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

(2)

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!

(4)

PYTHIA Status

ll

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 östrand, P. Ed én, C. Friberg, L. L önnblad, 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 γ^∗q → q

γ^∗γ^∗ physics γ_T^∗ γ_L^∗ → 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 Z⁰_LZ⁰_L → W_L⁺W⁻_L SUSY BSM

h⁰/H⁰/A⁰/H^± qq → h⁰A⁰ SUSY qq⁰ → ˜χ⁰_i χ˜^±_j R

/ SUSY χ˜⁰_i → bcs ⇒ junctions!

Other BSM

Technicolor qq⁰ → π_tc⁰ π_tc^±

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

Leptoquarks qg → `L_Q

H^±± (from LR-sym.) qq → H⁺⁺H⁻⁻

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

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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 ∝ dk_⊥² /k_⊥² 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

σ_tot^γ→ρ = P(γ → ρ) · σ_tot^ρ

PDF f_i^γ→ρ(x, µ²), σ_jet^γ→ρ = . . .

beam remnants, multiple interactions, . . .

? k_⊥ > k₀: perturbative γ → qq

PDF calculable: anomalous part of γ

but σ_tot^qq not ⇒ GVMD (Generalized VMD) geometric scaling ansatz σ_tot^qq ∝ k_V² /k_⊥² ,

k_V ' m_ρ/2 for light quarks

again hadronic character: beam remnants, . . .

(8)

Deeply Inelastic Scattering

(aim: extend photoproduction to Q² ∼ m²_ρ)

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

Virtual photon: γ^∗q → q σ_tot^γ^∗^p ' 4π²αem

Q² F₂(x, Q²) ' 4π²αem

Q²

X q,q

e²_q xq(x, Q²)

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

σ_DIS^γ^∗^p ' Q² Q² + m²_ρ

!₂

4π²αem

Q²

X q,q

e²_q xq(x, Q²)

where q(x, Q²) frozen for Q² < Q²₀;

and prefactor ensures σ_DIS → 0 for Q² → 0

O(αs) DIS =

( QCDC γ^∗q → qg BGF γ^∗g → qq

)

= dir

σ_{LO DIS}^γ^∗^p = σ_DIS^γ^∗^p − σ_dir^γ^∗^p → σ_DIS^γ^∗^p exp



−σ_dir^γ^∗^p σ_DIS^γ^∗^p





corresponds to Sudakov form factor

so 4 components: DIS + dir + VMD + GVMD

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From Real to Virtual Photons

σ_tot^γ^∗^p(W², Q²) = σ_DIS^γ^∗^p exp



−σ_dir^γ^∗^p σ_DIS^γ^∗^p



 + σ_dir^γ^∗^p

+ ^W

2

Q²+W²

!₃

σ_VMD^γ^∗^p + σ_GVMD^γ^∗^p

Direct photon: Q² in ME expression

Resolved photon:

total cross section σ_tot^γ→i dampened by dipole m²

m² + Q²

!₂

(fewer fluctuations, smaller size)

VMD: m = m_ρ, m_ω, m_φ, m_J/ψ GVMD: m ' 2k_⊥; in total

Z k₀²

dk_⊥² k_⊥²

k²_V k_⊥²

4k_⊥² 4k_⊥² + Q²

!2

f^γ

T∗

i (x, µ², Q²): SaS 1D (also dipole-based) f^γ

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 f_i(x₁, Q²) f_j(x₂, Q²) dˆσ_ij dˆt FSR = Final-State Radiation; timelike shower Q²_i = M² > 0 decreasing + coherence

ISR = Initial-State Radiation; spacelike shower Q²_i = −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

W^ME = 1 σ(LO)

dσ(LO + g) d(phasespace)

by shower generation + correction procedure

wanted z }| {

W^ME =

generated z }| {

W^PS

correction z }| {

W^ME W^PS Comments:

• Do not normalize W^ME 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:

W_actual^PS (Q²) =

W^ME(Q²) exp −

Z _Q²_max

Q² W^ME(Q⁰²) dQ⁰²

!

• Normally several shower histories

⇒ alternative approaches, largely equivalent

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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:

Q²_i = m²_i gives wrong singularity structure, Q²_i = m²_i − m²_i,onshell is relevant propagator!

W^ME = (. . .)

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

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Calculate for 1 → 2 processes in SM + MSSM:

W^ME(x₁, x₂) = 1

σ(a → bc)

dσ(a → bcg) dx₁ dx₂ Depends on

• mass ratios r₁ = m_b/m_a and r₂ = m_c/m_a

• 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˜q 3 → 3 + 1 0 → 0 + 1 1 ˜q → ˜q⁰W⁺ 1 → 3 + 3 0 → 0 + 0 1 H⁰ → ˜q˜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 → ˜tχ 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 → ˜t˜g

(15)

W^ME(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

y_c

Pythia 6.153 Pythia 6.152 Pythia 6.129 DELPHI ALEPH

R^bl₃ (y_c)

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

y_c

Vector Axial vector Scalar Pseudoscalar

R^bl₃ (y_c)

ECM = m_h/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)

W^ME W^PS

!

qq⁰→gW

= ˆt² + ˆu² + 2m²_Wˆs

ˆs² + m⁴_W ≤ 1 W^ME

W^PS

!

qg→q⁰W

= ˆs² + ˆu² + 2m²_Wˆt

(ˆs − m²_W)² + m⁴_W < 3

(17)

curve=ResBos

black=PYTHIA KPYTHIA = 1.4

Q²_max = 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 Q²_max = 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 m_t → ∞ 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

Leading order

q

q Q

Q Leading order

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 > m²_Q (so PDF> 0) and Q²_i < 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 − 4m²_Q/m²_g (1 + 2m²_Q/m²_g)

≈ s-channel graphs of gg, qq → QQ

Avoid doublecounting:

for 2 → 2: Q² = ˆp²_⊥+ (m²₃ + m²₄)/2 (⇒ ˆs∼ 4Q^> ²) for FSR: Q²_max = m²_max = 4Q²

for ISR: Q²_max = 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 x_F than c quark.

PYTHIA predicted qualitative behaviour.

Quantitative one sensitive to details

⇒ develop model & tune

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

• 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, . . .

• 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

x_F (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

x_F (b) Pair production

All channels WA82 WA92

D⁺ D⁻

A(x_F) =

#D⁻−#D⁺

#D⁻+#D⁺

in π⁻p

-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)

x_F 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

p_T² (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

p_T² (d) Pair production

All channels WA92

D⁺ D⁻

(24)

A(p_⊥) =

#D⁻−#D⁺

#D⁻+#D⁺

in π⁻p

-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 )

p_T² (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/d∆y

∆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

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)

(26)

r r

d

resolved

r r

d

screened

λ ∼ 1/p_⊥

hdi ∼ rp

qN_partons no correlations

∼ rp

N_partons with correlations?

N_partons ∼ Ng =

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

(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”.