[PPT] - Correlations in p-p Collisions Jeff Porter Firenze, IT July 7, PowerPoint Presentation

SLIDE 1

Correlations in p-p Collisions

Jeff Porter Firenze, IT July 7, 2006

SLIDE 2

Porter 2

Outline

Parton fragments in single-particle spectra
Two-particle fragment distributions on rapidity
Jet angular autocorrelations at low Q2
Low-Q2 physics phenomenology and LPHD
1D – 2D quantitative correspondence

low-Q2 partons in p-p collisions

before we try to understand QCD in A-A collisions we should understand it in elementary collisions

SLIDE 3

Porter 3

Two-component Analysis – pt Spectra

what is the ‘hard’ component?

pt (GeV/c) 1/nch 1/pt dN/dpt

nch = 1 nch = 11.5

yt 1/nch 1/yt dN/dyt

10

7

10

5

10

3

10

1

10 10 3 10 5 10 7 10 9 10 11 10 13 10 15 2 4 6 10

6

10

4

10

2

1 10 2 10 4 10 6 10 8 10 10 10 12 10 14 1 2 3 4

yt 1/ns 1/yt dn/dyt − S0(yt)

H(n ˆ ch,yt) nh ns

yt H(n ˆ ch,yt)

S0(yt) H(n ˆ ch,yt) H0(yt)

n ˆ ch 1 2 3 4 5

0.005 0.01 0.015 0.02 0.025 0.03 0.035 2 2.5 3 3.5 10

3

10

2

10

1

1 1 2 3 4

200 GeV p-p

pt (GeV/c) 1/ns 1/pt dn/dpt [(GeV/c)-2]

S0 total n ˆ ch= 11.5 1

H0/9 H0/140

yt 1/ns 1/yt dn/dyt

S0 total hard events H0/9 H0

10

6

10

5

10

4

10

3

10

2

10

1

1 10 2 4 6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1 2 3 4

S0 – soft component fixed reference H = data - S0 – hard component

separated components based on nch dependence

SLIDE 4

Porter 4

pt (GeV/c) 1/ns 1/pt dN/dpt yt 1/ns 1/yt dN/dyt

10

7

10

5

10

3

10

1

10 10 3 10 5 10 7 10 9 10 11 10 13 10 15 2 4 6 10

6

10

4

10

2

1 10 2 10 4 10 6 10 8 10 10 10 12 10 14 1 2 3 4

yt 1/ns 1/yt dN/dyt − S0(yt) yt H(nch,yt)

S0(yt) H(nch,yt) H0(yt)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 2 2.5 3 3.5 10

3

10

2

10

1

1 1 2 3 4

yt ∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

away

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

CI

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

Low-Q2 Partons in p-p Collisions

subtract soft reference minijet fragments

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

✁

∆ρ ∆ρ ∆ρ ∆ρ

2
1.5
1
0.5

0.5 1 1.5 2

1

1 2 3 4 0.005 0.01 0.015

ρ ρ ∆

∆

φ

∆

η

same side 1D 2D p-p 200 GeV

nch=1 nch=10

pt → yt

0.15 6 1

pt (GeV/c)

soft fragments

φ

∆

∆ρ / √ρref η

∆

2

2 4

2
1

1 2

0.01

0.01 0.02 0.03 0.04 0.05 0.06

away side

hadron pt ~ 0.6 GeV/c

yt1 yt2 yt2

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

✂

ρ ρ ρ ρref nch hard fragments

{ }

ln ( ) /

t t t

y m p m ≡ +

minimum-bias: no trigger condition

STAR preliminary

SLIDE 5

Porter 5

Correlation Analysis Methods

(yt1,yt2) correlations (η1,η2,φ1,φ2) correlations

yt ∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

φ∆ ∆ρ / √ρref η∆

2

2 4

2
1

1 2

0.01

0.01 0.02 0.03 0.04 0.05 0.06

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

( ) ( ) / |

a b ref ab a b

n n n n n n ρ ρ ε − − ∆ ≡ modified Pearson’s coefficient: normalized covariance density in each 2D bin:

ε ε ε ε = bin size

angular autocorrelation

,

( ) ( ) ( ) ( )

k a a k k ref a a k a

n n n n n n n n n n

average over kth diagonal

,

( ; ) ( ) ( ; ) ( )

x k ref x x k ref

n k n n n k n n

x1

x2 k a+k a x x k φ φ φ φ∆

∆ ∆ ∆=φ

=φ =φ =φ1

1 1 1−

− − −φ φ φ φ2

2 2 2

η η η η∆

∆ ∆ ∆=η

=η =η =η1

1 1 1−

− − −η η η η2

2 2 2

/

ref

ρ ρ ∆

τ τ τ τ = t1 – t2 ‘lag’ per pair

not an autocorrelation

per particle

(yt,η,φ)1⊗(yt,η,φ)2

SLIDE 6

Porter 6

p-p Correlations on (yt1,yt2)

y

t

∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

y

t

∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

y

t

∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

y

t

∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.4
0.2

0.2 0.4 0.6 0.8 1

φ∆ η∆

2
1.5
1
0.5

0.5 1 1.5 2 2 4

AS SS

SS – same side AS – away side LS – like sign US – unlike sign

‘string’ and parton fragmentation: first two-particle fragment distributions

0.15 1.0 10.0

pt (GeV/c)

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

HBT ‘soft’

away-side parton fragmentation is independent of charge combination same-side parton fragmentation is restricted to US pairs

parton parton parton

(except OPAL on ξ )

‘soft’ parton?

STAR preliminary

SLIDE 7

Porter 7

ymax = y(√s/2;m0) y(p;m0)

1 2 3 4 5 6 7 8 2 4 6 8

Low-Q2 Parton Fragment Distributions

yt ∆ρ / √ρref y

t

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

φ∆ η∆

2

2 4

2
1

1 2

US

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

STAR preliminary

Q/2 (GeV) yt

1 1.5 2 2.5 3 3.5 4 4.5 1 10

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

y*

Q/2

2 3

4

1 ξ ξ ξ ξ∗

∗ ∗ ∗

✁

ln(1/x*)

parton Q/2

fragment rapidity

nch

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

yt∆

∆ ∆ ∆

∆ ∆ ∆ ∆yt~ξ ξ ξ ξ

e-e fragmentation functions on yt universal form p-p intrajet two-particle fragment distribution transformation

fragment-parton joint distribution

n (yt,yt,max) ~ (xp,Q2)

symmetrize to fragment-fragment distribution on (yt,yt) compare with data

p-p 200 GeV

non-PID hadrons

{ }

ln ( )/

t t t

y m p mπ ≡ +

(yt − yt,min) / (yt,max − yt,min) 1/(yt,max − yt,min) 1/σtot dσ/dyt

14, 44, 91 GeV e-e jets

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

yt 1/σtot dσ/dyt

e-e OPAL 91 GeV TASSO √s 14, 44 GeV 1 2 3 4 5 6 7 8 2 4 6

pt ~ 0.6 GeV/c

hacking QCD

u

Q/2 (GeV)

SS-US

SLIDE 8

Porter 8

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

yt×yt Analysis and Trigger Particles

conditional distributions aka trigger-particle analysis

parton Q/2

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

yt∆

∆ ∆ ∆

∆ ∆ ∆ ∆yt~ξ ξ ξ ξ

yt d2n/dyt

2

y*

yt,max y*

10

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

1 2 3 4 5 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

1 7

riginal

sketch

conventional trigger- particle condition cut space locus of modes 2.0 1.0 0.5

pt (GeV)

gaussian curves – width same as hard component in yt spectrum

‘fragmentation functions’ extracted via analog to trigger-particle analysis

slope consistent with u* = 0.4

6.0

t

y

= 0.46

STAR preliminary

SLIDE 9

Porter 9

p-p Correlations on (η∆,φ∆)

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.2
0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.2
0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.05

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

local charge and momentum conservation

yt1 yt2

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

PF SF

SF – ‘string’ or soft fragments PF – parton or hard fragments LS – like sign US – unlike sign

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

away-side parton fragmentation is ~ independent of charge combination ‘string’ fragmentation reflects local measure conservation

HBT ‘string’ parton HBT? parton joint autocorrelation on two difference variables parton

STAR preliminary

SLIDE 10

Porter 10

φ∆ ∆ρ / √ρref η

∆

2 4

2
1

1 2

0.01

0.01 0.02 0.03 0.04

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ρ ρ ρ ρref

Jet Morphology Relative to Thrust

z φ pt1 pt2 jtη jtφ x η jet thrust axis (parton momentum) p-p collision axis ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ρ ρ ρ ρref

σ σ σ ση

η η η

σ σ σ σφ

φ φ φ

y

the most probable parton momentum for the distribution at right is 1 GeV/c

fragment momenta

200 GeV p-p

minijets

SLIDE 11

Porter 11

water drops vrel = 6 m/s

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.01

0.01 0.02 0.03 0.04

φ∆ ∆ρ / √ρref η∆

2 4

2
1

1 2

0.005

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Low-Q2 Parton Angular Correlations

yt1 yt2

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 yt ∆ρ / √ρref y

t

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref

low-Q2 partons – non-pQCD

conventional high-pt leading-particle analysis: pQCD p-p 200 GeV

STAR preliminary

small Q2 larger Q2

lo hi

non-pQCD pQCD

φ∆ η∆

2
1.5
1
0.5

0.5 1 1.5 2

1

1 2

φ∆ η∆

2
1.5
1
0.5

0.5 1 1.5 2

1

1 2

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

✁

ρ ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

✁

ρ ρ ρ ρref

hi lo hydrodynamics

f parton collisions?

Q2 softest jets ever! big non-perturbative effects

no trigger particle

1:1 aspect

SLIDE 12

Porter 12

yt, yx Correlations

yx yx

US US US US LS, US LS, US

SS AS AS SS g g π+ π− g g π+ π− π− π+

‘hard’

the softest detectable parton collisions → → → → LPHD

nch > 2

US

yt yt

1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4

high-pt

SS-US AS-CI

local parton-hadron duality: partons ‘blanche’ to become hadrons

g g π+ π−

‘soft’ small-angle scattering large-angle scattering

low-x gluons g g π±

LPHD: Ya. I. Azimov et al., Z. Phys. C 27, 65 (1985)

SLIDE 13

Porter 13

φ∆ η∆

2
1.5
1
0.5

0.5 1 1.5 2

1

1 2

Minijet Deformation on (η,φ) in Au-Au

peripheral

N(r-1) N(r-1) N(r-1)

central

N(r-1)

ν ση, σφ

ση σφ

STAR preliminary

0.4 0.6 0.8 1 1.2 1.4 1 2 3 4 5

η η η η

centrality

φ φ φ φ

σ σ σ ση

η η η

σ σ σ σφ

φ φ φ

130 GeV Au-Au

widths

minbias p-p

low Q2

fragmentation asymmetry reverses: p-p → → → → Au-Au

130 GeV Au-Au mid-central p-p Au-Au low Q2 p-p

z η η η η φ φ φ φ

⊗ ⊗ ⊗ ⊗

Hubble expansion

p-p HI dramatic evolution with centrality

STAR preliminary

SLIDE 14

Porter 14

mb mb

∆ρ/√ρref in hemi-cylinders

3 11 3 11

Pearson: pair density ratios

US LS US LS SS AS

STAR preliminary

SLIDE 15

Porter 15

∆ρ in hemi-cylinders

SS AS

mb mb 3 11 3 11

STAR preliminary

absolute correlated pair densities

US LS US LS

SLIDE 16

Porter 16

yt 1/ns 1/yt dN/dyt − S0(yt) yt H(nch,yt)

S0(yt) H(nch,yt) H0(yt)

0.005 0.01 0.015 0.02 0.025 0.03 0.035 2 2.5 3 3.5 10

3

10

2

10

1

1 1 2 3 4

∆ρ in 2π

mb

with eta weighting provides absolute pair yields

↔ ?

minbias CI

0.6

assume uniform distribution in circle with diameter = 1.13 on yt consistent with spectra hard component

US LS

max max

0.6 for minbias hard pairs unit area 0.6 pairs/event in hard peak at 5.75 however, divide by 4 for symmetrization and eta weighting 0.15 pairs per event in hard peak from

hard ch hard

n n n ρ ρ ∆ = ∆ = × ∆ = = ≈ ∆ →

2 hard

two-component spectra paper: n 0.01/ 2 0.17 particles per event in hard peak

ch

n = =

all pairs

+

=

unit-area circle

5.75

ch

n =

absolute comparison within 2× × × ×

STAR preliminary

SLIDE 17

Porter 17

n ˆ ch 10 nh / ns

end-point amplitude gaussian amplitude

0.2 0.4 0.6 0.8 1 1.2 1.4 2.5 5 7.5 10 12.5

1D vs 2D Correspondence

yt 1/ns 1/yt dn/dyt − S0(yt)

H(n ˆ ch,yt) nh ns

yt H(n ˆ ch,yt)

S0(yt) H(n ˆ ch,yt) H0(yt)

n ˆ ch 1 2 3 4 5

0.005 0.01 0.015 0.02 0.025 0.03 0.035 2 2.5 3 3.5 10

3

10

2

10

1

1 1 2 3 4

1D spectra: total hard-component pair integrals projection integrals onto sum variable no symmetrization

mb mb

1D and 2D are consistent

∝

2 h ch

n n

ch

n ∝

h s ch

n /n n

yt ∆ρ / √ρref yt

1 2 3 4 5 1 2 3 4 5 0.01 0.02 0.03 0.04 0.05 0.06 0.07

∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/

ρ

ρ ρ ρref ∆ρ ∆ρ ∆ρ ∆ρ ∆ρ ∆ρ ∆ρ ∆ρ

h

n /

h ch

n n

STAR preliminary

SLIDE 18

Porter 18

Summary

Low-Q2 parton fragmentation in p-p is precisely

accessible down to hadron pt ≅ 0.35 GeV/c

Jet morphology requires new treatment of

fragment yt distributions, angular correlations

Low-Q2 fragment distributions exhibit interesting

systematic behavior → the physics of LPHD

Jet angular correlations show strong asymmetry at

low Q2, ‘remember’ parton collision details

Moving toward a quantitative relation between