Nordic LHC Physics WorkshopLund 16–18 March 2000

Implementationof

New Physicsin

ll

PYTHIA

lh hh

Torbjorn SjostrandLund University

Event Physics overviewPYTHIA status

Subprocess surveyHow-to: new processes

as event weighthardcoded

as external processHow-to: new particles and decays

Problem areas

Event physics overview

Structure of the basic generation process:

1) Hard subprocess:dσ/dt, Breit-Wigners.

2) Resonance decays:includes correlations.

3) Final-stateparton showers:(or matrix elements).

4) Initial-stateparton showers:(or matrix elements).

5) Multipleparton–partoninteractions.

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-connectedto 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 isnever stronger than its weakest link!

PYTHIA status

JETSET 7.4PYTHIA 5.7SPYTHIA

4 March 1997 : PYTHIA 6.1

Currently PYTHIA 6.138 of 2 March 2000∼ 51k lines Fortran 77(PYTHIA 7 in C++: Leif Lonnblad)

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

Some PYTHIA 6.1 main news:

• JETSET routines renamed:LUxxxx → PYxxxx + some more

• All real variables in DOUBLE PRECISION

• New processes for SUSY, Higgs,technicolor, . . .

• Initial-state showers matched to (some)matrix elements

• Energy-dependent p⊥min in multipleinteractions

• Newer parton distributions (but . . . )

• Improved resonance decay machinery

• Improved charm/bottom hadronization

• Colour rearrangement options for W+W−

• Expanded Bose-Einstein algorithm

• New baryon production scheme (optional)

Subprocess survey

Process PYTH HERW ISAJ

QCD & relatedSoft QCD ? ? ?Hard QCD ? ? ?Heavy flavour ? ? ?Top threshold — — —γγ physics ? ? —DIS ? ? —γ∗γ∗ physics (?) (?) —

Electroweak SMSingle γ∗/Z0/W± ? ? ?

(γ/γ∗/Z0/W±/f/g)2 ? ? ?Light SM Higgs ? ? ?Heavy SM Higgs (?) ? ?

SUSY BSMh0/H0/A0/H± ? ? ?SUSY ? ? ?R/ SUSY — ? —

Other BSMTechnicolor ? — ?New gauge bosons ? — —Compositeness ? — —Leptoquarks ? — —H±± (from LR-sym.) ? — —Extra dimensions — — (?)

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

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

New gauge bosons:141 fif i → γ/Z0/Z′0

142 fifj → W′+

144 fifj → R

Compositeness:146 eγ → e∗

147 dg → d∗

148 ug → u∗

167 qiqj → d∗qk168 qiqj → u∗qk169 qiqi → e∗+e− + e+e∗−

165 fif i(→ γ∗/Z0) → fkfk166 fifj(→ W±) → fkf l

Subprocesses (3)No. SubprocessLeptoquarks:145 qi`j → LQ162 qg → `LQ

163 gg → LQLQ

164 qiqi → LQLQ

Technicolor:149 gg → ηtc191 fif i → ρ0tc192 fifj → ρ+tc193 fif i → ω0

tc

194 fif i → fkfk195 fifj → fkf l361 fif i → W+

L W−L

362 fif i → W±Lπ

∓tc

363 fif i → π+tcπ

−tc

364 fif i → γπ0tc

365 fif i → γπ′0tc

366 fif i → Z0π0tc

367 fif i → Z0π′0tc

368 fif i → W±π∓tc

370 fifj → W±LZ0

L

371 fifj → W±Lπ

0tc

372 fifj → π±tcZ

0L

373 fifj → π±tcπ

0tc

374 fifj → γπ±tc

375 fifj → Z0π±tc

376 fifj → W±π0tc

377 fifj → W±π′0tc

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

Implementing new processes

1. Convince a PYTHIA author to do it for youSUSY, technicolor: Steve Mrennathe rest: Torbjornbut please have necessary formulae ready

2. Reweight existing cross sectionwith PYEVWT: simple

3. Hardcode from scratch: for brave only

4. Hardcode by modifying existing process:rather safe, but dead end

5. Hardcode by copying existing process:more useful, but less trivial

6. Include as external process:the official standard path,good if you have a working parton generator, butnontrivial if you don’t

7. Use standard interfaces: mainly for e+e−

CALL PY2FRM(IRAD,ITAU,ICOM)CALL PY4FRM(ATOTSQ,A1SQ,A2SQ,ISTRAT,&IRAD,ITAU,ICOM)CALL PY6FRM(P12,P13,P21,P23,P31,P32,PTOP,&IRAD,ITAU,ICOM)CALL PY4JET(PMAX,IRAD,ICOM)

Event weight

Example: contact interaction modification toprocess 16, qiqj → gW±

FACWG=COMFAC*AS*AEM/XW*2D0/9D0*

&(TH2+UH2+2D0*SQM4*SH)/(TH*UH)

dσ

dt=

π

s2αsαem

sin2θW

2

9

t2 + u2 + 2m2Ws

tu|Vij|

2

Assume modification of character

t2 + u2 + 2m2Ws

tu−→

t2 + u2 + 2m2Ws

tu+N

s2

Λ4

C...Double precision and integer declarations.

IMPLICIT DOUBLE PRECISION(A-H, O-Z)

IMPLICIT INTEGER(I-N)INTEGER PYK,PYCHGE,PYCOMP

C...Commonblocks.

COMMON/PYSUBS/MSEL,MSELPD,MSUB(500),KFIN(2,-40:40),CKIN(200)

COMMON/PYPARS/MSTP(200),PARP(200),MSTI(200),PARI(200)

COMMON/MYCOMM/ANORM,ALAMDA

C...Select subprocess.

MSEL=0

MSUB(16)=1

C...Weighted events.

MSTP(142)=2

C...Contact couplings.

ANORM=1D0

ALAMDA=1000D0

C...Initialize.CALL PYINIT(’CMS’,’P’,’P’,14000D0)

C...Generate events.DO 100 IEV=1,100

CALL PYEVNT100 CONTINUE

C...Cross section.CALL PYSTAT(1)

END

C*************************************************************

SUBROUTINE PYEVWT(WTXS)

C...Double precision and integer declarations.IMPLICIT DOUBLE PRECISION(A-H, O-Z)IMPLICIT INTEGER(I-N)INTEGER PYK,PYCHGE,PYCOMP

C...Commonblocks.COMMON/PYINT1/MINT(400),VINT(400)COMMON/MYCOMM/ANORM,ALAMDASAVE /PYINT1/,/MYCOMM/

C...Set default weight for WTXS.WTXS=1D0

C...Read out subprocess number and kinematics.ISUB=MINT(1)SHAT=VINT(44)THAT=VINT(45)UHAT=VINT(46)

C...Modifications by user to be put here.IF(ISUB.EQ.16) THEN

WMSQ=SHAT+THAT+UHATWMEOLD=(THAT**2+UHAT**2+2D0*WMSQ*SHAT)/(THAT*UHAT)WMENEW=ANORM*SHAT**2/ALAMDA**4WTXS=(WMEOLD+WMENEW)/WMEOLD

ENDIF

RETURNEND

Hardcoding

0) Select empty ISUB numberin range 401 – 500.

1) In PYDATA or commonblocks:PROC(ISUB) = ’ process name ’ISET(ISUB) = 1 or 2 for 2 → 1 or 2 → 2 processKFPR(ISUB,1) = KF code of first productKFPR(ISUB,2) = KF code of second productcan have KFPR info in code instead;advantage with KFPR is possibility to modify or dupli-cate process,e.g. KFPR(86,1) = 443: gg → J/ψg is defaultbut KFPR(86,1) = 553: gg → Υg (+ coupling)

2) In PYSIGH:implement matrix elements, including loop over possi-ble incoming flavoursC...f + fbar -> gamma + gamma

ELSEIF(ISUB.EQ.18) THENC...COMFAC already contains factor pi/shat**2 for 2->2C...and preweighting of phase space

FACGG=COMFAC*AEM**2*2D0*(TH2+UH2)/(TH*UH)C...Loop over all flavours and check them

DO 380 I=MMINA,MMAXAIF(I.EQ.0.OR.KFAC(1,I)*KFAC(2,-I).EQ.0)

& GOTO 380

C...Charge; colour factor for quark annihilation.EI=KCHG(IABS(I),1)/3D0FCOI=1D0IF(IABS(I).LE.10) FCOI=FACA/3D0

C...One ’channel’ for each flavour, with incomingC...flavours, colour flow enumerator and cross section.

NCHN=NCHN+1ISIG(NCHN,1)=IISIG(NCHN,2)=-IISIG(NCHN,3)=1SIGH(NCHN)=0.5D0*FACGG*FCOI*EI**4

380 CONTINUE

Many complications, e.g.− Breit-Wigners for resonances− flavour-dependent interference (γ∗/Z0)− several colour flows

3) In PYSCAT:fill in final state for selected processC...f + fbar’ -> g + W+/-;C...th = (p(f)-p(W-))**2 or (p(fbar’)-p(W+))**2

ELSEIF(ISUB.EQ.16) THENC...MINT(15) and MINT(16) incoming partons;C...charges -> W+ or W-.

KCH1=KCHG(IABS(MINT(15)),1)*ISIGN(1,MINT(15))KCH2=KCHG(IABS(MINT(16)),1)*ISIGN(1,MINT(16))

C...Order of outgoing particles must reflectC...t-hat definition; JS=1 is default.

IF(MINT(15)*(KCH1+KCH2).LT.0) JS=2C...Fill outgoing particles in MINT(21) and MINT(22).

MINT(20+JS)=21MINT(23-JS)=ISIGN(24,KCH1+KCH2)

C...Colour flow code: always pick by analogyC...with similar existing process.

KCC=17+JS

External processes

Convenient when you already have parton-level gen-erator available;used e.g. by COMPHEP group

0) Select empty ISUB number(s)in range 401 – 500.

1) In main program before CALL PYINIT :

CALL PYUPIN(ISUB,TITLE,SIGMAX)

MSUB(ISUB)=1

TITLE = ’ process name ’SIGMAX = maximum of event weights to beencountered

2) Suppy subroutine that will be called from PYEVNT,and that for each call generates and returns an eventof kind ISUB:

SUBROUTINE PYUPEV(ISUB,SIGEV)

ISUB = inparameter to allow mixing of several externalprocessesSIGEV = cross section (or weight) for event,dσdΩ

∫

dΩ, with Ω (biased) phase space, and

SIGEV/SIGMAX : event survival probability.SIGEV = SIGMAX = 1D0 : accept all events,but no cross section info.

3) Subroutine PYUPEV must provide event info (minievent record) in

COMMON/PYUPPR/NUP,KUP(20,7),PUP(20,5),

&NFUP,IFUP(10,2),Q2UP(0:10)

NUP : number of entries, first two incomingpartons, the rest outgoing particlesKUP(I,1) : 1 normally, 2 for documentationKUP(I,2) : PDG particle codeKUP(I,3) : 0, or mother I where knownKUP(I,4) : origin of final-state colourKUP(I,5) : origin of final-state anticolourKUP(I,6) : destination of initial-state colourKUP(I,7) : destination of initial-state anticolourPUP(I,J) : (px, py, pz, E,m) in GeVQ2UP(0) : Q2 scale of initial-state shower (' s?)NFUP : number of final-state showersKFUP(IF,1),KFUP(IF,2) : pair of partons orparticles that shower (one non-radiatingparticle is OK; to take recoil)Q2UP(IF) : Q2 scale of final-state shower (' m2)

For a complete example, seehttp://www.thep.lu.se/∼torbjorn/pythia/main51.f

example 1:s-channelcolour singletexchange q(2)

q(1)Z0

q(4)

q(3)

colour anticol colour anticolfrom from to to

I KUP(I,4) KUP(I,5) KUP(I,6) KUP(I,7)

1 0 0 2 02 0 0 0 13 4 0 0 04 0 3 0 0

example 2:gg → gg,one of 6 possiblecolour flows g(2)

g(1)

g(4)

g(3)

colour anticol colour anticolfrom from to to

I KUP(I,4) KUP(I,5) KUP(I,6) KUP(I,7)

1 0 0 3 22 0 0 1 43 1 4 0 04 3 2 0 0

Most parton-level generators do not give colour info⇒ have to make sensible choices, e.g. mix accordingto

∏

1/m2ij where ij is any parton pair connected by

string.

New particles

0) Select flavour code KF, according toPDG rules.

1) Modify particle data in PYDATA,best by editing table:CALL PYUPDA(1,LFN) : writes table on unit LFNCALL PYUPDA(2,LFN) : reads table from unit LFNfor complete replacementCALL PYUPDA(3,LFN) : reads table from unit LFNfor new particles or a few updated old particles Usesimilar existing particle as template!

Example (here edited to fit page size;in real life column alignment is important)4000002 u* u*bar 2 1 1 400.00000 2.65499 26.54994 0.00000E+00 1 1

1 0 0.853165 21 2 0 0 01 0 0.021144 22 2 0 0 01 0 0.029361 23 2 0 0 01 0 0.096329 24 1 0 0 0

First line: PDG code, particle name,antiparticle name, 3*charge, colour chargeclassification, particle/antiparticle distinction,mass, width, cutoff of tails, lifetime,width rescaling (see below), decay on/off.Subsequent lines: decay channels with channelon/off, matrix-element code, branching ratio,PDG codes for up to 5 decay products.

2) Width treatment in PYWIDT routine:allows dynamic calculation of partial widths,e.g. Γh(mh) or γ∗/Z0 → tt

but normally overkill for narrow mass peak.Set 0 or 2 in width rescaling input on particle line toavoid need for PYWIDT implementation.

3) Decay treatmenta) in PYDECY routine: simple phase-space multibodydecay, up to 10 particles, isotropic or with some ma-trix element; obtained for width rescaling input = 0.b) in PYRESD routine: more sophisticated resonancedescription obtained for width rescaling input ≥ 1. Op-timized for two simultaneous decays to two particleseach, with automatic showering where possible, butcan handle three products.

q

qZ0

Z0

µ+

µ−

h0

W−

W+

ντ

τ−s

c

Allows non-isotropic decays, in several steps if re-quired. But nontrivial to program; may be easier to doisotropic decays (default) and reweight final events.

Problem areas

• Mass spectrum of resonance often shows extrapeak near lower cut-off (2 GeV by default) be-cause parton distributions may increase faster atsmall x than a Breit-Wigner decreases. But can’ttrust Breit-Wigner too far from main peak anyway,so cut tails e.g. with CKIN.

• Long-lived new coloured particles would form“hadrons”, e.g. g → gqq or gg. Not currentlyconsidered. Experience from top and leptoquarksshow small differences, mainly in soft-hadron re-gion.

• QCD showering off q, g still missing: to be done.

• Multibody final states: no efficient biased phasespace generator.

• SUSY R/ processes introducenew colour flow topologies withjunctions. Hadronization sup-ported (though not told how inmanual) but consistent shower-ing machinery missing.

q

q q

junction