sigma (mb)

3rd Nordic “LHC and Beyond” Workshop 2-3 February 2009 Lund, Sweden

QCD at LHC in pp

Torbj ¨ orn Sj ¨ ostrand

Department of Theoretical Physics, Lund University

⋆ Introduction: the structure of an event

⋆ Multiple Interactions

⋆ Hadronization

⋆ Observables and Summary

The structure of an event

Warning: schematic only, everything simplified, nothing to scale, . . .

p

p/p

Incoming beams: parton densities

p

p/p

u g

W⁺

d

Hard subprocess: described by matrix elements

p

p/p

u g

W⁺

d

c s

Resonance decays: correlated with hard subprocess

p

p/p

u g

W⁺

d

c s

Initial-state radiation: spacelike parton showers

p

p/p

u g

W⁺

d

c s

Final-state radiation: timelike parton showers

p

p/p

u g

W⁺

d

c s

Multiple parton–parton interactions . . .

p

p/p

u g

W⁺

d

c s

. . . with its initial- and final-state radiation

Beam remnants and other outgoing partons

Everything is connected by colour confinement strings Recall! Not to scale: strings are of hadronic widths

The strings fragment to produce primary hadrons

Many hadrons are unstable and decay further

ALICE simulated event

What is multiple interactions?

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆσ/dp²_⊥ ≈ 1/p⁴_⊥ for p_⊥ → 0.

integrate QCD 2 → 2 qq^′ → qq^′

qq → q^′q^′ qq → gg qg → qg gg → gg gg → qq

with CTEQ 5L PDF’s

0.01 0.1 1 10 100 1000 10000

0 5 10 15 20 25 30 35 40 45 50

sigma (mb)

pTmin (GeV)

Integrated cross section above pTmin for pp at 14 TeV jet cross section total cross section

σ_int(p_⊥min) =

ZZZ

p_⊥min dx₁ dx₂ dp²_⊥ f₁(x₁, p²_⊥) f₂(x₂, p²_⊥) dˆσ dp²_⊥ Half a solution to σ_int(p_⊥min) > σ_tot: many interactions per event

σ_tot =

∞ X

n=0

σ_n σ_int =

∞ X

n=0

n σ_n

σ_int > σ_tot ⇐⇒ hni > 1

n P_n

hni = 2

0 1 2 3 4 5 6 7

If interactions occur independently then Poissonian statistics

P_n = hniⁿ

n! e^−hni

but energy–momentum conservation

⇒ large n suppressed

Other half of solution:

perturbative QCD not valid at small p_⊥ since q, g not asymptotic states (confinement!).

Naively breakdown at

p_⊥min ≃ ¯h

rp ≈ 0.2 GeV · fm

0.7 fm ≈ 0.3 GeV ≃ Λ_QCD

. . . but better replace rp by (unknown) colour screening length d in hadron

r r

d resolved

r r

d

screened λ ∼ 1/p_⊥

so modify

dˆσ

dp²_⊥ ∝ α²_s(p²_⊥)

p⁴_⊥ → α²_s(p²_⊥)

p⁴_⊥ θ (p_⊥ − p_⊥min) (simpler) or → α²_s(p²_⊥0 + p²_⊥)

(p²_⊥0 + p²_⊥)² (more physical)

p²_⊥ dˆσ/dp²_⊥

0

where p_⊥min or p_⊥0 are free parameters, empirically of order 2 GeV

Typically 2 – 3 interactions/event at the Tevatron, 4 – 5 at the LHC, but may be more

in “interesting” high-p_⊥ ones.

PYTHIA implementation

(1) Simple scenario (1985):

first model for event properties based on perturbative multiple interactions no longer used (no impact-parameter dependence)

(2) Impact-parameter-dependence (1987):

still in frequent use (Tune A, Tune DWT, ATLAS tune, . . . )

• double Gaussian matter distribution,

• interactions ordered in decreasing p_⊥,

• PDF’s rescaled for momentum conservation,

• but no showers for subsequent interactions and simplified flavours

(3) Improved handling of PDFs and beam remnants (2004)

• Trace flavour content of remnant, including baryon number (junction)

u u

d

• Study colour (re)arrangement

among outgoing partons (ongoing!)

• Allow radiation for all interactions

(4) Evolution interleaved with ISR (2004)

• Transverse-momentum-ordered showers dP

dp_⊥ = dP_MI

dp_⊥ + ^X dP_ISR dp_⊥

!

exp −

Z _p⊥i−1 p_⊥

dP_MI

dp^′_⊥ + ^X dP_ISR dp^′_⊥

!

dp^′_⊥

!

with ISR sum over all previous MI

interaction number

p_⊥

p_⊥max

p_⊥min

hard int.

1 p_⊥1

mult. int.

2

mult. int.

3 p_⊥2

p_⊥3

ISR

ISR

ISR p^′_⊥1

(5) Rescattering (in progress)

is 3 → 3 instead of 4 → 4:

Figure 1:
S distribution for 1VTX data (points). The DP component to the data, determined by the two-dataset method to be 52.6% of the sample, is shown as the shaded region (the shape is taken from MIXDP). Also shown is the admixture 52.6% MIXDP + 47.4% PYTHIA, normalized to the data (line).

16

CDF 3-jet + prompt photon analysis Yellow region = double parton scattering (DPS) The rest =

PYTHIA showers

σ_DPS = σ_Aσ_B

σ_eff for A 6= B =⇒ σ_eff = 14.5 ± 1.7^+1.7_−2.3 mb Strong enhancement relative to naive expectations!

without multiple interactions

with multiple interactions

Jet pedestal effect

Events with hard scale (jet, W/Z, . . . ) have more underlying activity!

Events with n interactions have n chances that one of them is hard, so “trigger bias”: hard scale ⇒ central collision

⇒ more interactions ⇒ larger underlying activity.

Centrality effect saturates at p_⊥hard ∼ 10 GeV.

Studied in detail by Rick Field, comparing with CDF data:

“MAX/MIN Transverse” Densities

x Define the MAX and MIN “transverse” regions on an event-by-event basis with MAX (MIN) having the largest (smallest) density.

x The “transMIN” region is very sensitive to the “beam-beam remnant” and x

Jet #1 Direction 'I

“Toward”

“TransMAX” “TransMIN”

“Away”

Jet #1 Direction

'I

“TransMAX” “TransMIN”

“Toward”

“Away”

“Toward-Side” Jet

“Away-Side” Jet Jet #3

“TransMIN” very sensitive to the “beam-beam remnants”!

Colour correlations

hp_⊥i(n_ch) is very sensitive to colour flow

p p

long strings to remnants ⇒ much n_ch/interaction ⇒ hp_⊥i(n_ch) ∼ flat

p p

short strings (more central) ⇒ less n_ch/interaction ⇒ hp_⊥i(n_ch) rising

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0 5 10 15 20 25 30 35

<pT> [GeV/c]

Charged particle multiplicity CDF Run II Pythia 6.418 Pythia 8.114 Pythia 8.114 Deferred FSR Pythia 8.114 No reconnection Pythia 8.114 Deferred FSR, No reconnection

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0 5 10 15 20 25 30 35

<pT> [GeV/c]

Charged particle multiplicity CDF Run II Pythia 8.114 No reconnection Pythia 8.114 No reconnection + Rescattering Pythia 8.114, RR * p_⊥0 = 4.34 Pythia 8.114 Rescattering, RR * p_⊥0 = 4.12

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0 5 10 15 20 25 30 35

<pT> [GeV/c]

Charged particle multiplicity CDF Run II Pythia 8.114 No reconnection Pythia 8.114 No reconnection + ES1 Pythia 8.114 No reconnection + ES2 Pythia 8.114, RR * p_⊥0 = 5.56 Pythia 8.114 ES1, RR * p_⊥0 = 4.35 Pythia 8.114 ES2, RR * p_⊥0 = 3.08

dummy

• can describe data . . .

• . . . but need reconnection

• rescattering not important here

• enhanced screening gives significant effect . . .

• . . . but still need reconnection

Onium production

• Standard perturbative QCD fails to describe charmonium and bottomonium production, though improved in NNLO

• Non-relativistic QCD, a.k.a. colour octet model does better job, but ill-behaved at p_⊥ → 0

• Apply same regularization as for multiple interactions:

W = p²_⊥ p²_⊥0 + p²_⊥

!₂

× αs(p²_⊥0 + p²_⊥) αs(p²_⊥)

!3

(Bargiotti; Kraan)

5^thNovember 2004 Minimum-bias and the Underlying Event at the LHC

A. M. Moraes

LHC predictions: pp collisions at ¥s = 14 TeV

0 2 4 6 8 10

10² 10³ 10⁴ 10⁵

PYTHIA6.214 - tuned PYTHIA6.214 - default PHOJET1.12

pp interactions-

UA5 and CDF data

dN chg/dȘatȘ=0

¥s (GeV)

•PYTHIAmodels favour ln²(s);

•PHOJET suggests a ln(s)dependence.

LHC

2 4 6 8 10 12

0 10 20 30 40 50

CDF data

PYTHIA6.214 - tuned

PHOJET1.12 LHC

Tevatron

x1.5 x 3

dN_chg/dȘ ~ 30

dN_chg/dȘ ~ 15

Central Region

(min-bias dN_chg/dȘ ~ 7)

Transverse < Nchg>

P_t(leading jet in GeV)

Multiple Interactions Outlook

Issues requiring further thought and study:

• Multi-parton PDF’s f_a1a2a3···(x₁, Q²₁, x₂, Q²₂, x₃, Q²₃, . . .)

• Close-packing in initial state, especially small x

• Impact-parameter picture and (x, b) correlations

e.g. large-x partons more central!, valence quarks more central?

• Details of colour-screening mechanism

• Rescattering: one parton scattering several times

• Intertwining: one parton splits in two that scatter separately

• Colour sharing: two FS–IS dipoles become one FS–FS one

• Colour reconnection: required for hp_⊥i(n_charged)

• Collective effects (e.g. QGP, cf. Hadronization above)

• Relation to diffraction: eikonalization, multi-gap topologies, . . . Action items:

• Vigorous experimental program at LHC

• Study energy dependence: RHIC (pp) → Tevatron → LHC

• Develop new frameworks and refine existing ones Much work ahead!

Initiators and Remnants

p

g u s s u d

initiators:

in to hard interaction beam

remnants

Need to assign:

• correlated flavours

• correlated x_i = p_zi/p_ztot

• correlated primordial k_⊥i

• correlated colours

• correlated showers

• PDF after preceding MI/ISR activity:

0) Squeeze range 0 < x < 1 into 0 < x < 1 − ^P x_i (ISR: i 6= i_current) 1) Valence quarks: scale down by number already kicked out

2) Introduce companion quark q/q to each kicked-out sea quark q/q, with x based on assumed g → qq splitting

3) Gluon and other sea: rescale for total momentum conservation

Beam drag

Colour flow connects hard scattering to beam remnants.

Can have consequences, e.g. in π⁻p

A(x_F) = #D⁻ − #D⁺

#D⁻ + #D⁺

-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

(also B asymmetries at LHC, but small)

p⁺ π⁻

u u

c c

ud d

If low-mass string e.g.:

cd: D⁻, D^∗−

cud: Λ⁺_c , Σ⁺_c , Σ^∗+_c

⇒ flavour asymmetries

d c

s ssssssssss ss ss s sss ss s ss ss ss ss ss ss ss ss ss ss s ss ss ss ss ss s ss ss s ss ss ss s ss ss s ss ss s ss s sssss

s s ss ss s ss ss

s s ss s ss s ss s s

s ss s s ss s ss s s

s ss s s s ss s s ss s sssssssssssss

s s s ss s s s s s s s

ss sssssssssssssssssssssssssssss

D

Can give D ‘drag’ to larger x_F than c quark for any string mass

Fragmentation of junction topology

Encountered in R-parity violating SUSY decays χ˜⁰₁ → uds, or when 2 valence quarks kicked out of proton beam

lab frame

z x

u (r) d (g)

s (b)

J

junction rest frame

u (r) d (g)

s (b)

J

120^◦ 120^◦

120^◦

flavour space

q₃ q₄

q₅ q₃ q₂ q₂ qq₁ qq₁ u q₄

d

q₅ s

More complicated (but ≈solved) with gluon emission and massive quarks

Rapidity spectrum of original baryon number:

0 0.2 0.4 0.6

0 5

y

dN/dy

Tevatron: y - Junction Baryons

Old MI - Tune A New MI - Ran New MI - Rap New MI - Lam

0 0.2 0.4 0.6

0 2.5 5 7.5 10

y

dN/dy

LHC: y - Junction Baryons

Old MI - Tune A New MI - Ran New MI - Rap New MI - Lam

Strangeness content and p_⊥ of original baryon number:

10 ^-4 10 ^-3 10 ^-2 10 ^-1

1

0 1 2 3

|S|

P(|S|)

Tevatron: JB strangeness

Old MI - Tune A New MI - Ran New MI - Rap New MI - Lam

10 ^-4 10 ^-3 10 ^-2 10 ^-1

1

0 1 2 3

p_⊥ dN/p ⊥ LHC: p_⊥ - Junction Baryons

Old MI - Tune A New MI - Ran New MI - Rap New MI - Lam

Observables

Everything hangs together, but. . .

Measure Main physics interest

Prior knowledge (jet universality!?)

LEP hadrons hadronization

LEP jets Final-State Radiation

Multiple interactions (MI)

dn_ch/dη|_η=0 MI rate

multiplicity distribution MI fluctuations

forward-backward correlations MI fluctuations, string lengths

hp_⊥i(n_ch) reconnection rate (or other physics) jet pedestal impact-parameter picture

γ + 3 jets hard double parton scattering onium production low-p_⊥ regularization of MI

(1/σ)dσ/dn_jet; E_⊥ > 3, 5, 7; lumpiness (particle clustering), R = 0.4, 0.7, 1.0 screening/emergence of jets

energy dependence screening relation to small-x gluons

Measure Main physics interest

Jets (ISR/FSR = Initial/Final-State Radiation) dσ/dp_⊥jet PDFs, K factors

(1/σ)dσ/dp_⊥Z ISR + primordial k_⊥

∆ϕ(jet1, jet2) ISR

(1/E_⊥)dE_⊥/dR inside jet FSR, hadronization hard multijets ISR + FSR (+MI)

activity between jets colour flow, coherence Hadronization

flavour composition jet universality

charge/flavour correlations (de-)correlations between strings, (disoriented chiral condensate) baryon flow junction framework

charm, bottom flow beam drag (needs lower energies) dσ/dp_⊥hadron fragmentation function (q vs. g)

Other aspects

rapidity gaps Pomerons / reconnection dn_ch/dη for fix n_ch ditto

combined picture background for BSM searches

Summary and Outlook

⋆ Sad lack of communication between pp and AA communities (and e⁺e⁻ at LEP/ILC)

⋆ This meeting brings promise of better dialogue

⋆ RHIC data from 200 & 500 GeV extremely valuable reference points

⋆ Much already there — make it visible: HepData & Rivet

⋆ LHC detectors have complementary strengths — all can contribute

⋆ pp simpler than AA, but may contain the seeds of QGP etc.

⋆ QCD physics in pp remains big challenge!