Upload
tocho
View
50
Download
1
Tags:
Embed Size (px)
DESCRIPTION
Correlations at Intermediate p T. Rudolph C. Hwa University of Oregon. Correlations and Fluctuations in Relativistic Nuclear Collisions MIT, April 2005. Work done in collaboration with Chunbin Yang (Hua-Zhong Normal University, Wuhan) Ziguang Tan (Hua-Zhong Normal University, Wuhan) - PowerPoint PPT Presentation
Citation preview
Correlations at Intermediate pT
Rudolph C. HwaUniversity of Oregon
Correlations and Fluctuations in Relativistic Nuclear Collisions
MIT, April 2005
2
Work done in collaboration with
Chunbin Yang (Hua-Zhong Normal University, Wuhan)
Ziguang Tan (Hua-Zhong Normal University, Wuhan)
Charles Chiu (University of Texas, Austin)
3
Physics at Intermediate pT
pT0 2 4 6 8 10
hardsoft semi-hard
thermal-thermal
thermal-shower
shower-shower
low intermediate high
4
pdNπ
dp=
dq1
q1∫
dq2
q2
Fjj'(q1,q2)Rπ (q1,q2,p)
Fjj' =TT +TS+SS
Basic equations for pion production by recombination
Rπ (q1,q2,p)=
Shower parton distributions are determined from
Fragmentation function xDi
π (x) =dx1x1
∫dx2x2
Sij(x1),Si
j '(x2
1−x1
)⎧ ⎨ ⎩
⎫ ⎬ ⎭ Rπ(x1,x2,x)
q1q2
pδ(q1 +q2 −p)
5
Thermal partons are determined from the final state, not from the initial state.
Transverse plane
dNπ
pTdpT
(log scale)
pT2
No small parameter (rh/RA) in the problem.
6
thermal
fragmentation
soft
hard
TS Pion distribution (log scale)
Transverse momentum
TT
SS
Phenomenological successes of this picture
7
production in AuAu central collision at 200 GeV
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & CB Yang, PRC70, 024905 (2004)
TS
fragmentation
thermal
8
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.All in recombination/ coalescence model
Compilation of Rp/ by R. Seto (UCR)
9
kT broadening by multiple
scattering in the initial state.
Unchallenged for 30 years.
If the medium effect is before fragmentation, then should be independent of h= or p
Cronin Effect
p
q
in pA or dA collisionsCronin et al, Phys.Rev.D (1975)h
dNdpT
(pA→ πX)∝ Aα , α >1
A
RCPp >RCP
πSTAR, PHENIX (2003)
Cronin et al, Phys.Rev.D (1975)
p >
10
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
d+Au collisions
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & CB Yang, PRL 93, 082302 (2004)
No pT broadening by multiple scattering in the initial state.Medium effect is due to thermal (soft)-shower
recombination in the final state.
soft-soft
pion
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
11
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa, Yang, Fries, PRC 71, 024902 (2005)
Forward production in d+Au collisions
Underlying physics for hadron production is not changed from backward to forward rapidity.
BRAHMS
12
Correlations
2. Correlation in jets: trigger, associated particle, background subtraction, etc. (e.g., Fuqiang Wang’s talk)
1. Two-particle correlation with the two particles treated on equal footing.
(data to be presented tomorrow)
13
Correlation function
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
Normalized correlation function
K2(1,2) =C2(1,2)
ρ1(1)ρ1(2)=r2(1,2)−1 r2(1,2) =
ρ2(1,2)ρ1(1)ρ1(2)
In-between correlation function
G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
14
Correlation of partons in jets
A. Two shower partons in a jet in vacuum
Fixed hard parton momentum k (as in e+e- annihilation)
k
x1
x2
ρ1(1) =Sij(x1)
ρ2(1,2)= Sij(x1),Si
j'(x2
1−x1
)⎧ ⎨ ⎩
⎫ ⎬ ⎭
=12
Sij(x1)Si
j'(x2
1−x1
) +Sij (
x1
1−x2
)Sij'(x2)
⎧ ⎨ ⎩
⎫ ⎬ ⎭
r2(1,2) =ρ2(1,2)
ρ1(1)ρ1(2)
x1 +x2 ≤1
The two shower partons are correlated.
15
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
no correlation
16
B. Two shower partons in a jet in HIC
Hard parton momentum k is not fixed.
ρ1(1) =Sj(q1) =ξ dkkfi∫
i∑ (k)Si
j(q/ k)
ρ2(1,2)=(SS)jj'(q1,q2) =ξ dkkfi∫
i∑ (k) Si
j(q1
k),Si
j'(q2
k−q1
)⎧ ⎨ ⎩
⎫ ⎬ ⎭
r2(1,2) =ρ2(1,2)
ρ1(1)ρ1(2)fi(k)
fi(k) fi(k)
fi(k) is small for 0-10%, smaller for 80-92%
17
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
18
Correlation of pions in jets
Two-particle distribution
dNππ
p1dp1p2dp2=
1(p1p2)
2
dqi
qii∏
⎡
⎣ ⎢ ⎤
⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4, p2)
F4 =(TT+ST+SS)13(TT+ST+SS)24
k
q3
q
1
q4
q2
19
Correlation function of produced pions in HIC
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
ρ2(1,2)=dNπ1π2
p1dp1p2dp2
ρ1(1) =dNπ1
p1dp1
F4 =(TT+ST+SS)13(TT+ST+SS)24
Factorizable terms: (TT)13(TT)24 (ST)13(TT)24 (TT)13(ST)24
Do not contribute to C2(1,2)
Non-factorizable terms (ST+SS)13(ST+SS)24
correlated
20
C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
21
G2(1,2)=C2(1,2)
ρ1(1)ρ1(2)[ ]1/ 2
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
along the diagonal
22
23
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa and Tan, nucl-th/0503052
RCPG2 (1,2) =
G2(0−10%)(1,2)
G2(80−92%)(1,2)
24
Physical reasons for the big dip:
(a) central: (ST)(ST) dominates
S-S correlation weakened by separate recombination with uncorrelated (T)(T)
(b) peripheral: (SS)(SS) dominates
SS correlation strengthened by double fragmentation
The dip occurs at low pT because at higher
pT power-law suppression of 1(1) 1(2)
results in C2(1,2) ~ 2(1,2) > 0
25
Porter & Trainor, ISMD2004, APPB36, 353 (2005)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.Transverse rapidity yt
( pp collisions )
G2
STAR
26
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
27Hwa & Tan, nucl-th/0503052
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
28
Correlation with trigger particle
Study the associated particle distributions
29
STAR has measured: nucl-ex/0501016
Associated charged hadron distribution in pT
Background subtracted and distributions
Trigger 4 < pT < 6
GeV/c
30
Associated particle pT distribution
dNππ
p1dp1p2dp2=
1(p1p2)
2
dqi
qii∏
⎡
⎣ ⎢ ⎤
⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4, p2)
F4 =(TT+ST+SS)13(TT+ST+SS)24
After background subtraction, consider only:
dNπ
p2dp2trig =
dp1p1dNππ
p1dp1p2dp24
6
∫dp1p1
dNπ
p1dp14
6
∫
p1 -- trigger
p2 -- associated
(ST+SS)13(ST+SS)24
31
Reasonable agreement with data
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & Tan, nucl-th/0503052
32
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & Tan, nucl-th/0503060
33
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Very little dependence on centrality in dAu
34
and distributions (from Fuqiang Wang’s talk)
P1
P2
pedestal
subtraction point no pedestal
short-range correlation?
long-range correlation?
35
New issues to consider:
• Angular distribution (1D -> 3D)
shower partons in jet cone
• Thermal distribution enhanced due to
energy loss of hard parton
work done with C. Chiu
36
Longitudinal
Transverse
t=0 later
37
Events without jets T(q) =Cqe−q/T
Thermal medium enhanced due to energy loss of hard parton
Events with jets
T'(q) =Cqe−q/T 'in the vicinity of the jet
T’- T = T > 0new parameter
Thermal partons
38
For STST recombination
enhanced thermal
trigger associated particle
Sample with trigger particles and with background subtracted
Pedestal peak in &
F4
' =ξ dkkfi∫i
∑ (k)T'(q3){S(q1),S(q2)}T'(q4)G(ψ,q2 /k)
F4tr−bg =∑ ∫L (ST')13(T'T'−TT)24+(ST')13(ST')24G
39
1Ntrig
dNdΔη
=dη1 dp2p2 dp1p1
dNtrig−bg
p1dp1p2dp24
6
∫passocmin
4
∫−0.7
0.7
∫
dη1−0.7
0.7
∫ dp1p1dNtrig
p1dp14
6
∫
dNtrig
p1dp1=
ξp1
3 dkkfi∫i∑ (k) dq1∫ T'(p1 −q1)S
q1
k⎛ ⎝
⎞ ⎠
dNtrig−bg
p1dp1p2dp2=
ξ(p1p2)
3 dkkfi∫i∑ (k) dq1 dq2 ⋅∫∫
×
T'(p1 −q1)Sq1
k⎛ ⎝
⎞ ⎠
T'(q2)T'(p2 −q2)−T(q2)T(p2 −q2)[ ]
+T'(p1 −q1){Sq1
k⎛ ⎝
⎞ ⎠ ,S
q2
k−q1
⎛
⎝ ⎜ ⎞
⎠ ⎟ }T'(p2 −q2)G(ψ,q2 /k)
⎧
⎨ ⎪
⎩ ⎪
⎫
⎬ ⎪
⎭ ⎪
40
Pedestal in
P1,2 = dp2pmin(1,2)
4
∫dN(T'T'−TT)
dp2|trig
more reliable
0.15 < p2 < 4 GeV/c, P1 = 0.4
2 < p2 < 4 GeV/c, P2 = 0.04
P1
P2
less reliableparton distribution
T'(q) =Cqe−q/T ' T ’ adjusted to fit pedestal
find T ’= 0.332 GeV/c
cf. T = 0.317 GeV/cT = 15 MeV/c
41
z
1
p1
trigger
Assoc p2kq2
z
hard parton
shower parton
ψ =θ −θ1
η−η1 =Δη
tanψ2
=g(η,η1)=e−η −e−η1
1+e−η−η1
=e−η1e−Δη −1
1+e−Δη−2η1
⎡
⎣ ⎢ ⎤
⎦ ⎥
Expt’l cut on trigger: -0.7 < 1 < +0.7k
jet cone exp[−ψ 2 /2σ 2(x)]
42
kq2
z
hard parton
shower partonShower parton
angular distribution in jet cone
Cone width
σ(x) =σ 0(1−x)
another parameter ~ 0.22
G(ψ,q2 /k) =exp−(2tan−1g(η1 +Δη,η1))
2
2σ 2(q2 / k)
⎡
⎣ ⎢ ⎤
⎦ ⎥
43
Associated particle distribution in
Chiu & Hwa (2005)
44
Associated particle distribution in
Chiu & Hwa (2005)
45
We have not put in any (short- or long-range) correlation by hand.
The pedestal arises from the enhanced thermal medium.
The peaks in & arise from the recombination of enhanced thermal partons with the shower partons in jets with angular spread.
Correlation exists among the shower partons, since they belong to the same jet.
46
Conclusion
Parton recombination provides a framework to interpret the data on jet correlations.
There seems to be no evidence for any exotic correlation outside of shower-shower correlation in a jet.
For unbiased study without deciding on bkgd, we suggest the measure, G2(1,2).
Is there a hole in ?RCPG2
47
recombination
Comments to stimulate discussion
• Fragmentation is not important until pT > 9
GeV/c.• String model may be relevant for pp collisions,
• String/fragmentation has no phenomenological support in heavy-ion collisions.
but not for AA collisions.