QCD and Weak Boson Physics workshopFermilab 4–6 March 1999

RecentProgress

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PYTHIA

lh hh

Torbjorn SjostrandLund University

Introductioncurrent Subprocesses

W p⊥ spectrumCharm & bottom asymmetriesMultiple interactions

future Interconnection effectsImproved parton showersMatching to matrix elementsOn to C++!

Introduction

JETSET 7.4PYTHIA 5.7SPYTHIA

4 March 1997 : PYTHIA 6.1

General-purpose generator:

• Hard subprocess “library”

• Convolution with parton distributions(cross sections, kinematics)

• Resonance decays (process-dependent)

• Initial-state QCD (& QED) showers

• Final-state QCD & QED showers

• Multiple parton–parton interactions

• Beam remnants

• Hadronization (string fragmentation)

• Decay chains

• Analysis & utility routines

Currently PYTHIA 6.125 of 21 February 1999∼ 46.800 lines Fortran 77

Code, manuals, sample main programs:http://www.thep.lu.se/∼torbjorn/Pythia.html

PYTHIA 6.1 main news

• JETSET routines renamed:LUxxxx → PYxxxx + some more

• All real variables in DOUBLE PRECISION

• New SUSY processes and improved SUSY simu-lation; new PDG codes for sparticles

• New processes for Higgs, technicolour, . . .

• Alternative Higgs mass shape

• Newer parton distributions (but . . . )

• Several improved resonance decays

• Initial-state showers matched to (some) matrix el-ements

• QED radiation off an incoming muon

• New machinery to handle real and virtual photonfluxes and cross sections

• Energy-dependent p⊥min in multiple interactions

• Colour rearrangement options for W+W−

• Expanded Bose-Einstein algorithm

• New baryon production scheme (optional)

• One-dimensional histograms (GBOOK)

Subprocesses (1)

No. SubprocessW/Z production:

1 fif i → γ∗/Z0

2 fifj → W±

22 fif i → Z0Z0

23 fifj → Z0W±

25 fif i → W+W−

15 fif i → gZ0

16 fifj → gW±

30 fig → fiZ0

31 fig → fkW±

19 fif i → γZ0

20 fifj → γW±

35 fiγ → fiZ0

36 fiγ → fkW±

69 γγ → W+W−

70 γW± → Z0W±

Hard QCD processes:11 fifj → fifj12 fif i → fkfk13 fif i → gg28 fig → fig

53 gg → fkfk68 gg → gg

Soft QCD processes:91 elastic scattering92 single diffraction (XB)93 single diffraction (AX)94 double diffraction95 low-p⊥ production

Open heavy flavour:(also fourth generation)81 fif i → QkQk

82 gg → QkQk83 qifj → Qkfl84 gγ → QkQk

85 γγ → FkFk

No. SubprocessClosed heavy flavour:

86 gg → J/ψg87 gg → χ0cg88 gg → χ1cg89 gg → χ2cg

104 gg → χ0c

105 gg → χ2c

106 gg → J/ψγ107 gγ → J/ψg108 γγ → J/ψγ

Prompt-photonproduction:

14 fif i → gγ18 fif i → γγ29 fig → fiγ

114 gg → γγ115 gg → gγ

Deep inelastic scattering10 fifj → fifj

Photon-inducedprocesses:

33 fiγ → fig34 fiγ → fiγ54 gγ → fkfk58 γγ → fkfk80 qiγ → qkπ

±

131 fiγ∗T → fig132 fiγ∗L → fig133 fiγ∗T → fiγ134 fiγ∗L → fiγ

135 gγ∗T → fif i136 gγ∗L → fif i137 γ∗Tγ

∗T → fif i

138 γ∗Tγ∗L → fif i

139 γ∗Lγ∗T → fif i

140 γ∗Lγ∗L → fif i

Subprocesses (2)No. SubprocessLight SM Higgs:

3 fif i → h0

24 fif i → Z0h0

26 fifj → W±h0

102 gg → h0

103 γγ → h0

110 fif i → γh0

121 gg → QkQkh0

122 qiqi → QkQkh0

123 fifj → fifjh0

124 fifj → fkflh0

Heavy SM Higgs:5 Z0Z0 → H0

8 W+W− → H0

71 Z0LZ

0L → Z0

LZ0L

72 Z0LZ

0L → W+

L W−L

73 Z0LW

±L → Z0

LW±L

76 W+L W−

L → Z0LZ

0L

77 W±LW±

L → W±LW±

L

BSM Neutral Higgses:151 fif i → H0

152 gg → H0

153 γγ → H0

171 fif i → Z0H0

172 fifj → W±H0

173 fifj → fifjH0

174 fifj → fkflH0

181 gg → QkQkH0

182 qiqi → QkQkH0

156 fif i → A0

157 gg → A0

158 γγ → A0

176 fif i → Z0A0

177 fifj → W±A0

178 fifj → fifjA0

179 fifj → fkflA0

186 gg → QkQkA0

187 qiqi → QkQkA0

No. SubprocessCharged Higgs:143 fifj → H+

161 fig → fkH+

Higgs pairs:297 fifj → H±h0

298 fifj → H±H0

299 fif i → A0h0

300 fif i → A0H0

301 fif i → H+H−

Doubly-charged Higgs:341 `i`j → H±±

L342 `i`j → H±±

R343 `±i γ → H±±

L e∓

344 `±i γ → H±±R e∓

345 `±i γ → H±±L µ∓

346 `±i γ → H±±R µ∓

347 `±i γ → H±±L τ∓

348 `±i γ → H±±R τ∓

349 fif i → H++L H−−

L

350 fif i → H++R H−−

R351 fifj → fkflH

±±L

352 fifj → fkflH±±R

Subprocesses (3)No. SubprocessTechnicolour:149 gg → ηtechni

191 fif i → ρ0techni

192 fifj → ρ+techni

193 fif i → ω0techni

194 fif i(→ ρ0techni/ω0techni)

→ fkfkNew gauge bosons:141 fif i → γ/Z0/Z′0

142 fifj → W′+

144 fifj → R

Compositeness:147 dg → d∗

148 ug → u∗

167 qiqj → d∗qk168 qiqj → u∗qk165 fif i(→ γ∗/Z0) → fkfk166 fifj(→ W±) → fkf lLeptoquarks:145 qi`j → LQ162 qg → `LQ

163 gg → LQLQ

164 qiqi → LQLQ

No. SubprocessSUSY:201 fif i → eLe

∗L

202 fif i → eRe∗R

203 fif i → eLe∗R + e∗

LeR204 fif i → µLµ

∗L

205 fif i → µRµ∗R

206 fif i → µLµ∗R + µ∗

LµR207 fif i → τ1τ∗1208 fif i → τ2τ∗2209 fif i → τ1τ∗2 + τ∗1 τ2210 fifj → ˜Lν

∗` + ˜∗

Lν`211 fifj → τ1ν∗τ + τ∗1 ντ212 fifj → τ2ντ ∗ + τ∗2ντ213 fif i → ν`ν`

∗

214 fif i → ντ ν∗τ216 fif i → χ1χ1

217 fif i → χ2χ2

218 fif i → χ3χ3

219 fif i → χ4χ4

220 fif i → χ1χ2

221 fif i → χ1χ3

222 fif i → χ1χ4

223 fif i → χ2χ3

224 fif i → χ2χ4

225 fif i → χ3χ4

226 fif i → χ±1 χ

∓1

227 fif i → χ±2 χ

∓2

228 fif i → χ±1 χ

∓2

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

Subprocesses (4)

No. SubprocessSUSY:237 fif i → gχ1

238 fif i → gχ2

239 fif i → gχ3

240 fif i → gχ4

241 fifj → gχ±1

242 fifj → gχ±2

243 fif i → gg244 gg → gg246 fig → qiLχ1

247 fig → qiRχ1

248 fig → qiLχ2

249 fig → qiRχ2

250 fig → qiLχ3

251 fig → qiRχ3

252 fig → qiLχ4

253 fig → qiRχ4

254 fig → qjLχ±1

256 fig → qjLχ±2

258 fig → qiLg259 fig → qiRg

261 fif i → t1t∗1

262 fif i → t2t∗2

263 fif i → t1t∗2 + t∗1t2

264 gg → t1t∗1

265 gg → t2t∗2

271 fifj → qiLqjL272 fifj → qiRqjR273 fifj → qiLqjR + qiRqjL274 fifj → qiLq

∗jL

275 fifj → qiRq∗jR

276 fifj → qiLq∗jR + qiRq

∗jL

277 fif i → qjLq∗jL

278 fif i → qjRq∗jR

279 gg → qiLq∗i L

280 gg → qiRq∗i R

No. SubprocessSUSY:281 bqi → b1qiL282 bqi → b2qiR283 bqi → b1qiR+

b2qiL284 bqi → b1q∗

i L

285 bqi → b2q∗i R

286 bqi → b1q∗i R+

b2q∗i L

287 qiqi → b1b∗1

288 qiqi → b2b∗2

289 gg → b1b∗1

290 gg → b2b∗2

291 bb → b1b1

292 bb → b2b2

293 bb → b1b2

294 bg → b1g295 bg → b2g

296 bb → b1b∗2+

b2b∗1

W p⊥ spectrum

(G. Miu & TS, hep-ph/9812455 → PLB)

Alternative descriptions:

1. Order-by-order matrix elements (ME)+ systematic expansion in αs

+ powerful for multiparton Born level– loop calculations tough– messy cancellations (jet substructure)

2. Resummed matrix elements+ good p⊥W predictivity– no exclusive accompanying event

3. Parton showers (PS)– only leading logs (and some NLL)– approximate exclusive multijet rates± process-independent+ event classes smoothly blend

(Sudakovs, physical collinear regions)+ natural match to hadronization

Merging strategy: correct hardest emissions in show-ers so as to reproduce one order higher matrix ele-ments

2 → 1 process q(1) + q′(2) → W(0) starting pointfor backwards shower evolution:

34

15

6

20

2 → 2 process q(3) + q′(2) → g(4) + W(0):

s = (p3 + p2)2 =

(p1 + p2)2

z=m2

W

zt = (p3 − p4)

2 = p21 = −Q2

u = m2W − s− t = Q2 − 1 − z

zm2

W

Relate ME and PS rates:

dσ

dt

∣∣∣∣ME

=σ0s

αs

2π

4

3

t2 + u2 + 2m2Ws

tu

Q2→0−→ σ0αs

2π

4

3

1 + z2

1 − z

1

Q2=

dσ

dQ2

∣∣∣∣∣PS1

dσ

dt

∣∣∣∣PS1

=σ0s

αs

2π

4

3

s2 +m4W

t(t+ u)

Add mirror q(1) + q′(5) → g(6) + W(0):

dσ

dt

∣∣∣∣PS

=dσ

dt

∣∣∣∣PS1

+dσ

dt

∣∣∣∣PS2

=σ0s

αs

2π

4

3

s2 +m4W

tu

Rqq′→gW(s, t) =(dσ/dt)ME

(dσ/dt)PS=t2 + u2 + 2m2

Ws

s2 +m4W

1

2< Rqq′→gW(s, t) ≤ 1

Similarly for q(1) + g(5) → q′(6) + W(0):

dσ

dt

∣∣∣∣ME

=σ0s

αs

2π

1

2

s2 + u2 + 2m2Wt

−suQ2→0−→ σ0

αs

2π

1

2(z2 + (1 − z)2)

1

Q2=

dσ

dQ2

∣∣∣∣∣PS

dσ

dt

∣∣∣∣PS

=σ0s

αs

2π

1

2

s2 + 2m2W(t+ u)

−su

Rqg→q′W(s, t) =(dσ/dt)ME

(dσ/dt)PS=

s2 + u2 + 2m2Wt

(s−m2W)2 +m4

W

1 ≤ Rqg→q′W(s, t) ≤√

5 − 1

2(√

5 − 2)< 3

(?) Larger Rqg than Rqq′

since PS misses s-channelgraph of ME:“resonance decay”,“final-state radiation”

q

gq

q′

W

Improve PS:

• Q2max = s, not Q2

max ≈ m2W (intermediate)

• MC correction by R(s, t) for first (≈ hardest)emission on each side (new)

Toy simulation at 1.8 TeV:

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 50 100 150 200 250 300 350

dσ

/dp

W(n

b/G

eV)

pW (GeV)

PS oldPS intermediate

PS newME

qq′ → gW

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 50 100 150 200 250 300 350

dσ

/dp

W(n

b/G

eV)

pW (GeV)

PS oldPS intermediate

PS newME

qg → q′W

1

10

100

1000

10000

100000

1e+06

0.5 1 1.5 2 2.5 3

dN

/dR

(s,t)

R(s,t)

PS similar to qq’->gWPS similar to qg->q’W

dN/dR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250 300 350

R(s

,t)

pW (GeV)

PS similar to qq’->gWPS similar to qg->q’W

〈R〉(p⊥W)

Complete simulation at 1.8 TeV:

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 10 20 30 40 50 60 70 80 90 100 110

(1/ N

)(d

N/d

pW

)(G

eV-1)

p W (GeV)

PS,k =0.44 GeVPS,k =4 GeV

D0 data

Primordial k⊥ reduced in shower: input 4 GeV gives√〈p2⊥W〉 = 2.1 GeV.

Large value in line with resummation descriptions,prompt photons, charm, . . .Solved by better understanding of soft part of show-ers: BFKL, CCFM, . . . ?

In summary:• economical (complete events)• promising (cf. data)• extensible (same for all colourless vector gauge

bosons: γ∗, Z0, Z′0, W′±, . . . )

Charm & bottom asymmetries(E. Norrbin & TS, PLB442 (1998) 407)

Sizeable D/D asymmetries observed in π−p, in dis-agreement with perturbative c/c predictions.

A = A(xF, p⊥) =σ(D−) − σ(D+)

σ(D−) + σ(D+)

Asymmetry in xF and p⊥, new model:

−0.5 0 0.5 1−1

−0.5

0

0.5

1

(a)X WA82@340 GeV

+ E769@250 GeV

o E791@500 GeV

xF

A(x

F)

0 2 4 6 8 10−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5 (b)

o E791@500 GeV

pt2

A(p

t2 )

xF spectra of D− and D+, old and new model:

0 0.2 0.4 0.6 0.8 110

0

101

102

103

104

(c) D+

xF

dN/d

x F (

arbi

trar

y un

its)

0 0.2 0.4 0.6 0.8 110

0

101

102

103

104

(d) D−

xF

dN/d

x F (

arbi

trar

y un

its)

PYTHIA predicted qualitative behaviour.Quantitative one sensitive to details⇒ develop model & tune (6= E791)

Three hadronization mechanisms (regions):1. Normal string fragmentation:

continuum of phase-space states.2. Cluster decay:

low mass ⇒ exclusive two-body state.3. Cluster collapse:

very low mass ⇒ only one hadron.

p+

π−

u

u

c

c

ud

d

�

�

�

�If collapse:cd: D−, D∗−, . . .cud: Λ+

c , Σ+c , Σ∗+

c , . . .⇒ flavour asymmetries

Can give D “drag” to larger xF than c quark.

Buildup of D− and D+ xF distributions:

−0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

xF

dN/d

x F

(i) (ii)

(iii) (iv)

(v)

−0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

xF

dN/d

x F

(iii) (iv)

(v)

But also normal string fragmentation:

c d z

p± = E ± pz

p−D = zp−c 0 < z < 1

⇒ p+D =m2

⊥D

p−D=m2

⊥D

zp−c

normally>

m2⊥c

zp−c=p+c

z

i.e. again drag.

Technical components of modelling:• Charm mass: c cross section (mc = 1.5)• Light-quark masses: threshold for cluster mass

spectrum, together with mc

(mu = md = 0.33, ms = 0.50)• Beam remnant distribution function:

(p − g = ud0 + u in colour octet state) hadronasymmetries also without collapse(uneven sharing, but not extremely so)

• Primordial k⊥: collapse rate at large p⊥(Gaussian width 1 GeV)

• Threshold behaviour for non-collapse:all at Dπ or gradually at Dπ, D∗π, Dρ, . . .(intermediate)

• Collapse energy–momentum conservation:practical solution to mass δ function(several models tried; not very sensitive)

Inclusive rapidity distribution:

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-8 -6 -4 -2 0 2 4 6 8

(1/N

)dN

/dy

y

Bottom

Charm

Bottom hadronsBottom quarksCharm hadronsCharm quarks

Pair rapidity separation:

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6

(1/N

)dN

/dy ∆

y∆=|yquark - yantiquark|

b-hadrons

c-hadrons

b-hadronsb-quarks

c-hadronsc-quarks

Average hadronization rapidity shift:

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-4 -2 0 2 4

<∆y

>=

<y H

adro

n -

y Qua

rk>

y

BottomCharm

1.8 TeV pp. So far: qq,gg → QQ only

Asymmetry (B0 − B0)/(B0 + B0):

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

xF

Asymmetry (B0s − B0

s )/(B0s + B0

s ):

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

xF

Asymmetry (D+ − D−)/(D+ + D−):

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

xF

Note: horizontal scale xF, not y

Multiple interactions

(TS & M. van Zijl, PRD36 (1987) 2019)

Consequence ofcomposite natureof hadrons:

Evidence:

• direct observation: AFS, UA1, CDF

• implied by width of multiplicity distribution+ jet universality: UA5

• forward–backward correlations: UA5

• pedestal effect: UA1, H1

One free parameter: p⊥min

1

2σjet =

∫ s/4p2⊥min

dσ

dp2⊥dp2⊥

⇐∫ s/40

dσ

dp2⊥

p4⊥(p2⊥0 + p2⊥)2

dp2⊥

Measure of colour screening length d in hadronp⊥min 〈d〉 ≈ 1(= h)

r r

d

resolved

r r

d

screenedλ ∼ 1/p⊥

〈d〉 ∼ rp√Npartons

no correlations

∼ rp

Npartonswith correlations?

Npartons ∼ Ng =

∫ 1

∼4p2⊥min/sg(x,∼ p2⊥min) dx

Olden days:

xg(x,Q20) → const. for x→ 0

⇒ Npartons ∼ lns

4p2⊥min

∼ const.

Post-HERA:

xg(x,Q20) ∼ x−ε for x→ 0, ε >∼0.08

⇒ Npartons ∼(

s

4p2⊥min

)ε

⇒ p⊥min ∼ 1

〈d〉∼ Npartons ∼ sε

Mean charged multiplicity in inelasticnon-diffractive “minimum bias”:

New PYTHIA default:

p⊥min = (1.9 GeV)

(s

1 TeV2

)0.08

Importance:• comparison of data at 630 GeV & 1.8 TeV• extrapolations to LHC

Interconnection effects(V.A. Khoze & TS, ZPC62 (1994) 281,PLB328 (1994) 466, EPJC6 (1999) 271;L. Lonnblad & TS, EPJC2 (1998) 165)

ΓW,ΓZ,Γt ≈ 2 GeVΓh > 1.5 GeV for mh > 200 GeVΓSUSY ∼ GeV (often)

τ =1

Γ≈ 0.2GeV fm

2GeV= 0.1 fm � rhad ≈ 1 fm

⇒ hadronic decay systems overlap, between pairs ofresonances & with underlying events⇒ cannot be considered separate systems!

Three main eras for interconnection:

1. Perturbative: suppressed for ω > Γ by propaga-tors/timescales ⇒ only soft gluons.

2. Nonperturbative, hadronization process:colour rearrangement.

B0

d

bc

W− c

s

�

�

�

�

B0

d

b

c

W−c

sg

�

�

K0S

�

�

J/ψ

3. Nonperturbative, hadronic phase:Bose–Einstein.

Above topics among unsolved problems of strong in-teractions: confinement dynamics, 1/N2

C effects, QMinterferences, . . . :

• opportunity to study dynamics of unstable parti-cles,

• opportunity to study QCD in new ways, but

• risk to limit/spoil precision mass measurements.

So far mainly studied for mW at LEP2:

1. Perturbative: 〈δmW〉 <∼5 MeV.

2. Colour rearrangement: many models, in general〈δmW〉 <∼40 MeV.

e−

e+

W−

W+

q3

q4

q2

q1

�

�

π+

π+

�

� BE

3. Bose-Einstein: symmetrization of unknown am-plitude, wider spread 0–100 MeV among models,but realistically 〈δmW〉 <∼40 MeV.

In sum: 〈δmW〉tot < mπ, 〈δmW〉tot/mW<∼0.1%; a

small number that becomes of interest only becausewe aim for high accuracy.

Connectometry – diagnosing interconnections:

Threshold: low-momentum particles depleted

realistic models unrealistic ones

∼ 4σ (∼ 2σ) signal/experiment if 500 pb−1 at 172(195) GeV. LEP1 Z0 gives ‘Z0Z0 no-reconnection’reference. Few alternatives.Much above threshold: few but interesting intercon-nection events; enhanced particle rate.

BE: getting close, e.g.

C∗2(Q) =

N±±WW→4j(Q) − 2N±±

WW→2j`ν(Q)

N+−WW→4j(Q) − 2N+−

WW→2j`ν(Q)

0.5

1

1.5

0 0.5 1 1.5 2

C2*

Q (GeV)

DELPHI dataBE0BE3

BE32

0.5

1

1.5

0 0.5 1 1.5 2

C2*

Q (GeV)

DELPHI dataBE0BEλBEm

Top near threshold:e+e− → tt → bW+bW− → bb`+ν``

′−ν′`.

Hadronic multiplicity as function of θbb

:

cos θparton

〈nch〉

cos θcluster

〈nch(|p| < 1 GeV)〉

Curves: various scenarios for QCD radiation from tb,tb and bb colour dipoles, realistically

I ∝ ω2

Γ2t + ω2

(tb + tb

)+

Γ2t

Γ2t + ω2

bb

Unrealistic: 〈δmt〉 = 100 − 500 MeV.Realistic: 〈δmt〉 ≈ 30 MeV.(W. Beenakker et al., hep-ph/9902304:) 〈δmt〉 <∼100 MeV.

Interconnection outlook for hadron colliders:• ‘trivial’ to exend from W+W− to any pair of res-

onances;• more bookkeeping for ‘triplets’ like

tt → bbq1q2q3q4;• extension to pp underlying event requires further

thought.Wild guess: 〈δmt〉 ∼ 200 MeV.

Soft colour interactions and the Pomeron:(A. Edin, G. Ingelman & J. Rathsman, ZPC75 (1997) 57;PRD56 (1997) 7317)

Can generate rapidity gaps in ep:

Can produce J/ψ (Υ) from g → cc (g → bb):

0 10 20p⊥ [GeV]

Improved parton showers(B. Andersson, G. Gustafson, H. Kharraziha & L. Lonnblad,ZPC71 (1996) 613, JHEP9803 (1998) 006)

CCFM (Ciafaloni; Catani, Fiorani, Marchesini) is thebest tool we have to describe perturbative final stateproperties of (small and large x) DIS.

The ladders to be summed over are chosen by requir-ing the rungs (initial-state emissions) to have increas-ing angles of emission.

Each emission gets an extra weight — the non-Sudakov form factor — making it difficult and inef-ficient (but not impossible: SMALLX) to implementCCFM in an event generator.

But we can choose other ladders to sum over, e.g. an-other separation between initial- and final-state emis-sions:

≈ “+”

pk0

q1k1

q2k2

qnγ∗

e

+ zi ≡ k+i /k+i−1

zi assumed small

k2i⊥ =∣∣∣∑j≤i ~qj⊥

∣∣∣2

Angular (rapidity) ordering in the CCFM:

k2i⊥ > ziq2i⊥

(less infrared sensitive than BFKL)

Each rung in ladder contributes with weight

dWi =α

π

dzizi

d2qi⊥q2i⊥

∆CCFMNS (zi, k

2i⊥, q

2i⊥)

∆NS(zi, k2i⊥, q

2i⊥) = exp

(−α ln

1

ziln

k2i⊥ziq

2i⊥

)

α =3αs

2π

The Linked Dipole Chain (LDC) model is CCFM, butwith more emission put in final-state. Everything thatis allowed as dipole radiation from the colour dipolesspanned by the partons emitted in the initial state (withq2⊥fs < k2i⊥) is moved to the final state. Thusq2i⊥ > min(k2i⊥, k

2i−1⊥))

We must modify ∆NS to include the sum of all emis-sions moved to the final state: ∆LDC

NS ≡ 1

3

q3

kn

2q

y

κ

1qk1

k2

q2

q’2

k’

Each rung in ladder contributes with weight

dWi =α

π

dzizi

d2qi⊥q2i⊥

Integrating over azimuthal angle and changing vari-ables:

dWi ≈ αdzizi

dk2i⊥k2i⊥

min(1,k2i⊥k2i−1⊥

)

Final-state properties

dE⊥dη , small x, small Q2:

0

1

2

-5 -2.5 0 2.5 5

dEt/d

η (G

eV)

η

LDC AAriadne

LeptoLepto SCI

γ∗p

dE⊥dη , medium x, medium Q2:

0

1

2

-5 -2.5 0 2.5 5

dEt/d

η (G

eV)

η

LDC AAriadne

LeptoLepto SCI

Improvements under way.

1Nev

dnchdk⊥

, 0.5 < η < 1.5:

0.001

0.01

0.1

1

0 2 4 6

1/N

dn/

dkt

kt (GeV)

LDC AAriadne

LeptoLepto SCI

1Nev

dnchdη , k⊥ch < 1 GeV:

0

0.1

0.2

0.3

-2 0 2 4

1/N

dn/

dη

η

LDC AAriadne

LeptoLepto SCI

Limitations:

• need matching fj(x0, k2⊥0)

• quark ladders problematical (not part of CCFM)• so far not extended to pp/pp

Other CCFM implementations:

RAPGAP (H. Jung)Implements CCFM in backwards evolution (wasthought to be impossible), and is fast!Starts with γ∗g∗ → qq and evolves the incoming vir-tual photon backwards using splitting functions, non-Sudakov form factors, and evolved unintegrated gluondensities∫ µo

d2k⊥Fg(x, k⊥) = xg(x, µ2)

(from SMALLX).Includes kinematical cuts (to avoid random walk ink⊥).Results comparable with LDC.

Milano CCFM generator (G. Salam)Capable of generating semi-inclusive observables ac-cording to CCFM.Target activity at small x again problem.

SMALLX (B.R. Webber, G. Marchesini, . . . )Original forward evolution program, now improved toinclude hadronization.Not yet compared with data.

Much activity, but still disappointing.Best hope to solve “primordial k⊥ problem”?Stay tuned!

Matching to matrix elements

Parton shower (PS) matching to matrix elements (ME)ever more needed for

• correct evaluation of complicated signals andbackgrounds (usually multiparton LO), and

• precision measurements (fewer partons butNLO).

Work for the years ahead. No unique solution, butsome recurring themes:

1) Is all of phase space covered by PS emissions?

HERWIG: strict angular ordering (proven only for softemission) ⇒ dead zones.Solution: split phase space; use higher order ME’s topopulate dead zones.Examples: Z0/W± → 3 jets, top decay t → bW (G.

Corcella & M.H. Seymour, hep-ph/9809451).

PYTHIA: evolution in virtuality with angular orderingveto (more primitive!) ⇒ easy to open up all of phasespace and include ME correction factors.Examples: Z0/W± → 3 jets, W p⊥.

2) How start a shower from an arbitrary multipartonconfiguration?

HERWIG:(i) pick one colour configuration, e.g. weighted to-wards small masses along colour flow;(ii) evolve each parton separately, inside a cone de-fined by its colour partner;(iii) solve energy–momentum conservation.Status: existing (VECBOS: M. Mangano et al.).

PYTHIA:(i) enumerate all possible shower histories leading upto the given ME parton configuration;

1

2

3= or

(ii) evaluate weight for each history from propagatorsand splitting kernels (and pdf’s)Wi = (1/m2

i3)Pq→qg(z ≈ Ei/(Ei +E3)), i = 1,2

and pick one history according to weights;(iii) let this particular shower evolve further.Status: only e+e− → 4 jets so far (J. Andre & TS, PRD57

(1998) 5767).Request: Must know parton flavours!

3) How to include information on NLO loop correc-tions?

Key problem: nasty collinear cancellations; negativeprobabilities.

If σtot independent of jet clustering then strategy likeW p⊥.

Sketch of more general solution:(i) keep wide jet ‘cones’ so weights are always clearlypositive (negative weights ⇒ large Sudakovs ⇒shower better!);(ii) obtain cross sections inside cones by combininganalytical approximations with a Monte Carlo estimateof the difference between exact and approximate (MCintegration in parallel with event generation);(iii) evolve from known n-parton configuration;(iv) interface shower algorithm to ‘cone’ jet finder toveto emissions outside the allowed jet regions.

On to C++!(L. Lonnblad, hep-ph/9810208 → CPC; M. Bertini, TS)

Why Fortran → C++?• SLAC →, FNAL →, CERN → LHC era.• Industrial standard.• Educational and professional continuity for stu-

dents.• Better to program — for experts.• User-friendy interfaces — for the rest of us

(cooperation with GEANT4, LHC++).

Milestones:• January 1998: project formally started (Leif

∼half-time).• Exists today: strategy document, code for the

event record and the particle object.• In progress: particle data and other data base

handling, event generation handler structure,string fragmentation.

• Next: decay routines, very simple matrix ele-ments.

• By summer: proof of concept.• End 2000: most of current PYTHIA functionality

(?).• ??: more and better than current PYTHIA.

Input welcome: leif@thep.lu.se

The event record:

stl::set

Event

stl::vector

stl::vector

Step*

stl::set

Collision*

Particle*

SubCollision*

ParticleData

• An Event contains a TriggerCollision and a fur-ther number of pileup Collisions.

• A Collision contains many Steps: hard subpro-cess, showers, fragmentation, . . . .

• A Step contains a list of produced Particles.

• A Particle contains

• a pointer to a ParticleData object,

• pointers to other particles: mother(s), daugh-ters, colour partners, . . . ,

• value of mass, four-momentum, productionvertex, spin (?), . . . .

• A ParticleData object contains

• PDG particle code (also enumeration),

• particle name character string(also LATEX and HTML?),

• various kinds of masses like constituent, run-ning MS, Breit–Wigner function,

• charge, spin, colour, . . . ,

• a decay table.

• A decay table entry contains

• branching ratio and/or partial width function(DecayRater),

• decay products,

• pointer to a Decayer object (phase-spacegenerator, matrix element).

With the help of ParticleMatcher objects, decaychannels may be switched on/off.

Simpler lists of particles may be extracted based ona Selector object.

The event generation process

A

CollisionHandler*

EventHandler

CollisionHandler

SubProcessHandler*

CascadeHandler DecayHandlerHadronizationHandler

StepHandler

PartonXSecFn*

LuminosityFunction

SubProcessHandler

list

StepHandler*

list

list

list

PartonXSecFn

PartonExtractor

AAA

AA

A

is based on a set of handlers for the various Steps,such as hard subprocess, parton cascades, multipleinteractions, hadronization, decays, and so on.The execution order may be changed dynamically anda Hint may provide information what is to be done.