PYTHIA RecentProgressin

QCD and Weak Boson Physics workshop Fermilab 4–6 March 1999

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PYTHIA

lh

hh

Torbj ¨orn Sj ¨ostrand Lund University Introduction

current Subprocesses W p_⊥ spectrum

Charm & bottom asymmetries Multiple interactions

future Interconnection effects Improved parton showers Matching to matrix elements On to C++!

Introduction

JETSET 7.4 PYTHIA 5.7 SPYTHIA







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 photon fluxes 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. Subprocess W/Z production:

1 f_if_i → γ^∗/Z⁰ 2 f_if_j → W^± 22 f_if_i → Z⁰Z⁰ 23 f_if_j → Z⁰W^± 25 f_if_i → W⁺W⁻ 15 f_if_i → gZ⁰ 16 f_if_j → gW^± 30 f_ig → fⁱZ⁰ 31 f_ig → fkW^± 19 f_if_i → γZ⁰ 20 f_if_j → γW^± 35 f_iγ → fⁱZ⁰ 36 f_iγ → fkW^± 69 γγ → W⁺W⁻ 70 γW^± → Z⁰W^± Hard QCD processes:

11 f_if_j → fⁱf_j 12 f_if_i → fkf_k 13 f_if_i → gg 28 f_ig → fig 53 gg → fkf_k 68 gg → gg Soft QCD processes:

91 elastic scattering

92 single diffraction (XB) 93 single diffraction (AX) 94 double diffraction 95 low-p_⊥ production Open heavy flavour:

(also fourth generation) 81 f_if_i → QkQ_k 82 gg → QkQ_k 83 q_if_j → Qkf_l 84 gγ → QkQ_k 85 γγ → F^kF_k

No. Subprocess Closed heavy flavour:

86 gg → J/ψg 87 gg → χ^0cg 88 gg → χ^1cg 89 gg → χ^2cg 104 gg → χ^0c 105 gg → χ^2c 106 gg → J/ψγ 107 gγ → J/ψg 108 γγ → J/ψγ Prompt-photon production:

14 f_if_i → gγ 18 f_if_i → γγ 29 f_ig → fⁱγ 114 gg → γγ 115 gg → gγ

Deep inelastic scattering 10 f_if_j → fⁱf_j

Photon-induced processes:

33 f_iγ → fⁱg 34 f_iγ → fⁱγ 54 gγ → fkf_k 58 γγ → fkf_k 80 q_iγ → qkπ^± 131 f_iγ_T^∗ → fⁱg 132 f_iγ_L^∗ → fⁱg 133 f_iγ_T^∗ → fⁱγ 134 f_iγ_L^∗ → fⁱγ 135 gγ_T^∗ → fⁱf_i 136 gγ_L^∗ → fⁱf_i 137 γ_T^∗γ_T^∗ → fⁱf_i 138 γ_T^∗γ_L^∗ → fⁱf_i 139 γ_L^∗γ_T^∗ → fⁱf_i 140 γ_L^∗γ_L^∗ → fⁱf_i

Subprocesses (2)

No. Subprocess Light SM Higgs:

3 f_if_i → h⁰ 24 f_if_i → Z⁰h⁰ 26 f_if_j → W^±h⁰ 102 gg → h⁰ 103 γγ → h⁰ 110 f_if_i → γh⁰ 121 gg → QkQ_kh⁰ 122 q_iq_i → Q^kQ_kh⁰ 123 f_if_j → fⁱf_jh⁰ 124 f_if_j → f^kf_lh⁰ Heavy SM Higgs:

5 Z⁰Z⁰ → H⁰ 8 W⁺W⁻ → H⁰ 71 Z⁰_LZ⁰_L → Z⁰_LZ⁰_L 72 Z⁰_LZ⁰_L → W_L⁺W⁻_L 73 Z⁰_LW_L^± → Z⁰_LW^±_L 76 W⁺_LW⁻_L → Z⁰_LZ⁰_L 77 W^±_LW_L^± → W^±_LW^±_L BSM Neutral Higgses:

151 f_if_i → H⁰ 152 gg → H⁰ 153 γγ → H⁰ 171 f_if_i → Z⁰H⁰ 172 f_if_j → W^±H⁰ 173 f_if_j → fⁱf_jH⁰ 174 f_if_j → f^kf_lH⁰ 181 gg → QkQ_kH⁰ 182 q_iq_i → Q^kQ_kH⁰ 156 f_if_i → A⁰

157 gg → A⁰ 158 γγ → A⁰ 176 f_if_i → Z⁰A⁰ 177 f_if_j → W^±A⁰ 178 f_if_j → fⁱf_jA⁰ 179 f_if_j → fkf_lA⁰ 186 gg → QkQ_kA⁰ 187 q_iq_i → Q^kQ_kA⁰

No. Subprocess Charged Higgs:

143 f_if_j → H⁺ 161 f_ig → f^kH⁺ Higgs pairs:

297 f_if_j → H^±h⁰ 298 f_if_j → H^±H⁰ 299 f_if_i → A⁰h⁰ 300 f_if_i → A⁰H⁰ 301 f_if_i → H⁺H⁻ Doubly-charged Higgs:

341 `i`j → H^±±_L 342 `i`j → H^±±_R 343 `<sup>±</sup><sub>i</sub> γ → H<sup>±±</sup><sub>L</sub> e<sup>∓</sup> 344 `^±_i γ → H^±±_R e^∓ 345 `<sup>±</sup><sub>i</sub> γ → H<sup>±±</sup><sub>L</sub> µ<sup>∓</sup> 346 `^±_i γ → H^±±_R µ^∓ 347 `<sup>±</sup><sub>i</sub> γ → H<sup>±±</sup><sub>L</sub> τ<sup>∓</sup> 348 `^±_i γ → H^±±_R τ^∓ 349 f_if_i → H⁺⁺_L H⁻⁻_L 350 f_if_i → H⁺⁺_R H⁻⁻_R 351 f_if_j → fkf_lH^±±_L 352 f_if_j → fkf_lH^±±_R

Subprocesses (3)

No. Subprocess Technicolour:

149 gg → ηtechni

191 f_if_i → ρ⁰_techni 192 f_if_j → ρ⁺_techni 193 f_if_i → ω_techni⁰

194 f_if_i(→ ρ⁰_techni/ω_techni⁰ )

→ f^kf_k New gauge bosons:

141 f_if_i → γ/Z⁰/Z⁰⁰ 142 f_if_j → W⁰⁺

144 f_if_j → R Compositeness:

147 dg → d^∗ 148 ug → u^∗ 167 q_iq_j → d^∗q_k 168 q_iq_j → u^∗q_k

165 f_if_i(→ γ^∗/Z⁰) → fkf_k 166 f_if_j(→ W^±) → f^kf_l Leptoquarks:

145 q_i`j → L<sup>Q</sup> 162 qg → `L^Q 163 gg → L^QL_Q 164 q_iq_i → LQL_Q

No. Subprocess SUSY:

201 f_if_i → ˜e_L˜e^∗_L 202 f_if_i → ˜e_R˜e^∗_R

203 f_if_i → ˜e_L˜e^∗_R+ ˜e^∗_L˜e_R 204 f_if_i → ˜µLµ˜^∗_L

205 f_if_i → ˜µ_Rµ˜^∗_R

206 f_if_i → ˜µLµ˜^∗_R + ˜µ^∗_L˜µR

207 f_if_i → ˜τ1˜τ₁^∗ 208 f_if_i → ˜τ2˜τ₂^∗

209 f_if_i → ˜τ1˜τ₂^∗ + ˜τ₁^∗˜τ2

210 f_if_j → ˜`L˜ν<sub>`</sub>^∗+ ˜`<sup>∗</sup><sub>L</sub>˜ν`

211 f_if_j → ˜τ1˜ν_τ^∗ + ˜τ₁^∗ν˜τ

212 f_if_j → ˜τ2˜ντ∗ + ˜τ₂^∗ν˜τ

213 f_if_i → ˜ν`ν˜`∗

214 f_if_i → ˜ντν˜_τ^∗ 216 f_if_i → ˜χ1χ˜1

217 f_if_i → ˜χ2χ˜2

218 f_if_i → ˜χ3χ˜3

219 f_if_i → ˜χ4χ˜4

220 f_if_i → ˜χ1χ˜2

221 f_if_i → ˜χ1χ˜3

222 f_if_i → ˜χ1χ˜4

223 f_if_i → ˜χ2χ˜3

224 f_if_i → ˜χ2χ˜4

225 f_if_i → ˜χ3χ˜4

226 f_if_i → ˜χ^±₁χ˜^∓₁ 227 f_if_i → ˜χ^±₂χ˜^∓₂ 228 f_if_i → ˜χ^±₁χ˜^∓₂ 229 f_if_j → ˜χ1χ˜^±₁ 230 f_if_j → ˜χ2χ˜^±₁ 231 f_if_j → ˜χ3χ˜^±₁ 232 f_if_j → ˜χ4χ˜^±₁ 233 f_if_j → ˜χ1χ˜^±₂ 234 f_if_j → ˜χ2χ˜^±₂ 235 f_if_j → ˜χ3χ˜^±₂ 236 f_if_j → ˜χ4χ˜^±₂

Subprocesses (4)

No. Subprocess SUSY:

237 f_if_i → ˜g˜χ1

238 f_if_i → ˜g˜χ2

239 f_if_i → ˜g˜χ3

240 f_if_i → ˜g˜χ4

241 f_if_j → ˜g˜χ^±₁ 242 f_if_j → ˜g˜χ^±₂ 243 f_if_i → ˜g˜g 244 gg → ˜g˜g 246 f_ig → ˜q_iLχ˜1

247 f_ig → ˜q_iRχ˜1

248 f_ig → ˜q_iLχ˜2

249 f_ig → ˜q_iRχ˜2

250 f_ig → ˜q_iLχ˜3

251 f_ig → ˜q_iRχ˜3

252 f_ig → ˜q_iLχ˜4

253 f_ig → ˜q_iRχ˜4

254 f_ig → ˜q_jLχ˜^±₁ 256 f_ig → ˜q_jLχ˜^±₂ 258 f_ig → ˜q_iL˜g 259 f_ig → ˜q_iR˜g 261 f_if_i → ˜t¹˜t^∗₁ 262 f_if_i → ˜t²˜t^∗₂

263 f_if_i → ˜t¹˜t^∗₂ + ˜t^∗₁˜t₂ 264 gg → ˜t¹˜t^∗₁

265 gg → ˜t²˜t^∗₂ 271 f_if_j → ˜q_iL˜q_jL 272 f_if_j → ˜q_iR˜q_jR

273 f_if_j → ˜q_iL˜q_jR + ˜q_iR˜q_jL 274 f_if_j → ˜q_iL˜q^∗_{j L}

275 f_if_j → ˜q_iR˜q^∗_{j R}

276 f_if_j → ˜q_iL˜q^∗_{j R} + ˜q_iR˜q^∗_{j L} 277 f_if_i → ˜q_jL˜q^∗_{j L}

278 f_if_i → ˜q_jR˜q^∗_{j R} 279 gg → ˜q_iL˜q^∗_{i L} 280 gg → ˜q_iR˜q^∗_{i R}

No. Subprocess SUSY:

281 bq_i → ˜b₁˜q_iL 282 bq_i → ˜b₂˜q_iR 283 bq_i → ˜b₁˜q_iR+

˜b₂˜q_iL 284 bq_i → ˜b₁˜q^∗_{i L} 285 bq_i → ˜b₂˜q^∗_{i R} 286 bq_i → ˜b₁˜q^∗_{i R}+

˜b₂˜q^∗_{i L} 287 q_iq_i → ˜b₁˜b^∗₁ 288 q_iq_i → ˜b₂˜b^∗₂ 289 gg → ˜b₁˜b^∗₁ 290 gg → ˜b₂˜b^∗₂ 291 bb → ˜b₁˜b₁ 292 bb → ˜b₂˜b₂ 293 bb → ˜b₁˜b₂ 294 bg → ˜b₁˜g 295 bg → ˜b₂˜g 296 bb → ˜b₁˜b^∗₂+

˜b₂˜b^∗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) + q⁰(2) → W(0) starting point for backwards shower evolution:

3

4

1 5

6 2 0

2 → 2 process q(3) + q⁰(2) → g(4) + W(0): ˆs = (p₃ + p₂)² = (p₁ + p₂)²

z = m²_W z ˆt = (p₃ − p4)² = p²₁ = −Q²

u = mˆ ²_W − ˆs − ˆt = Q² − 1 − z

z m²_W Relate ME and PS rates:

dˆσ dˆt

_ME = σ₀

ˆs αs

2π 4 3

ˆt² + ˆu² + 2m²_Wˆs ˆtˆu

Q²→0

−→ σ₀ αs

2π 4 3

1 + z² 1 − z

1

Q² = dˆσ dQ²

_PS1

dˆσ dˆt

_PS1 = σ₀

ˆs αs

2π 4 3

ˆs² + m⁴_W ˆt(ˆt + ˆu)

Add mirror q(1) + q⁰(5) → g(6) + W(0): dˆσ

dˆt

_PS = dˆσ dˆt

_PS1 + dˆσ dˆt

_PS2 = σ₀ ˆs

αs

2π 4 3

ˆs² + m⁴_W ˆtˆu

R_qq0→gW(ˆs, ˆt) = (dˆσ/dˆt)_ME

(dˆσ/dˆt)_PS = ˆt² + ˆu² + 2m²_Wˆs ˆs² + m⁴_W

1

2 < R_qq0→gW(ˆs, ˆt) ≤ 1

Similarly for q(1) + g(5) → q⁰(6) + W(0):

dˆσ dˆt

_ME = σ₀

ˆs αs

2π 1 2

ˆs² + ˆu² + 2m²_Wˆt

−ˆsˆu

Q²→0

−→ σ₀ αs

2π 1

2 (z² + (1 − z)²) 1

Q² = dˆσ dQ²

  _PS

dˆσ dˆt

PS = σ₀ ˆs

αs

2π 1 2

ˆs² + 2m²_W(ˆt + ˆu)

−ˆsˆu R_qg→q0W(ˆs, ˆt) = (dˆσ/dˆt)_ME

(dˆσ/dˆt)_PS = ˆs² + ˆu² + 2m²_Wˆt (ˆs − m²_W)² + m⁴_W 1 ≤ R_qg→q⁰W(ˆs, ˆt) ≤

√5 − 1 2(√

5 − 2) < 3 (?) Larger Rqg than R_qq0

since PS misses s-channel graph of ME:

“resonance decay”,

“final-state radiation”

q g

q

q⁰ W

Improve PS:

• Q²max = s, not Q²_max ≈ m²_W (intermediate)

• MC correction by R(ˆs, ˆt) 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/dpW(nb/GeV)

p_W(GeV) PS old PS intermediate PS new ME

qq⁰ → gW

1e-06 1e-05 0.0001 0.001 0.01 0.1 1

0 50 100 150 200 250 300 350 dσ/dpW(nb/GeV)

p_W(GeV) PS old PS intermediate PS new ME

qg → q⁰W

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’->gW PS 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)

p_W(GeV) PS similar to qq’->gW PS similar to qg->q’W

hRi(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)(dN/dpW)(GeV-1 )

p_W(GeV)

PS,k =0.44 GeV PS,k=4 GeV D0 data

Primordial k_⊥ reduced in shower: input 4 GeV gives

qhp²_⊥Wi = 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, Z⁰⁰, W^0±, . . . )

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(x_F, p_⊥) = σ(D⁻) − σ(D⁺) σ(D⁻) + σ(D⁺) Asymmetry in x_F 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

x_F 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

p_t² A(p t

2 )

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

0 0.2 0.4 0.6 0.8 1

10⁰ 10¹ 10² 10³ 10⁴

(c) D⁺

xF

dN/dx F (arbitrary units)

0 0.2 0.4 0.6 0.8 1

10⁰ 10¹ 10² 10³ 10⁴

(d) D⁻

xF

dN/dx F (arbitrary units)

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 x_F than c quark.

Buildup of D⁻ and D⁺ x_F distributions:

−0.5 0 0.5 1

0 0.1 0.2 0.3 0.4 0.5

xF

dN/dx F

(i) (ii)

(iii) (iv) (v)

−0.5 0 0.5 1

0 0.1 0.2 0.3 0.4 0.5

xF

dN/dx F

(iii) (iv)

(v)

But also normal string fragmentation:

c d z

p_± = E ± p^z

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 (m_c = 1.5)

• Light-quark masses: threshold for cluster mass spectrum, together with mc

(mu = m_d = 0.33, ms = 0.50)

• Beam remnant distribution function:

(p − g = ud⁰ + u in colour octet state) hadron asymmetries 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 hadrons Bottom quarks Charm hadrons Charm 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_∆=|y_quark - y_antiquark| b-hadrons

c-hadrons

b-hadrons b-quarks c-hadrons c-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>=<yHadron - yQuark>

y Bottom

Charm

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

x_F

Asymmetry (B⁰_s − B⁰s)/(B⁰_s + 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

x_F

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

x_F

Note: horizontal scale x_F, not y

Multiple interactions

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

Consequence of composite nature of 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

2σ_jet =

Z _s/4

p²_⊥min

dσ

dp²_⊥ dp²_⊥

⇐

Z _s/4

0

dσ dp²_⊥

p⁴_⊥

(p²_⊥0 + p²_⊥)² dp²_⊥

Measure of colour screening length d in hadron p_⊥min hdi ≈ 1(= ¯h)

r r

d

resolved

r r

d

screened

λ ∼ 1/p_⊥

hdi ∼ rp

qN_partons no correlations

∼ rp

N_partons with correlations?

N_partons ∼ N^g =

Z ₁

∼4p²_⊥min/s g(x, ∼ p²_⊥min) dx Olden days:

xg(x, Q²₀) → const. for x → 0

⇒ N_partons ∼ ln s

4p²_⊥min ∼ const.

Post-HERA:

xg(x, Q²₀) ∼ x^− for x → 0, ∼ 0.08^>

⇒ N_partons ∼ s 4p²_⊥min

!_

⇒ p_⊥min ∼ 1

hdi ∼ N_partons ∼ s^

Mean charged multiplicity in inelastic non-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. L ¨onnblad & TS, EPJC2 (1998) 165)

Γ_W, Γ_Z, Γ_t ≈ 2 GeV

Γ_h > 1.5 GeV for m_h > 200 GeV Γ_SUSY ∼ GeV (often)

τ = 1

Γ ≈ 0.2 GeV fm

2 GeV = 0.1 fm  rhad ≈ 1 fm

⇒ hadronic decay systems overlap, between pairs of resonances & 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

b c

W⁻ c

s

B⁰

d b

c

W⁻

c gs

K⁰_S

J/ψ

3. Nonperturbative, hadronic phase:

Bose–Einstein.