PYTHIA Status

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H1 Collaboration Meeting Lund, 3 October 2002

Monte Carlos and NLO

Torbj ¨orn Sj ¨ostrand

Apology: not specifically ep, but photoproduction ∼ pp

Event Physics Overview PYTHIA Status

Improved Parton Showers Heavy Flavour Production Heavy Flavour Hadronization

Multiple Interactions Summary

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Event physics overview

Structure of the basic generation process:

1) Hard subprocess:

dˆσ/dˆt, Breit-Wigners

2) Resonance decays:

includes correlations (where implemented)

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

(3)

6) Beam remnants:

colour-connected to rest of event

7) Hadronization (or fragmentation)

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 (within & between strings).

10) The forgotten/unexpected: a chain is never stronger than its weakest link!

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PYTHIA Status

















































































































































































































































                                                                                                                                                                                                                                                                                                                                                               

                                                                                                                                                                                                                                                                                                                                                     

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PYTHIA

lh hh

JETSET 7.4 PYTHIA 5.7 SPYTHIA

4 March 1997 : PYTHIA 6.1

Currently PYTHIA 6.210 of 25 September 2002

∼ 58, 900 lines Fortran 77

Code, manual, sample main programs, more:

www.thep.lu.se/

torbjorn/Pythia.html

short writeup in T. Sj ¨ostrand, P. Ed ´en, C. Friberg, L. L ¨onnblad, G. Miu, S. Mrenna and E. Norrbin

Computer Phys. Commun. 135 (2001) 238 [hep-ph/0010017]

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Subprocess summary

Processes Examples

QCD & related

Soft QCD low-p; diffraction

Hard QCD qg → qg

Open heavy flavour qq → tt Closed heavy flavour gg → gJ/ψ

γγ physics γq → qg

DIS γq → q

γγ physics γT γL → qq Electroweak SM

Single γ/Z0/W± qq → γ/Z0 (γ/γ/Z0/W±/f/g)2 qq → W+W Light SM Higgs gg → h0

Heavy SM Higgs Z0LZ0L → WL+WL SUSY BSM

h0/H0/A0/H± qq → h0A0 SUSY qq0 → ˜χ0i χ˜±j R

/ SUSY χ˜0i → bcs ⇒ junctions!

Other BSM

Technicolor qq0 → πtc0 πtc±

New gauge bosons qq → γ/Z0/Z00 Compositeness qq → e±e∗∓

Leptoquarks qg → `LQ

H±± (from LR-sym.) qq → H++H−−

Extra dimensions gg → G → e+e + New User-Defined Process Machinery

(7)

Photoproduction

(G.A. Schuler & TS, NPB407 (1993) 539, ZPC73 (1997) 677)

Direct VMD Anomalous

Direct: point-like Resolved: hadronic state

Spectrum of fluctuations γ ↔ qq ∝ dk2 /k2 alt. m ' 2k; dm2/m2

? k < k0 ' 0.5 GeV: nonperturbative γ → qq hadronic physics ⇒ VMD

(Vector Meson Dominance) parameterized couplings to ρ0, ω, φ, J/ψ

σtotγ→ρ = P(γ → ρ) · σtotρ

PDF fiγ→ρ(x, µ2), σjetγ→ρ = . . .

beam remnants, multiple interactions, . . .

? k > k0: perturbative γ → qq

PDF calculable: anomalous part of γ

but σtotqq not ⇒ GVMD (Generalized VMD) geometric scaling ansatz σtotqq ∝ kV2 /k2 ,

kV ' mρ/2 for light quarks

again hadronic character: beam remnants, . . .

(8)

Deeply Inelastic Scattering

(aim: extend photoproduction to Q2 ∼ m2ρ)

(Ch. Friberg & TS, EPJC13 (2000) 151, JHEP09 (2000) 10)

Virtual photon: γq → q σtotγp ' 4π2αem

Q2 F2(x, Q2) ' 4π2αem

Q2

X q,q

e2q xq(x, Q2)

but F2 → 0 for Q2 → 0 by gauge invariance, + limit doublecounting with photoproduction

σDISγp ' Q2 Q2 + m2ρ

!2

2αem

Q2

X q,q

e2q xq(x, Q2)

where q(x, Q2) frozen for Q2 < Q20;

and prefactor ensures σDIS → 0 for Q2 → 0

O(αs) DIS =

( QCDC γq → qg BGF γg → qq

)

= dir

σLO DISγp = σDISγp − σdirγp → σDISγp exp

−σdirγp σDISγp

corresponds to Sudakov form factor

so 4 components: DIS + dir + VMD + GVMD

(9)

From Real to Virtual Photons

σtotγp(W2, Q2) = σDISγp exp

−σdirγp σDISγp

+ σdirγp

+ W

2

Q2+W2

!3 

σVMDγp + σGVMDγp



Direct photon: Q2 in ME expression

Resolved photon:

total cross section σtotγ→i dampened by dipole m2

m2 + Q2

!2

(fewer fluctuations, smaller size)

VMD: m = mρ, mω, mφ, mJ/ψ GVMD: m ' 2k; in total

Z k02

dk2 k2

k2V k2

4k2 4k2 + Q2

!2

fγ

T

i (x, µ2, Q2): SaS 1D (also dipole-based) fγ

L

i (x, µ2, Q2): simple multiplicative factor or Ch´yla (hep-ph/0006232) (1 − x)3 reduces doublecounting at large x

⊕ virtual photon flux (T & L)

(10)

Parton Shower approach

2 → n = (2 → 2) ⊕ ISR ⊕ FSR

q q

Q Q Q2

2 → 2 Q22

Q21

ISR

Q24 Q23

FSR

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

ZZZ

dx1 dx2 dˆt fi(x1, Q2) fj(x2, Q2) dˆσij dˆt FSR = Final-State Radiation; timelike shower Q2i = M2 > 0 decreasing + coherence

ISR = Initial-State Radiation; spacelike shower Q2i = −M2 > 0 increasing + ∼ coherence backwards evolution: start at hard scattering

Do not doublecount! Q2 > Q21, Q22, Q23, Q24 2 → 2 = most virtual = shortest distance

(11)

ME vs. PS

ME : Matrix Elements

+ systematic expansion in αs (‘exact’) + powerful for multiparton Born level + flexible phase space cuts

− loop calculations very tough

− negative cross section in collinear regions

⇒ unpredictive jet/event structure

no easy match to hadronization

PS : Parton Showers

− approximate, to LL (or NLL)

− main topology not predetermined

⇒ inefficient for exclusive states

+ process-generic ⇒ simple multiparton + Sudakov form factors/resummation

⇒ sensible jet/event structure + easy to match to hadronization

Marriage desirable! But how?

Problems: • gaps in coverage?

• doublecounting of radiation?

• Sudakov?

• NLO consistency?

(12)

Merging

= smooth transition ME/PS, no sharp edge.

+ emissions can cover full phase space

− coherence not straightforward Want to reproduce

WME = 1 σ(LO)

dσ(LO + g) d(phasespace)

by shower generation + correction procedure

wanted z }| {

WME =

generated z }| {

WPS

correction z }| {

WME WPS Comments:

• Do not normalize WME to σ(NLO),

since extra work without clear gain (expect radiation also in events added by K-factor ≥ 1)

• Exponentiate ME correction by shower Sudakov form factor:

WactualPS (Q2) =

WME(Q2) exp −

Z Q2max

Q2 WME(Q02) dQ02

!

• Normally several shower histories

⇒ alternative approaches, largely equivalent

(13)

Final-state showers

Merging with γ/Z0 → qqg since long

(M. Bengtsson & TS, PLB185 (1987) 435, NPB289 (1987) 810)

. . . but problems with γ/Z0 → bbg noted:

Q2i = m2i gives wrong singularity structure, Q2i = m2i − m2i,onshell is relevant propagator!

WME = (. . .)

Q21Q22 − (. . .)

Q41 − (. . .) Q42

(also weight from splitting kernels in PS) Coloured decaying particle also radiates:

0 (t)

1 (b) 2 (W+) i

3 (g)

0 (t)

1 (b) 2 (W+)

i 3 (g)

ME 1

Q20Q21 matches PS b → bg

⇒ can merge PS with generic a → bcg ME

(E. Norrbin & TS, NPB603 (2001) 297)

Subsequent branchings q → qg: also matched to ME, with reduced energy of system

(14)

Calculate for 1 → 2 processes in SM + MSSM:

WME(x1, x2) = 1

σ(a → bc)

dσ(a → bcg) dx1 dx2 Depends on

• mass ratios r1 = mb/ma and r2 = mc/ma

• colour and spin structure

• vector vs. axial vector etc. (γ5)

colour spin γ5 example

1 → 3 + 3 (eikonal)

1 → 3 + 3 1 → 12 + 12 1, γ5, 1 ± γ5 Z0 → qq 3 → 3 + 1 12 12 + 1 1, γ5, 1 ± γ5 t → bW+ 1 → 3 + 3 0 → 12 + 12 1, γ5, 1 ± γ5 H0 → qq 3 → 3 + 1 12 12 + 0 1, γ5, 1 ± γ5 t → bH+ 1 → 3 + 3 1 → 0 + 0 1 Z0 → ˜q 3 → 3 + 1 0 → 0 + 1 1 ˜q → ˜q0W+ 1 → 3 + 3 0 → 0 + 0 1 H0 → ˜q 3 → 3 + 1 0 → 0 + 0 1 ˜q → ˜q0H+ 1 → 3 + 3 12 12 + 0 1, γ5, 1 ± γ5 χ → q˜q 3 → 3 + 1 0 → 12 + 12 1, γ5, 1 ± γ5 ˜q → qχ 3 → 3 + 1 12 → 0 + 12 1, γ5, 1 ± γ5 t → ˜ 8 → 3 + 3 12 12 + 0 1, γ5, 1 ± γ5 ˜g → q˜q 3 → 3 + 8 0 → 12 + 12 1, γ5, 1 ± γ5 ˜q → q˜g 3 → 3 + 8 12 → 0 + 12 1, γ5, 1 ± γ5 t → ˜g

(15)

WME(x1, x2)

g emission rate for different colour, spin and parity structures r1 = r2 = 0.2, x3 = 0.3

θqg

3 → 3 + 8

1 → 3 + 3 8 → 3 + 3 3 → 3 + 1

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

0 0.02 0.04 0.06 0.08 0.1

R3bl

yc

Pythia 6.153 Pythia 6.152 Pythia 6.129 DELPHI ALEPH

Rbl3 (yc)

ECM = 91 GeV mb = 4.8GeV

ratio of 3-jets in b and uds (=l) events

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16

0 0.02 0.04 0.06 0.08 0.1

R3bl

yc

Vector Axial vector Scalar Pseudoscalar

Rbl3 (yc)

ECM = mh/H/A

= 120 GeV mb = 4.8GeV reference light q from γ/Z

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Initial-state showers

p⊥Z dσ/dp⊥Z

physical Z + 1 jet ‘exact’

LO

‘exact’

NLO virtual

resummation: physical p⊥Z spectrum

shower: ditto + accompanying jets (exclusive)

Merged with matrix elements for

qq → (γ/Z0/W±)g and qg → (γ/Z0/W±)q0:

(G. Miu & TS, PLB449 (1999) 313)

WME WPS

!

qq0→gW

= ˆt2 + ˆu2 + 2m2Wˆs

ˆs2 + m4W ≤ 1 WME

WPS

!

qg→q0W

= ˆs2 + ˆu2 + 2m2Wˆt

(ˆs − m2W)2 + m4W < 3

(17)

curve=ResBos

black=PYTHIA KPYTHIA = 1.4

Q2max = s

C. Bal ´azs, J. Huston and I. Puljak, PRD63 (2001) 014021

Problem: requires large primordial k ≈ 2 GeV

⇒ need BFKL/CCFM non-ordered evolution ? Modified algorithm also affects other processes

• prefer Q2max = s where no doublecounting

⇒ more radiation at large p

• require ˆu = Q2 − ˆs(1 − z) < 0 in branchings

⇒ fewer but harder emissions

Similarly for Higgs production in mt → ∞ limit:

• gg → gh0 and qg → qh0 simple

• qq → gh0 nonsingular & small ⇒ add Challenges:

• gauge boson pairs (S. Burby)

• QCD 2 → 2 with ISR+FSR+interference

(18)

Production graphs

Examples of Q = c/b production diagrams, not ex- haustive:

g Q

g Q

Leading order

q

q Q

Q Leading order

g Q

g Q

g Pair creation

(with gluon emission)

g g

g

Q Q

Flavour excitation

g g

g

Q Q

Gluon splitting

g g

g

Q Q g

Gluon splitting (flavour excitation)

(19)

PS approach to heavy quarks

3 main sources (arbitrary names):

1) pair creation:

based on gg → QQ and qq → QQ with masses + additional showering

2) flavour excitation:

based on c and b content of standard PDF’s + Qg → Qg and Qq → Qq ME’s;

massive kinematics but massless ME’s;

with Q2 > m2Q (so PDF> 0) and Q2i < Q2; g → bb by backwards evolution (improved)

≈ t-channel graph of gg → QQ

3) gluon splitting:

ordinary 2 → 2 processes, e.g. gg → gg + g → QQ branching with threshold

q1 − 4m2Q/m2g (1 + 2m2Q/m2g)

≈ s-channel graphs of gg, qq → QQ

Avoid doublecounting:

for 2 → 2: Q2 = ˆp2+ (m23 + m24)/2 (⇒ ˆs∼ 4Q> 2) for FSR: Q2max = m2max = 4Q2

for ISR: Q2max = Q2

(20)

Beam Remnant Physics

Strings normally ‘large’ mass, but at times small because of beam remnant structure or by g → qq in shower. Thus 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.

PYTHIA predicted qualitative behaviour.

Quantitative one sensitive to details

⇒ develop model & tune

(21)

Improved description of when collapse occurs (mass spectrum ⇐ constituent quark masses)

example:

charm string in πp collision

2 2.5 3 3.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Msinglet

(1/N)dN/dM

(a)

1-body

2-body cluster

2-body string

3-body

0.01 0.1

100 1000 10000

Collapse rate

√s

(a) Default

Small quark masses

Even BRDF charm string

collapse rate in pp collisions

(variations)

and

1-body collapse: energy-momentum shuffling 2-body decay: smoother joining to string

picture (matched anisotropic decay)

(22)

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 and bottom masses: c and b cross sec- tions (mc = 1.5, mb = 4.8)

• 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) 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, Dπ, Dρ, . . .

• Collapse energy–momentum conservation:

practical solution to mass δ function

(several models tried; not very sensitive)

(23)

Asymmetries and correlations

0.001 0.01 0.1 1 10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (1/N)dN/dxF

xF (a) Pair production

All channels WA82 WA92

0.001 0.01 0.1 1 10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (1/N)dN/dxF

xF (b) Pair production

All channels WA82 WA92

D+ D

A(xF) =

#D−#D+

#D+#D+

in πp

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 A(xF)

xF Pair production (a)

All channels WA92, 350 GeV WA82, 340 GeV E791, 500 GeV E769, 250 GeV

1e-05 0.0001 0.001 0.01 0.1 1

0 2 4 6 8 10 12 14 16 18 (1/N)dN/dpT2

pT2 (c) Pair production

All channels WA92

1e-05 0.0001 0.001 0.01 0.1 1

0 2 4 6 8 10 12 14 16 18 (1/N)dN/dpT2

pT2 (d) Pair production

All channels WA92

D+ D

(24)

A(p) =

#D−#D+

#D+#D+

in πp

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 2 4 6 8 10

A(pT2 )

pT2 (b)

Pair production All channels WA92, 350 GeV E791, 500 GeV

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.5 1 1.5 2 2.5 3 3.5

(1/N)dN/d∆φ

∆φ (a)

Pair production All channels WA92

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

-4 -3 -2 -1 0 1 2 3 4

(1/N)dN/dy

∆y

(b) Pair production All channels WA92 data

φ correlations improved . . .

. . . but

y correlations worsened

(25)

Multiple Interactions

(TS & M. van Zijl, PRD36 (1987) 2019, J. Dischler & TS, EPJdir C2 (2001) 1)

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 new free parameter: p⊥min 1

jet =

Z s/4 p2⊥min

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)

(26)

r r

d

resolved

r r

d

screened

λ ∼ 1/p

hdi ∼ rp

qNpartons no correlations

∼ rp

Npartons with correlations?

Npartons ∼ Ng =

Z 1

∼4p2⊥min/s g(x, ∼ p2⊥min) dx Olden days:

xg(x, Q20) → const. for x → 0

⇒ Npartons ∼ ln s

4p2⊥min ∼ const.

Post-HERA:

xg(x, Q20) ∼ x− for x → 0, ∼ 0.08>

⇒ Npartons ∼ s 4p2⊥min

!

⇒ p⊥min ∼ 1

hdi ∼ Npartons ∼ s

(27)

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

(28)

Summary

• PYTHIA evolving – do not use old versions!

• Test photoproduction/DIS transition region.

• Many ongoing efforts to improve showers.

Objective not NLO but good description.

Merging: “NLO ME” ⇒ shower smoothly;

applicable to ISR and FSR alike.

• Heavy flavour production/hadronization understood in pp?

Perturbative by non-overlapping

LO + flavour excitation + gluon splitting.

Combined with string hadronization;

small string = cluster, with special treatment

• Multiple interactions getting to be orthodoxy!

CDF: min bias & underlying event agree.

Varying impact parameter ⇒ “hot spots”.

Figure

Updating...

References

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