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

Correlations in p-p Collisions Jeff Porter Firenze, IT July 7, 2006

Outline low-Q 2 partons in p-p collisions • Parton fragments in single-particle spectra • Two-particle fragment distributions on rapidity • Jet angular autocorrelations at low Q 2 • Low- Q 2 physics phenomenology and LPHD • 1D – 2D quantitative correspondence before we try to understand QCD in A-A collisions we should understand it in elementary collisions Porter 2

Two-component Analysis – p t Spectra 200 GeV p-p H = data - S 0 – hard component 10 14 10 15 1/n s 1/y t dn/dy t − S 0 (y t ) ˆ ch ,y t ) 0.035 n ˆ ch 1 1/n ch 1/p t dN/dp t 1/n ch 1/y t dN/dy t n h 10 12 H(n ˆ ch ,y t ) 10 13 n ch = 11.5 n s 2 1 0.03 10 11 10 10 H(n 3 H(n ˆ ch ,y t ) 10 9 10 8 4 0.025 -1 10 7 10 5 10 6 0.02 10 5 10 4 10 3 S 0 (y t ) 10 2 0.015 -2 10 10 1 -1 0.01 10 -2 H 0 (y t ) -3 10 10 -3 -4 0.005 -5 10 10 n ch = 1 10 -6 -7 10 0 10 2 2.5 3 3.5 1 2 3 4 0 2 4 6 1 2 3 4 y t y t p t (GeV/c) y t 10 0.45 1/n s 1/p t dn/dp t [(GeV/c) -2 ] 1/n s 1/y t dn/dy t S 0 – soft component 0.4 1 hard events fixed reference 0.35 -1 10 H 0 0.3 -2 H 0 /9 10 total 0.25 -3 10 H 0 /140 0.2 separated components n ˆ ch = -4 0.15 10 11.5 based on n ch dependence total -5 0.1 10 S 0 1 0.05 -6 S 0 H 0 /9 10 0 0 2 4 6 1 2 3 4 p t (GeV/c) y t what is the ‘hard’ component? Porter 3

✁ ✂ � Low- Q 2 Partons in p-p Collisions STAR preliminary minijet 10 14 10 15 n ch =10 1/n s 1/p t dN/dp t 1/n s 1/y t dN/dy t 1/n s 1/y t dN/dy t − S 0 (y t ) H(n ch ,y t ) 0.035 ∆ρ ∆ρ ∆ρ ∆ρ 10 12 10 13 fragments n ch 1 0.07 10 11 10 10 0.03 ∆ρ / √ρ ref 0.06 H(n ch ,y t ) 10 9 10 8 0.05 ρ ref 0.025 0.04 -1 10 7 10 6 10 0.03 ρ ρ ρ 10 5 0.02 0.02 10 4 0.01 10 3 10 2 0 S 0 (y t ) 0.015 -2 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 10 10 1 1 -1 0.01 10 -2 H 0 (y t ) -3 10 10 n ch =1 -4 0.005 -3 -5 2 10 10 1D 10 -6 -7 10 2D 0 10 p-p 2 2.5 3 3.5 1 2 3 4 0 2 4 6 1 2 3 4 3 y t y t p t (GeV/c) y t y t subtract soft reference 5 4 200 GeV { } 4 p t → y t ln ( ) / ≡ + y m p m 3 y t 5 1 2 0 t t t STAR preliminary away side same side hadron p t ~ 0.6 GeV/c 4.5 4.5 y t2 y t2 away CI 4 4 2 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ρ ρ ref ρ ρ 3.5 3.5 0.015 3 3 0.06 ∆ ρ ∆ρ / √ρ ref 0.01 0.05 ρ 0.04 2.5 2.5 0.03 0.005 0.02 2 2 0.01 0 0 -2 2 -0.01 4 1.5 1.5 1.5 1 3 -1 0.5 2 4 φ η 0 1 1 1 -0.5 0 1 2 3 4 1 2 3 4 2 0.15 1 6 ∆ ∆ η 0 -1 y t1 ∆ -1.5 φ -1 0 p t (GeV/c) 1 -2 ∆ 2 soft fragments hard fragments minimum-bias: no trigger condition Porter 4

� � Correlation Analysis Methods ( y t1 , y t2 ) correlations ( η 1 ,η 2 ,φ 1 ,φ 2 ) correlations ( y t , η,φ ) 1 ⊗ ( y t , η,φ ) 2 ρ ref 0.07 2 ∆ρ / √ρ ref η η η ∆ η ∆ =η =η =η 1 =η 1 − − − −η η 2 η η 0.06 ρ ρ ρ 0.05 ∆ ∆ 1 1 2 2 2 0.04 0.03 0.02 0.06 0.01 ρ ref ∆ρ / √ρ ref ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ ρ ρ / 0.05 0 φ φ φ ∆ φ ∆ =φ =φ 1 =φ =φ 1 − − − −φ φ 2 φ φ 0.04 ρ ρ ρ 1 ref ∆ ∆ 1 1 2 2 2 0.03 0.02 0.01 2 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0 -2 per τ τ τ τ = t 1 – t 2 -0.01 3 -1 4 y t particle 0 5 ‘lag’ 4 2 η ∆ 4 φ ∆ 0 3 1 y t 5 1 2 2 not an autocorrelation angular autocorrelation per pair in each 2D bin: � � k ( ) ( ) ( ) � � � � � n n n n n n x � � � k a a k � x � � x 2 ( ) n n ( ) ( ) n n − − n n n n � � � � , k ref a a k � / | ∆ ρ ρ ≡ a a b ref ab ε n n a b average over k th diagonal ε ε = bin size ε ε a modified Pearson’s coefficient: � � ( ; � ) n k ( ) � n n x � k � normalized covariance density x 1 k a+k ( ; ) ( ) � � � n k n n , ref x x k ref � � Porter 5

� � � � 2 1 η ∆ p-p Correlations on (y t1 ,y t2 ) 1.5 0.8 1 0.6 0.5 0.4 0 ‘string’ and parton fragmentation: 0.2 -0.5 0 -1 SS AS first two-particle fragment distributions -0.2 -1.5 -2 -0.4 0 2 4 (except OPAL on ξ ) φ ∆ LS – like sign US – unlike sign SS – same side HBT 0.08 0.08 ρ ref ρ ref 0.07 ‘soft’ ∆ρ / √ρ ref 0.07 ∆ρ / √ρ ref 0.06 0.06 ρ ρ ρ ρ ρ ρ 0.05 0.05 parton 0.04 0.04 0.03 0.03 same-side parton 0.02 0.02 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0.01 parton? 0.01 0 0 1 1 fragmentation is 2 2 restricted to US pairs 3 3 y y 5 5 t 4 t 4 4 4 3 3 y t y t 5 1 2 5 1 2 STAR preliminary AS – ‘soft’ away side 0.07 0.07 away-side parton ρ ref ∆ρ / √ρ ref ρ ref ∆ρ / √ρ ref 0.06 0.06 parton parton 0.05 0.05 ρ ρ ρ ρ ρ ρ 0.04 0.04 0.03 0.03 0.02 0.02 fragmentation is ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0.01 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0.01 0 0 1 1 independent of 2 2 3 3 charge combination y y 10.0 5 5 t 4 t 4 4 4 1.0 3 3 p t (GeV/c) y t y t 5 1 2 5 1 2 0.15 Porter 6

✁ � Low- Q 2 Parton Fragment Distributions { } ln ( )/ ≡ + p-p 200 GeV y m p m π 4.5 4.5 fragment rapidity y t y t ln(1/x * ) ξ ξ ∗ ξ ξ ∗ ∗ ∗ n ch fragment-parton t t t 4 4 STAR preliminary 4 joint distribution p-p intrajet two-particle 3 3.5 3.5 Q/2 p t ~ 0.6 GeV/c 2 1 on ( y t , y t,max ) ~ ( x p , Q 2 ) 3 3 fragment distribution 2 2.5 2.5 2 2 8 y * 0.08 y(p;m 0 ) ρ ref SS-US 0.07 ∆ρ / √ρ ref 1.5 1.5 -2 7 0.06 ρ ρ ρ 0.05 -1 0.04 6 4 1 1 0.03 1 2 Q/2 (GeV) 3 4 0 2 η ∆ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0.02 1 10 y t 5 φ ∆ 0.01 0 1 Q/2 (GeV) 0 4 4.5 4.5 2 ∆ ∆ y t ~ ξ ξ y t ∆ ∆ ξ ξ 1 3 non-PID hadrons 4 4 parton Q/2 2 2 y t ∆ 8 3.5 3.5 1 ∆ ∆ ∆ 1/ σ tot d σ /dy t 3 e-e 0 7 3 3 0 2 4 6 8 y t y max = y( √ s/2;m 0 ) 5 4 6 4 2.5 2.5 symmetrize to 3 y 5 5 1 2 t 2 2 OPAL fragment-fragment 4 91 GeV universal form 1.5 1.5 3 distribution on ( y t , y t ) √ s 1 1 2 1 1 2 2 3 3 4 4 1/(y t,max − y t,min ) 1/ σ tot d σ /dy t 1 y t TASSO 1 4.5 14, 44 GeV y t US compare with data 0.8 4 0 2 4 6 y t 0.6 3.5 e-e fragmentation 3 0.4 e-e jets functions on y t 2.5 0.2 14, 44, 91 GeV 2 hacking QCD 0 0 0.2 0.4 0.6 0.8 1 1.5 transformation (y t − y t,min ) / (y t,max − y t,min ) 1 u 1 2 3 4 Porter 7 y t

� y t × y t Analysis and Trigger Particles cut space STAR preliminary 6.0 4.5 -1 4.5 y t 10 2 y* d 2 n/dy t -2 1 slope consistent 4 10 4 p t (GeV) -3 with u* = 0.4 10 3.5 -4 3.5 10 2.0 -5 3 3 10 -6 1.0 10 2.5 2.5 -7 10 0.5 -8 2 2 10 -9 10 1 7 1.5 1.5 7 y* -10 10 1 1 1 2 3 4 5 1 2 3 4 1 2 3 4 y t y t,max y t conditional distributions locus of modes conventional trigger- aka trigger-particle analysis particle condition 4.5 4.5 ∆ y t ~ ξ ∆ ∆ ∆ ξ ξ ξ y t gaussian curves – width same 4 4 parton Q/2 y t ∆ as hard component in y t spectrum 3.5 3.5 ∆ ∆ ∆ = 0.46 3 3 y 2.5 2.5 t original ‘fragmentation functions’ extracted 2 2 sketch 1.5 1.5 via analog to trigger-particle analysis 1 1 1 1 2 2 3 3 4 4 y t Porter 8

� � � � 4.5 y t2 p-p Correlations on ( η ∆ , φ ∆ ) 4 3.5 3 PF local charge and momentum conservation 2.5 2 SF 1.5 joint autocorrelation on two difference variables 1 1 2 3 4 y t1 SF – LS – like sign US – unlike sign ‘string’ or soft fragments HBT ‘string’ ‘string’ fragmentation 0.4 0.4 ∆ρ / √ρ ref ∆ρ / √ρ ref 0.35 0.35 ρ ref ρ ref 0.3 0.3 0.25 0.25 ρ ρ ρ ρ ρ ρ 0.2 0.2 reflects local measure 0.15 0.15 0.1 0.1 0.05 0.05 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ -2 -2 0 0 -0.05 -0.05 conservation -1 -1 4 4 0 0 2 2 η ∆ η ∆ φ ∆ φ ∆ 0 0 1 1 2 2 PF – STAR preliminary parton or hard fragments parton parton parton HBT? away-side parton 0.8 0.8 0.7 ∆ρ / √ρ ref 0.7 ∆ρ / √ρ ref ρ ref ρ ref 0.6 0.6 0.5 0.5 0.4 ρ ρ ρ ρ ρ ρ fragmentation is 0.4 0.3 0.3 0.2 0.2 0.1 0.1 ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ ∆ρ/ 0 -2 0 -2 -0.1 -0.1 ~ independent of -0.2 -0.2 -1 -1 4 4 0 0 2 2 η ∆ η ∆ charge combination φ ∆ φ ∆ 0 0 1 1 2 2 Porter 9

Jet Morphology Relative to Thrust fragment momenta jet thrust axis z p t2 j t η p-p collision axis j t φ p t1 (parton momentum) y 200 GeV p-p φ x η σ σ σ σ η η η η 0.04 ρ ref ∆ρ / √ρ ref 0.03 ∆ρ/ � ρ ρ ρ 0.02 0.01 ∆ρ/ ∆ρ/ ∆ρ/ σ σ φ σ σ 0 the most probable parton momentum ρ ref φ φ φ ρ ρ ∆ρ/ � ρ -2 -0.01 ∆ρ/ for the distribution at right is 1 GeV/c ∆ρ/ ∆ρ/ -1 4 0 2 minijets η ∆ φ ∆ 0 1 2 Porter 10