Theoretical Physics Lund University

Introduction

Generator Overview Subprocess Survey

Matrix Elements vs. Parton Showers Hadronization

Multiple Interactions Generator Standards How To Run PYTHIA (Beam Remnant Physics)

(QCD Interconnection)

Outlook

(2)

Higgs candidates from ALEPH

m

h

= 112.4 GeV, m

Z

= 93.3 GeV

Made on 29-Aug-2000 17:06:54 by DREVERMANN with DALI_F1.Filename: DC054698_004881_000829_1706.PS_H_CAND

DALI_F1 ECM=206.7 Pch=83.0 Efl=194. Ewi=124. Eha=35.9 BEHOLD Nch=28 EV1=0 EV2=0 EV3=0 ThT=0 00−06−14 2:32 Detb= E3FFFF Run=54698 Evt=4881

ALEPH

End of detector End of tracks

5 Gev EC 5 Gev HC

P>.50 Z0<10 D0<2 F.C. imp.

ROTPC

0

−1cm 1cm X"

0.3cm 0.6cm

Y"

(φ−138)*SIN(θ)

θ=180 θ=0

x

x

x x

x x

x

x

x

x

x

x x

x

x x

x x

o oo

o oo

o

o oo o

o o o

o o

o

o

o o

o o

o o o

oo o

o o

o o

o o

15 GeV

µ

m

h

= 109.8 GeV, m

Z

= 93.2 GeV

Made on 30-Aug-2000 17:24:02 by konstant with DALI_F1.Filename: DC056698_007455_000830_1723.PS

DALI Run=56698 Evt=7455

ALEPH

Z0<5 D0<2

ROTPC

0

−1cm 1cm X"

0 −1cm 1cm

Y"

(φ−175)*SIN(θ)

θ=180 θ=0

x

x x

x

x x

x

x

x

x

x x x x

x

x

x

x

x x

x

x

x

x

x

x −

x x

x ooo

o o

ooo

o o

oo o o

o o

o o o o

o

o o o

o o o

o o o

o o

o

15 GeV 3 Gev EC

6 Gev HC

(3)

'

&

$

%

Distributions of Reconstructed Mass

Sequence: “Loose”, “Medium” and “Tight” selection ()

0 10 20 30 40

0 20 40 60 Reconstructed Mass m80 100 H [GeV/c120 2]

Events / 3 GeV/c2

√s = 200-210 GeV

LEP S/B=0.3 background hZ Signal (mh=115 GeV)

all cnd= 200 bgd= 201.75 sgl= 10.26

> 109 GeV 27 20.41 6.11

0 5 10 15

0 20 40 60 Reconstructed Mass m80 100 H [GeV/c120 2]

Events / 3 GeV/c2

√s = 200-210 GeV

LEP S/B=1.0 background hZ Signal (mh=115 GeV)

all cnd= 59 bgd= 55.26 sgl= 4.66

> 109 GeV 6 3.56 2.94

0 2 4 6 8

0 20 40 60 80 100 120

Reconstructed Mass mH [GeV/c2]

Events / 3 GeV/c2

√s = 200-210 GeV

LEP S/B=2.0 background hZ Signal (mh=115 GeV)

all cnd= 24 bgd= 22.79 sgl= 2.74

> 109 GeV 4 1.13 1.78

()Special selection ... not biasing the mass distribution

P. Igo-Kemenes - LEP Seminar - Nov. 3, 2000 Page 17

'

&

$

%

−2 ln(Q)... REF, DELTA, TOTAL

-10 -5 0 5 10 15 20 25

100 102 104 106 108 110 112 114 116 118 120 mH(GeV/c2)

-2 ln(Q)

Observed

Expected background Expected signal + background

LEP REF

-10 -5 0 5 10 15 20 25

100 102 104 106 108 110 112 114 116 118 120 mH(GeV/c2)

-2 ln(Q)

Observed

Expected background Expected signal + background

LEP DELTA

-10 -5 0 5 10 15 20 25

100 102 104 106 108 110 112 114 116 118 120 mH(GeV/c2)

-2 ln(Q)

Observed

Expected background Expected signal + background

LEP TOTAL

Minimum @mH ≈ 115GeV

Agreement with SM Higgs cross-sect. for

mH = 115.0+1.3−0.9 GeV

P. Igo-Kemenes - LEP Seminar - Nov. 3, 2000 Page 8

(4)

True Theory: L = iψγ

µ

D

µ

ψ −

14

F

µν

F

µν

+ . . .

Applied Theory:

e

e+

Z0 Z0

h0

q q b b

Phenomenology:

Z0

q q primary hadrons g

primaryhadrons andsecondaryproducts

hadronization

Reality:

Event Discussion (4-jet)

Run : even t 13978 : 6299 Da t e 000627 T ime 111338 Ebeam 102 . 70 Ev i s 210 . 0 Emi s s - 4 . 6 V t x ( - . 05 , . 04 , - 1 . 07 ) Bz=4 . 350 Bunch l e t 1 / 1 Th r us t = . 8614 Ap l an= . 0601 Ob l a t = . 1396 Sphe r = . 2098

C t r k (N= 91 Sump=119 . 6 ) Eca l (N=102 SumE=105 . 7 ) Hca l (N=26 SumE= 43 . 0 ) Muon (N= 2 ) Sec V t x (N=11 ) Fde t (N= 0 SumE= . 0 )

Y

X Z

200 . cm.

Cen t r e o f s c r een i s ( . 0000 , . 0000 , . 0000 )

50 GeV 20 10 5

27.June mh= 112.6 GeV B-tag(1) = 0.345 B-tag(2) = 0.960

s= 205.4 GeV

L= 0.999 s/b(105 GeV) = 0.2844 s/b(110 GeV) = 1.1355 s/b(115 GeV) = 0.5234

.Highest weight OPAL candidate

LEPC Seminar 3.November 2000, Results from the OPAL Experiment, Arnulf Quadt Page 8

(5)

Event Generator Position

“real life” “virtual reality”

Machine, interactions

⇒ events

Event Generator

Detector,

Data Acquisition

Detector Simulation

Event

Reconstruction

Physics Analysis produce

events

observe & store events

what is knowable?

compare real and simulated

data

conclusions, articles, talks, . . .

“quick and dirty”

feasibility

studies

(6)

Why Generators?

Allow theoretical and experimental studies of com- plex multiparticle physics

• Large flexibility in physical quantities that can be ad- dressed

• Vehicle of ideology to disseminate ideas from theo- rists to experimentalists

Can be used to

• predict event rates and topologies

⇒ can estimate feasibility

• simulate possible backgrounds

⇒ can devise analysis strategies

• study detector requirements

⇒ can optimize detector/trigger design

• study detector imperfections

⇒ can evaluate acceptance corrections God does not throw dice . . .

. . . but Mother Nature does!

(7)

Which Generators?

Large spectrum, from big to small

“Lund family” and Lund-based

PYTHIA (⇐ JETSET): general-purpose

ARIADNE, LDC: dipole showers (L ¨ onnblad) LEPTO: leptoproduction (Ingelman)

and many more: RAPGAP, SPHINX, . . .

HERWIG: general-purpose (Webber et al.)

ISAJET: pp & general-purpose (Paige et al.)

Specialized: TAUOLA, HDECAY, DTUjet, NLLjet, . . .

Single- or multiprocess parton-level only:

ALPGEN, MadCUP, VECBOS, NJETS, SUSYGEN, KORALZ, PANDORA, . . .

Generators of generators:

CompHEP, GRACE, HELAS, MADGRAPH,

AMEGIC++, O’Mega/WHIZARD, . . .

Many more documented in workshops: LEP 1, LEP 2,

HERA, Tevatron, LHC, . . .

(8)

Event Physics Overview

Structure of the basic generation process:

1) Hard subprocess:

dˆ σ/dˆ t, Breit-Wigners.

2) Resonance decays:

includes correlations.

3) Final-state parton showers:

(or matrix elements).

4) Initial-state parton showers:

(or matrix elements).

5) Multiple

parton–parton interactions.

q

q Z0 Z0

h0

Z0

µ+ µ

h0

W W+

ντ

τ s c

q → qg g → gg g → qq q → qγ

g q

Z0

(9)

6) Beam remnants:

colour-connected to rest of event

7) Hadronization (PYTHIA: string;

HERWIG: cluster;

ISAJET: independent).

8) Normal decays:

hadronic, τ , charm, . . .

p p

b b

ud ud

u u







q g g q

hadrons

ρ+

π0

π+

γ γ

9) QCD interconnection effects:

e e+

W W+

q3 q4

q2 q1





π+

π+ BE

a) colour rearrangement (⇒ rapidity gaps?);

b) Bose-Einstein.

10) The forgotten/unexpected: a chain is

never stronger than its weakest link!

(10)

Subprocess Survey

Process PYT HER ISA

QCD & related

Soft QCD ? ? ?

Hard QCD ? ? ?

Heavy flavour ? ? ?

Electroweak SM

Single γ

/Z

0

/W

±

? ? ? (γ/γ

/Z

0

/W

±

/f/g)

2

? ? ?

Light SM Higgs ? ? ?

Heavy SM Higgs ? ? ?

SUSY BSM

h

0

/H

0

/A

0

/H

±

? ? ?

SUSY ? ? ?

R

/ SUSY ? ? —

Other BSM

Technicolor ? — (?)

New gauge bosons ? — —

Compositeness ? — —

Leptoquarks ? — —

H

±±

(from LR-sym.) ? — —

Extra dimensions (?) (?) (?) User-defined processes

Les Houches accord ? ? —

? = yes, (?) = partial/in progress, — = no

(11)

No. Subprocess Hard QCD processes:

11 fifj→ fifj

12 fifi→ fkfk

13 fifi→ gg 28 fig → fig 53 gg → fkfk

68 gg → gg Soft QCD processes:

91 elastic scattering 92 single diffraction (XB) 93 single diffraction (AX) 94 double diffraction 95 low-pproduction Open heavy flavour:

(also fourth generation) 81 fifi→ QkQk 82 gg → QkQk 83 qifj→ Qkfl

84 gγ → QkQk 85 γγ → FkFk

Closed heavy flavour:

86 gg → J/ψg 87 gg → χ0cg 88 gg → χ1cg 89 gg → χ2cg 104 gg → χ0c

105 gg → χ2c 106 gg → J/ψγ 107 gγ → J/ψg 108 γγ → J/ψγ W/Z production:

1 fifi→ γ/Z0 2 fifj→ W± 22 fifi→ Z0Z0 23 fifj→ Z0W± 25 fifi→ W+W 15 fifi→ gZ0 16 fifj→ gW± 30 fig → fiZ0 31 fig → fkW± 19 fifi→ γZ0 20 fifj→ γW± 35 fiγ → fiZ0 36 fiγ → fkW± 69 γγ → W+W 70 γW±→ Z0W± Prompt photons:

14 fifi→ gγ 18 fifi→ γγ 29 fig → fiγ 114 gg → γγ 115 gg → gγ Deep inelastic scatt.:

10 fifj→ fifj

99 γfi→ fi

Photon-induced:

33 fiγ → fig 34 fiγ → fiγ 54 gγ → fkfk

58 γγ → fkfk

131 fiγT→ fig 132 fiγL→ fig 133 fiγT→ fiγ 134 fiγL→ fiγ 135 T→ fifi

136 L→ fifi

137 γTγT→ fifi

138 γTγL→ fifi

No. Subprocess 139 γLγT→ fifi

140 γLγL→ fifi

80 qiγ → qkπ± Light SM Higgs:

3 fifi→ h0 24 fifi→ Z0h0 26 fifj→ W±h0 102 gg → h0 103 γγ → h0 110 fifi→ γh0 111 fifi→ gh0 112 fig → fih0 113 gg → gh0 121 gg → QkQkh0 122 qiqi→ QkQkh0 123 fifj→ fifjh0 124 fifj→ fkflh0 Heavy SM Higgs:

5 Z0Z0→ h0 8 W+W→ h0 71 Z0LZ0L→ Z0LZ0L

72 Z0LZ0L→ W+LWL 73 Z0LW±L → Z0LW±L

76 WL+WL→ Z0LZ0L 77 WL±W±L → W±LW±L BSM Neutral Higgses:

151 fifi→ H0 152 gg → H0 153 γγ → H0 171 fifi→ Z0H0 172 fifj→ W±H0 173 fifj→ fifjH0 174 fifj→ fkflH0 181 gg → QkQkH0 182 qiqi→ QkQkH0 183 fifi→ gH0 184 fig → fiH0 185 gg → gH0 156 fifi→ A0 157 gg → A0 158 γγ → A0 176 fifi→ Z0A0 177 fifj→ W±A0 178 fifj→ fifjA0 179 fifj→ fkflA0 186 gg → QkQkA0 187 qiqi→ QkQkA0 188 fifi→ gA0 189 fig → fiA0 190 gg → gA0 Charged Higgs:

143 fifj→ H+ 161 fig → fkH+ Higgs pairs:

297 fifj→ H±h0 298 fifj→ H±H0 299 fifi→ A0h0 300 fifi→ A0H0 301 fifi→ H+H Left–right symmetry:

341 `i`j→ H±±L

342 `i`j→ H±±R 343 `±iγ → H±±L e 344 `±iγ → H±±R e 345 `±iγ → H±±L µ 346 `±iγ → H±±R µ 347 `±iγ → H±±L τ 348 `±iγ → H±±R τ 349 fifi→ H++L H−−L 350 fifi→ H++R H−−R 351 fifj→ fkflH±±L 352 fifj→ fkflH±±R 353 fifi→ Z0R

354 fifj→ W±R New gauge bosons:

141 fifi→ γ/Z0/Z00 142 fifj→ W0+

144 fifj→ R

No. Subprocess Technicolor:

149 gg → ηtc

191 fifi→ ρ0tc

192 fifj→ ρ+tc

193 fifi→ ω0tc

194 fifi→ fkfk

195 fifj→ fkfl

361 fifi→ W+LWL

362 fifi→ W±Lπtc

363 fifi→ πtc+πtc

364 fifi→ γπtc0

365 fifi→ γπ00tc

366 fifi→ Z0π0tc

367 fifi→ Z0π00tc

368 fifi→ W±πtc

370 fifj→ W±LZ0L

371 fifj→ W±Lπ0tc

372 fifj→ πtc±Z0L

373 fifj→ πtc±π0tc

374 fifj→ γπtc±

375 fifj→ Z0π±tc

376 fifj→ W±π0tc

377 fifj→ W±π00tc

Compositeness:

146 eγ → e 147 dg → d 148 ug → u 167 qiqj→ dqk

168 qiqj→ uqk

169 qiqi→ e±e∗∓

165 fifi(→ γ/Z0) → fkfk

166 fifj(→ W±) → fkfl

Leptoquarks:

145 qi`j→ LQ

162 qg → `LQ

163 gg → LQLQ

164 qiqi→ LQLQ

SUSY:

201 fifi→ ˜eL˜eL 202 fifi→ ˜eR˜eR 203 fifi→ ˜eL˜eR+ 204 fifi→ ˜µLµ˜L 205 fifi→ ˜µRµ˜R 206 fifi→ ˜µLµ˜R+ 207 fifi→ ˜τ1τ˜1

208 fifi→ ˜τ2τ˜2

209 fifi→ ˜τ1τ˜2+ 210 fifj→ ˜`L˜ν`+ 211 fifj→ ˜τ1ν˜τ+ 212 fifj→ ˜τ2ν˜τ+ 213 fifi→ ˜ν`ν˜`

214 fifi→ ˜ντν˜τ 216 fifi→ ˜χ1χ˜1

217 fifi→ ˜χ2χ˜2

218 fifi→ ˜χ3χ˜3

219 fifi→ ˜χ4χ˜4

220 fifi→ ˜χ1χ˜2

221 fifi→ ˜χ1χ˜3

222 fifi→ ˜χ1χ˜4

223 fifi→ ˜χ2χ˜3

224 fifi→ ˜χ2χ˜4

225 fifi→ ˜χ3χ˜4

226 fifi→ ˜χ±1χ˜1

227 fifi→ ˜χ±2χ˜2

228 fifi→ ˜χ±1χ˜2

No. Subprocess 229 fifj→ ˜χ1χ˜±1 230 fifj→ ˜χ2χ˜±1 231 fifj→ ˜χ3χ˜±1 232 fifj→ ˜χ4χ˜±1

233 fifj→ ˜χ1χ˜±2

234 fifj→ ˜χ2χ˜±2 235 fifj→ ˜χ3χ˜±2

236 fifj→ ˜χ4χ˜±2

237 fifi→ ˜g ˜χ1

238 fifi→ ˜g ˜χ2

239 fifi→ ˜g ˜χ3

240 fifi→ ˜g ˜χ4

241 fifj→ ˜g ˜χ±1

242 fifj→ ˜g ˜χ±2

243 fifi→ ˜g 244 gg → ˜g˜g 246 fig → ˜qiLχ˜1

247 fig → ˜qiRχ˜1

248 fig → ˜qiLχ˜2

249 fig → ˜qiRχ˜2

250 fig → ˜qiLχ˜3

251 fig → ˜qiRχ˜3

252 fig → ˜qiLχ˜4

253 fig → ˜qiRχ˜4

254 fig → ˜qj Lχ˜±1 256 fig → ˜qj Lχ˜±2

258 fig → ˜qiLg˜ 259 fig → ˜qiR˜g 261 fifi→ ˜t1˜t1 262 fifi→ ˜t2˜t2 263 fifi→ ˜t1˜t2+ 264 gg → ˜t1˜t1

265 gg → ˜t2˜t2 271 fifj→ ˜qiL˜qj L

272 fifj→ ˜qiR˜qj R

273 fifj→ ˜qiL˜qj R+ 274 fifj→ ˜qiL˜qj L 275 fifj→ ˜qiR˜qj R 276 fifj→ ˜qiL˜qj R+ 277 fifi→ ˜qj L˜qj L 278 fifi→ ˜qj R˜qj R 279 gg → ˜qiL˜qi L 280 gg → ˜qiRq˜i R 281 bqi→ ˜b1˜qiL

282 bqi→ ˜b2˜qiR

283 bqi→ ˜b1˜qiR+ ˜b2˜qiL

284 bqi→ ˜b1˜qi L 285 bqi→ ˜b2˜qi R 286 bqi→ ˜b1˜qi R+ ˜b2q˜i L 287 qiqi→ ˜b1˜b1

288 qiqi→ ˜b2˜b2

289 gg → ˜b1b˜1

290 gg → ˜b2b˜2

291 bb → ˜b1˜b1

292 bb → ˜b2˜b2

293 bb → ˜b1˜b2

294 bg → ˜b1˜g 295 bg → ˜b2˜g 296 bb → ˜b1˜b2+ Extra dimensions:

391 fifi→ G 392 gg → G 393 qiqi→ gG 394 qig → qiG 395 gg → gG

(12)

Cross sections and kinematics

u (1)

d (4) d (2)

u (3) g

ˆ s = (p

1

+ p

2

)

2

ˆ t = (p

1

− p

3

)

2

ˆ u = (p

1

− p

4

)

2

qq

0

→ qq

0

: dˆ σ

dˆ t = π ˆ s

2

4

9 α

2s

ˆ s

2

+ ˆ u

2

ˆ t

2

p (A)

p (B)

s = (p

A

+ p

B

)

2

x

1

≈ E

1

/E

A

x

2

≈ E

2

/E

B

ˆ s = x

1

x

2

s

σ =

X

i,j

ZZZ

dx

1

dx

2

dˆ t f

i

(x

1

, Q

2

) f

j

(x

2

, Q

2

) dˆ σ

ij

dˆ t

f

i

(x, Q

2

): parton distribution functions at characteristic scale Q

2

≈ p

2

= ˆ tˆ u/ˆ s

luminosity L ∝ N

1

N

2

f A counting rate dN

event

dt = σ L total rate N

event

= σ

Z

L(t) dt

(13)

Higher Order Matrix Elements

O(1)

e e+

q

q

Matrix Elements exact to

given order. . . but blind to higher orders O(α

s

)

e e+

q q

g

O(α

s

L

2

)

O(α

s

)

e e+

q q

L ' − ln y y ' min

m

2ij

Ecm2

O(α

2s

)

e e+

q q

g

g

O(α

2s

L

4

)

O(α

2s

)

e e+

q q

g

collinear and soft emission divergences

⇒ large

higher orders O(α

2s

)

e e+

q q

(14)

From ME’s to Parton Showers

0

1 (q) i

2 (q)

3 (g)

e+e → qqg

0

1 (q) i

2 (q)

3 (g)

x

j

= 2E

j

/E

cm

⇒ x

1

+ x

2

+ x

3

= 2 m

q

= 0 : 1

σ

0

ME

dx

1

dx

2

= α

s

2π 4 3

x

21

+ x

22

(1 − x

1

)(1 − x

2

) rewrite for x

2

→ 1 :

1 − x

2

=

m213

Ecm2

=

Q2

Ecm2

x

1

≈ z

x

3

≈ 1 − z

q

q g

⇒ dP = dσ

σ

0

≈ α

s

dQ

2

Q

2

4 3

1 + z

2

1 − z dz

generalizes to dP

a→bc

= α

s

dQ

2

Q

2

P

a→bc

(z) dz P

q→qg

= 4

3

1 + z

2

1 − z

P

g→gg

= 3 (1 − z(1 − z))

2

z(1 − z) P

g→qq

= n

f

2 (z

2

+ (1 − z)

2

)

(15)

Iteration gives final-state

parton showers

Sudakov form factor

P

corr

(Q

2

) = dP

dQ

2

exp −

Z Q2max Q2

dP

dQ

2

dQ

2

!

(cf. radioactive decay; ‘time’ ordering);

compensated by subsequent branchings

Coherence ⇒ angular ordering +

2

=

2

Loop corrections ⇒ α

s

(p

2

)

Soft/collinear cut-off m

0

= min(m

ij

) ≈ 1 GeV

at hadronic mass scales

(16)

Parton Shower approach

2 → n = (2 → 2) ⊕ ISR ⊕ FSR

q q

Q Q Q

2

2 → 2 Q

22

Q

21

ISR

Q

24

Q

23

FSR

2 → 2 = hard scattering (on-shell) σ =

ZZZ

dx

1

dx

2

dˆ t f

i

(x

1

, Q

2

) f

j

(x

2

, Q

2

) dˆ σ

ij

dˆ t FSR = Final-State Radiation; timelike shower Q

2i

= M

2

> 0 decreasing + coherence

ISR = Initial-State Radiation; spacelike shower

Q

2i

= −M

2

> 0 increasing + ∼ coherence

backwards evolution: start at hard scattering

Do not doublecount! Q

2

> Q

21

, Q

22

, Q

23

, Q

24

2 → 2 = most virtual = shortest distance

(17)

Parton Distribution Functions

Hadrons are composite,

with time-dependent structure:

u d g u p

f

i

(x, Q

2

) = number density of partons i at momen- tum fraction x and probing scale Q

2

F

2

(x, Q

2

) =

X

i

e

2i

xf

i

(x, Q

2

)

structure function parton distributions Resolution dependence by DGLAP:

df

b

(x, Q

2

)

d(ln Q

2

) =

X

a

Z 1 x

dz

z f

a

(x

0

, Q

2

) α

s

2π P

a→bc



z = x x

0



Absolute normalization at small Q

20

unknown:

• first principles: lattice QCD

• reality: data from DIS, pp

(18)

useful pdf plotting facility at

http://durpdg.dur.ac.uk/HEPDATA/

(19)

Initial-state showers

• Parton cascades are continually born, and are subsequently recombined.

• A hard scattering at scale Q

2

probes fluctuations up to that scale.

• The hard scattering inside a fluctuation inhibits full recombination of the cascade.

• Convenient reinterpretation:

m

2

= 0

m

2

< 0

Q

2

= −m

2

> 0

and increasing

m

2

> 0 m

2

= 0

m

2

= 0

Monte Carlo approach: recast df

b

dt =

X

a

Z 1 x

dz

z f

a

(x

0

, Q

2

) α

s

2π P

a→bc

(z) with t = ln(Q

2

2

) and z = x/x

0

to

dP

b

= df

b

f

b

= |dt|

X

a Z

dz x

0

f

a

(x

0

, t) xf

b

(x, t)

α

s

2π P

a→bc

(z) then solve by backwards evolution,

starting at high Q

2

and moving towards lower,

with Sudakov form facter

(20)

Ladder representation combines whole event:

p

p

Q

22

Q

23

Q

2max

Q

21

Q

25

Q

24

DGLAP: Q

2max

> Q

21

> Q

22

∼ Q

20

Q

2max

> Q

23

> Q

24

> Q

25

∼ Q

20

BFKL/CCFM: go beyond Q

2

ordering;

important at small x and Q

2

(Ideal) Monte Carlo order:

1) Hard scattering

2) Initial-state shower from center outwards

3) Final-state shower

(21)

Initial- vs. final-state showers

Both controlled by same evolution equations

dP

a→bc

= α

s

dQ

2

Q

2

P

a→bc

(z) dz · (Sudakov) but

Final-state showers: Q

2

timelike (≈ m

2

) E

0

, m

20

E

1

, m

21

E

2

, m

22

θ

decreasing E decreasing m

2

decreasing θ

daughters on equal footing, both m

2

≥ 0 Q

2

, z, . . . choice gives several algorithms

Initial-state showers: Q

2

spacelike (≈ −m

2

)

E

0

, Q

20

E

1

, Q

21

E

2

, m

22

θ

decreasing E increasing Q

2

increasing θ daughters unequal, one m

2

≥ 0, one m

2

< 0

⇒ kinematics & coherence more complicated + more messy hadronic environment

gives many attempts: BFKL, CCFM, GLR, . . .

References

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