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
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
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Made on 30-Aug-2000 17:24:02 by konstant with DALI_F1.Filename: DC056698_007455_000830_1723.PS
DALI Run=56698 Evt=7455
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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
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%
−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
True Theory: L = iψγ
µD
µψ −
14F
µνF
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
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
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!
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, . . .
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
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!
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
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-p⊥production 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 γ∗fi→ 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 gγT∗→ fifi
136 gγL∗→ fifi
137 γT∗γ∗T→ fifi
138 γT∗γ∗L→ fifi
No. Subprocess 139 γL∗γT∗→ fifi
140 γL∗γL∗→ 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+LW−L 73 Z0LW±L → Z0LW±L
76 WL+W−L→ 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+LW−L
362 fifi→ W±Lπ∓tc
363 fifi→ πtc+π−tc
364 fifi→ γπtc0
365 fifi→ γπ00tc
366 fifi→ Z0π0tc
367 fifi→ Z0π00tc
368 fifi→ W±π∓tc
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→ d∗qk
168 qiqj→ u∗qk
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˜e∗L 202 fifi→ ˜eR˜e∗R 203 fifi→ ˜eL˜e∗R+ 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˜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˜t∗1 262 fifi→ ˜t2˜t∗2 263 fifi→ ˜t1˜t∗2+ 264 gg → ˜t1˜t∗1
265 gg → ˜t2˜t∗2 271 fifj→ ˜qiL˜qj L
272 fifj→ ˜qiR˜qj R
273 fifj→ ˜qiL˜qj R+ 274 fifj→ ˜qiL˜q∗j L 275 fifj→ ˜qiR˜q∗j R 276 fifj→ ˜qiL˜q∗j R+ 277 fifi→ ˜qj L˜q∗j L 278 fifi→ ˜qj R˜q∗j R 279 gg → ˜qiL˜q∗i L 280 gg → ˜qiRq˜∗i R 281 bqi→ ˜b1˜qiL
282 bqi→ ˜b2˜qiR
283 bqi→ ˜b1˜qiR+ ˜b2˜qiL
284 bqi→ ˜b1˜q∗i L 285 bqi→ ˜b2˜q∗i R 286 bqi→ ˜b1˜q∗i R+ ˜b2q˜∗i L 287 qiqi→ ˜b1˜b∗1
288 qiqi→ ˜b2˜b∗2
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˜b∗2+ Extra dimensions:
391 fifi→ G∗ 392 gg → G∗ 393 qiqi→ gG∗ 394 qig → qiG∗ 395 gg → gG∗
Cross sections and kinematics
u (1)
d (4) d (2)
u (3) g
ˆ s = (p
1+ p
2)
2ˆ t = (p
1− p
3)
2ˆ u = (p
1− p
4)
2: dˆ σ
dˆ t = π ˆ s
24
9 α
2sˆ s
2+ ˆ u
2ˆ t
2p (A)
p (B)
s = (p
A+ p
B)
2x
1≈ E
1/E
Ax
2≈ E
2/E
Bˆ s = x
1x
2s
σ =
Xi,j
ZZZ
dx
1dx
2dˆ t f
i(x
1, Q
2) f
j(x
2, Q
2) dˆ σ
ijdˆ t
f
i(x, Q
2): parton distribution functions at characteristic scale Q
2≈ p
2⊥= ˆ tˆ u/ˆ s
luminosity L ∝ N
1N
2f A counting rate dN
eventdt = σ L total rate N
event= σ
Z
L(t) dt
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
sL
2)
O(α
s)
e− e+
q q
L ' − ln y y ' min
m2ij
Ecm2
O(α
2s)
e− e+
q q
g
g
O(α
2sL
4)
O(α
2s)
e− e+
q q
g
collinear and soft emission divergences
⇒ large
higher orders O(α
2s)
e− e+
q q
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
0dσ
MEdx
1dx
2= α
s2π 4 3
x
21+ x
22(1 − x
1)(1 − x
2) rewrite for x
2→ 1 :
1 − x
2=
m213Ecm2
=
Q2Ecm2
x
1≈ z
x
3≈ 1 − z
q
q g
⇒ dP = dσ
σ
0≈ α
s2π
dQ
2Q
24 3
1 + z
21 − z dz
generalizes to dP
a→bc= α
s2π
dQ
2Q
2P
a→bc(z) dz P
q→qg= 4
3
1 + z
21 − z
P
g→gg= 3 (1 − z(1 − z))
2z(1 − z) P
g→qq= n
f2 (z
2+ (1 − z)
2)
Iteration gives final-state
parton showers
Sudakov form factor
P
corr(Q
2) = dP
dQ
2exp −
Z Q2max Q2
dP
dQ
2dQ
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
Parton Shower approach
2 → n = (2 → 2) ⊕ ISR ⊕ FSR
q q
Q Q Q
22 → 2 Q
22Q
21ISR
Q
24Q
23FSR
2 → 2 = hard scattering (on-shell) σ =
ZZZ
dx
1dx
2dˆ t f
i(x
1, Q
2) f
j(x
2, Q
2) dˆ σ
ijdˆ 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
242 → 2 = most virtual = shortest distance
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
2F
2(x, Q
2) =
Xi
e
2ixf
i(x, Q
2)
structure function parton distributions Resolution dependence by DGLAP:
df
b(x, Q
2)
d(ln Q
2) =
Xa
Z 1 x
dz
z f
a(x
0, Q
2) α
s2π P
a→bc
z = x x
0
Absolute normalization at small Q
20unknown:
• first principles: lattice QCD
• reality: data from DIS, pp
useful pdf plotting facility at
http://durpdg.dur.ac.uk/HEPDATA/
Initial-state showers
• Parton cascades are continually born, and are subsequently recombined.
• A hard scattering at scale Q
2probes 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
bdt =
Xa
Z 1 x
dz
z f
a(x
0, Q
2) α
s2π P
a→bc(z) with t = ln(Q
2/Λ
2) and z = x/x
0to
dP
b= df
bf
b= |dt|
Xa Z