Download - Low-Q 2 Partons in p-p and Au-Au Collisions Tom Trainor ISMD 2005 – Kroměříž, CR August, 2005
Trainor 2
Agenda
• Survey of p-p correlations
• Fragment distributions on (yt,yt) in p-p
• Fragment distributions in Au-Au
• Angular correlations on () in p-p
• Angular correlations in Au-Au
• pt correlations in p-p and Au-Au
QCD from the bottom up
Trainor 3
Low-Q2 Partons in p-p Collisions
subtract soft reference
minijetfragments
√ r
ef
√
same side
1D 2Dp-p200 GeV
nch=1
nch=10
pt yt
0.15 61pt (GeV/c)
string fragments
away side hadron pt ~ 0.5 GeV/c
yt1
yt2 yt2
√ref
nch
parton fragments
0ln ( ) /t t ty m p m
minimum-bias: no trigger condition
Trainor 4
Analysis Method(yt1,yt2) correlations () correlations
√ r
ef
√ r
ef
( ) ( )/ | a b
ref ab
a b
n n n n
n n
modified Pearson’s coefficient:normalized covariance density
in each 2D bin:
– bin size
number of correlated pairs ‘per particle’
autocorrelations can be determined by pair countingor by inversion of fluctuation scale dependence
joint autocorrelation on two difference variables
,
( ) ( ) ( )
( )k a a k
k ref a a k a
A n n n n n
A n n n+
+
ì üD - -ï ïº í ýï ïî þ
average over aon kth diagonal
,
( ; ) ( )
( ; ) ( )x k
ref x x k ref
n k A n
n k A n
r e
r e eD
D D
D Dº
x1
x 2
k a+k
a
x x
k
(yt,)
/
/
ref
ref
Trainor 5
p-p Correlations on (yt1,yt2)
ASSS
SS – same side
AS – away side
LS – like sign US – unlike sign
string and parton fragmentation: first two-particle fragment distributions
0.151.0
10.0
p t (GeV/c)
√ r
ef
√ r
ef
√ r
ef
√ r
efHBT
stringaway-side partonfragmentation isindependent ofcharge combination
same-side partonfragmentationrestricted to US pairs
parton
parton parton
(except OPAL on )
string
Trainor 6
p-p Correlations on (,)local charge and momentum conservation
PF
SF
SF – string fragments
PF – parton fragments
LS – like sign US – unlike sign
√ r
ef
√ r
ef
√ r
ef
√ r
ef
away-side partonfragmentation isindependent ofcharge combination
string fragmentationreflects local measureconservation
HBT string
partonHBT
parton
joint autocorrelation on two difference variables
parton
Trainor 7
p-p jets: 105, 225, 350, 625 GeV e-e jets: 14, 44, 91 GeV
Single-particle Fragmentation – I
= ln(1/xp)
OPAL – 91 GeV
TASSO – 14 GeV
ln(pt)conventional
fragmentation functions on logarithmic variables
e-e fragmentation functions ontransverse rapidity yt –systematic variation described by single model function
transverse rapidity yt
xp =pt /Ejet
LEPPETRA
e-e
ln ( ) /t t ty m p m CDF PRD 68 (2003) 012003 OPAL PLB 247 (1990) 617 Biebel, Nason and Webber hep-ph/0109282 617
ssampling:
not full data!
LEP
Trainor 8
Single-particle Fragmentation – II
2 2,max 0 0 ,minln ( ) / 0.35t jet jet ty E m E m y
1 1( ; , ) (1 ) / ( , )p qu p q u u B p q
p = 2.9q = 3.55
14, 44, 91 GeV
e-e
2 2 2,max( , ) ( ln ) ( ln / ln )h
p tD x Q F y Q G u x Q
~ independent of yt,max
2
ch t,max t,minn = A y - y
nch and peak values from Bethke hep-ex/9812026
simple e-e systematics on transverse rapidity
unidentified hadrons from unidentified partons
A = 0.65
10.425
2peak
pu
p q
upeak
slope = 0.41
mode
t,max t,miny - y
u=
mode:
e-e
two-particle fragment distribution
fit: distribution
Trainor 9
Two-particle Fragment Distributions
US – same side
STAR preliminary
yt
yt~
yt,peak
Q/2 2 3 4
1
p≡ln(xp)
1 10
Q/2 (GeV)
an approach derived from fragmentation functions
construct a surfacerepresenting frag-mentation functions vs parton momentum Q/2
parton momentum
frag
men
t rap
idity
symmetrize the surface to representfragment-fragmentcorrelations
compare to data:general featuresagree; string fragments appear at small yt
nch
one can sketch a two-particle minimum-bias fragment distribution starting with a surface from which fragmentation functions are conditional slices
conditional: trigger particle data
Trainor 10
Number Correlations on ytyt
peripheral
centralSTAR preliminary
evolution of fragment distribution with Au-Au centrality
200 GeV p-p
√ r
ef
√ r
ef
√ r
ef
√ r
ef
√ r
ef
√ r
ef
200 GeV Au-Au
RAA
same-side - US
Trainor 11
Jet Morphology Relative to Thrust
z
pt1
pt2 jtjt
x
jet thrust axis (parton momentum)p-p collision axis
jt – transverse momentumrelative to jet thrust axis
jt
jt
y
most-probable parton Q/2 at right is 1-2 GeV/c, comparable to the intrinsic parton kt
parton kt
hadron momenta
√ r
ef
angular correlations
Trainor 12
Symmetrized Angular Kinematics
pout
pt1,2, independent random variables
ˆy f®
pt,2
p
remove the trigger/associated asymmetry
pt,part
jt scaling (not generally valid)
pt,1
2 2 2 2 2 2 2 2, , , , ,sin 1 2 /out t assoc ta ty assoc at ty trig ty assoc t assocSS SS SS SS SS
p p j x j j p
asymmetric:
symmetric:
kinematic limit
ˆ ˆˆ ,y jf®
,1tyj
,2tyj
symmetrize:trigger, associated particles 1, 2
2 2,2 ,12 2 2 2 2 2 2
,1 ,2 ,1 ,2 12 1 22 2,1 ,2
sin 2 sin sint t
t t t t SSt t
p pj j p p
p p
J. Rak, J. Jia
T. Trainor, J. Porter
remove trigger-associated asymmetry
Trainor 13
Symmetrize | jt| and | kt|
0.15 61pt (GeV/c)
yt2 yt yt
SS
22
2 2 2
12
/ 2 expsin / 2 2 sin / 2 2
2cosht
tSS
t
m yj
y
autocorrelation ()
yt
yt1 ,t ty y
2
12,t t tj y y same for 2 2sin / 2 sin /
STAR preliminary
2 22
2 2
12 2
sin / 2 sin / 2/ 2 exp
2cosh 1 2 sin / 2
t AS SSt
tSS
m yz k
y
0.15 61pt (GeV/c)
yt2 yt yt
yt
yt1
AS SS
AS
no small-angle approximation, similar fragment pt
Trainor 14
Angular Correlation Measurements yt
SS - same side AS - away side
SSAS
jt jt kt
large same-side ( asymmetry
STAR preliminaryjt scaling
Trainor 15
Fragment Asymmetry about Thrust
two-particle fragmentation
jt jt
previously unexplored region!
pQCD pQCD
STAR preliminary
evolution with Q2 of soft jet angular asymmetry
small Q2 larger Q2
200 GeV p-p
• Small-Q2 partons down to 1 GeV are detectable
• These softest jets are strongly elongated
in the azimuth direction in p-p collisions
no trigger particle t t t πy ln m + p /m
lo hi
hi
lo
yt cut space
pt combinations determine Q2 of parton interaction
softest jets ever! big non-perturbative effects
yt
1:1 aspect ratio
Trainor 16
Interpretation
contact plane
contactplane
water dropsvrel = 6 m/s
pt
low-Q2 fragmentation
broadened in contactplane (,pt), narrowedperpendicular to it ()
z
z
hydrodynamicsof parton collisions
Trainor 17
Minijet Deformation on () in Au-Au
p-p
HI
p-p HIperipheral
central
centrality
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
low Q2
Trainor 18
The Other kt Broadening
azimuth broadening
pt,part,1 pt,part,2
kty,1+ kty,2
pt,part,1 pt,part,21 2||t tk klargest kt effects:
small q/2,
q/2-q/2
1tk
2tk
US
y t2
yt1
yt yt
STAR preliminary
interaction between intrinsic kt and momentum transfer q
||tk q
tk q
orientationtk vs q
pt broadening
the alignment between parton kts and q determines whether relative azimuth or relative pt of fragments will broaden
condition on (yt1,yt2) biasesaway-side azimuth broadening
SS - intrajet
AS - interjet
√ r
ef
Trainor 19
pt Fluctuations and pt Correlations
70-80%
20-30%
0-5%
full STAR acceptance
variance excess
fluctuation scaling
fluctuationinversion
subtractmultipoles
autocorrelation
STAR preliminary
centrality
pt fluctuations
partons and velocity correlations: how is pt distributed on ()?
• pt fluctuations invertible to pt autocorrelations
√ r
ef
√ r
ef
√ r
ef
√ r
ef
T. A. Trainor, R. J. Porter and D. J Prindle, J. Phys. G: Nucl. Part. Phys. 31 (2005) 809-824; hep-ph/0410182
Trainor 20
Compare with p-p pt Autocorrelations
Hijing Au-Au 200 GeV
p-p 200 GeV minbias
data Au-Au 200 GeV
p-p 200 GeV nch > 9
CI=LS+US
CD=LS–US
direct – from pair counting
from fluctuation inversion
70-80%
STAR preliminary
√ r
ef
√ r
ef
√ r
ef
√ r
ef
√ r
ef
net-charge correlations
Trainor 21
Model Fits
20-30%
data fit peakfit residuals
fitdatafit peak
red shifts and blue shifts
0-10%
0-10%
70-80%
quenchoff quench
on
Hijing
collision centrality
hijing
hijing
B1
B3
B2Hijing does not predict strong broadening or negative structure
peak amplitudes peak widths
negative structure is unanticipated –what is the origin?
Trainor 22
red shift
low-x partons
parton fragments
Au-Au pt autocorrelation
2q
1q
STAR preliminary
p-p pt autocorrelation
Au-Au200 GeV
bulk medium
• Response of medium to minimum-bias parton stopping
• Momentum transfer to medium
• Velocity structure of medium• Medium recoil observed via
same-side pt correlations
red shift: particle production may be from a recoiling sourceRecoil Response to Parton Stopping
20-30%
data model peak
recoil
fit residuals
fitdatamodel peak
STAR preliminary
80-90% ~ p-p
20-30% 0-5%
40-50%
Trainor 23
Energy Dependence: SPS RHIC
:t tp p n
CERES NPA 727 (2003) 97
2
dramatic increase of pt fluctuations with
increasing sNN
STAR preliminary
CERES
STAR
Hijing
full acceptance
centrality
STAR
ln /10 GeVNNsstring structure in Hijing does not appear in Au-Au data
!
Trainor 24
Summary• Precision survey of p-p correlation structure• Model-independent access to low-Q2 partons• Hydrodynamic aspects of parton scattering?
• The other kt broadening: pt asymmetry
• Low-Q2 partons as Brownian probes of A-A• Dissipation: p-p fragment distributions modified in A-A• Non-pQCD p-p angular correlations modified in A-A
• pt correlations: temperature/velocity structure of A-A
• Strong disagreement with pQCD Hijing Monte Carlo• Recoil response of A-A bulk medium: viscosity 0