1 high-p t physics at rhic and evidences of recombination rudolph c. hwa university of oregon...
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High-pT Physics at RHIC and Evidences of Recombination
Rudolph C. Hwa
University of Oregon
International Symposium on Multiparticle Dynamics
Sonoma, CA, July 2004
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Outline
Anomalies at high pT according to the
“standard model”
Alternative to the “standard model” at high
pT • Recombination in fragmentation• Shower partons• Inclusive distributions at all pT•
Dihadron correlations
All anomalies can be understood in terms of parton recombination
4
Conventional approach to hadron production at high pT
D(z)
h
qA A
Hard scattering near the surface because of energy loss in medium --- jet quenching.
5
If hard parton fragments in vacuum, then the fragmentation
products should be independent of the medium.
h
q
Particle ratio should depend on the FF D(z) only.
The observed data reveal several anomalies according to that picture.
D(z)
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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
Anomaly #2 in pA or dA collisions
Cronin Effect Cronin et al, Phys.Rev.D (1975)
p
q
hdNdpT
(pA→ πX)∝ Aα , α >1
A
p >
RHIC expt (2003)
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RHIC data from dAu collisions at 200 GeV per NN pair
Ratio of central to peripheral collisions:
RCP
RCPh (pT ) =
dNh
dpT
1NColl
central( )
dNh
dpT
1NColl
peripheral( )
PHENIX and STAR experiments found (2002)
RCPp (pT )>RCP
π (pT )
Can’t be explained by fragmentation.
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Anomaly #3 Jet structure
Hard parton jet { (p1) + (p2) + (p3) + ···· }
trigger particle associated particles
The distribution of the associated particles should be independent of the medium if fragmentation takes place in vacuum.
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Anomaly #3 Jet structure for Au+Au collisions is different from that for p+p collisions
pp
Fuqiang Wang (STAR) nucl-ex/0404010
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Azimuthal anisotropy Anomaly #4
Anomaly #5 Forward-backward asymmetry at intermediate pT
Come back later when there is time.
Resolution of the anomalies
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How can recombination solve the puzzles?
Parton distribution (log scale)
p
p1+p2p q
(recombine) (fragment)
hadron momentum
higher yield heavy penalty
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The black box of fragmentation
q
A QCD process from quark to pion, not calculable in pQCD
z1
Momentum fraction z < 1
Phenomenological fragmentation function
D/q
z1
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Let’s look inside the black box of fragmentation.
q
fragmentation
z1
gluon radiation
quark pair creation
Although not calculable in pQCD (especially when Q2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons.
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Description of fragmentation by recombination
known from data (e+e-, p, … )
known from recombination model
can be determined
hard partonmeson
fragmentationshower partons recombination
xD(x) =dx1x1
∫dx2
x2Fq,q (x1,x2)Rπ (x1,x2,x)
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Shower parton distributions
Fqq '(i )(x1,x2) =Si
q(x1)Siq ' x2
1−x1
⎛
⎝ ⎜ ⎞
⎠ ⎟
Sij =
K L Ls
L K Ls
L L Ks
G G Gs
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
u
gs
s
d
du
K =KNS+L
Ks =KNS +Ls
Sud,d ,u ,u(sea) =L
valence
sea
L L DSea
KNS L DV
G G DG L
Ls DKSea
G Gs DKG
R
RK
5 SPDs are determined from 5 FFs.
18Hwa & CB Yang, hep-ph/0312271
Shower Parton Distributions
u -> u valence
g -> u
u -> d
u -> s
g -> s
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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.
The recombination of thermal partons with shower partons becomes conceptually unavoidable.
D(z)
h
qA A
Conventional approach
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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.
The recombination of thermal partons with shower partons becomes conceptually unavoidable.
hNow, a new component
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Inclusive distribution of pions in any direction
r p
pdNπ
dp=
dp1p1
∫dp2
p2Fqq (p1,p2)Rπ (p1, p2,p)
dNπ
pdp=
1p3 dp10
p∫ Fqq (p1,p−p1)
pTPion Distribution
p1p2
pδ(p1 +p2 −p)
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Pion formation: qq distribution
thermal
shower
soft component
soft semi-hard components
usual fragmentation
(by means of recombination)
Fqq =TT+TS+(SS)1+(SS)2
Proton formation: uud distribution
Fuud =TTT+TTS +T(SS)1+(SSS)1+T(SS)2+((SS)1S)2+(SSS)3
T
S
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T(p1)=p1dNq
th
dp1=Cp1exp(−p1/T)
Thermal distribution
Fit low-pT data to determine C & T.
Shower distribution in AuAu collisions
S(p2)=ξ∑i ∫dkkfi(k)Sij(p2 /k)
hard parton momentum
distribution of hard parton i in AuAu collisions
SPD of parton j in shower of hard parton i
fraction of hard partons that get out of medium to produce shower
calculable
Contains hydrodynamical properties, not included in our model.
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fi (k) =dNi
hard
kdkdyy=0density of hard partons with pT = k
Input: parton distributions CTEQ5L nuclear shadowing EKS98 hard scattering pQCD
Srivastava, Gale, Fries, PRC 67, 034903 (2003)
dNjet
d2 pTdyy=0
=K C(1+pT / B)β
C, B, are tabulated for i=u, d, s, u, d, g K=2.5
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2-shower partons in 1 jet:
×Rπ (p1,p2,p)
Diπ (p/k)
Negligible at RHIC, but can be important at LHC.
(SS)1(p1, p2) =ξ dkk∫i∑ fi(k)Si
j(p1
k)Si
j'(p2
k −p1
)
2-shower partons in 2 jets:
(SS)2(p1,p2) =δyφξ dkk∫i∑ fi(k)Si
j (p1
k)×ξ dk'k' fi'(k' )Si'
j'(p2
k')∫
i'∑
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production in AuAu central collision at 200 GeV
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & CB Yang, nucl-th/0401001, PRC(2004)
TS
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Proton production in AuAu collisions
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
TTS+TSS
TSS
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Anomaly #1 Proton/pion ratio
resolved
33
d
d
central peripheral
more T more TS
less T less TS
RCPh (pT ) =
dNh
dpT
1NColl
central( )
dNh
dpT
1NColl
peripheral( ) ⇒
more TSless TS
>1
Anomaly #2 d+Au collisions (to study the Cronin Effect)
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d+Au collisions
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Hwa & CB Yang, nucl-th/0403001, PRL(2004)
Pions
No pT broadening by multiple scattering in the initial state.Medium effect due to thermal-shower
recombination.
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Proton
Thermal-shower recombination is negligible.
nucl-th/0404066
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Nuclear Modification Factor
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
RCPp >RCP
πbecause 3q p, 2q
Anomaly #2 resolved
37
Jet Structure
Since TS recombination is more important in Au+Au than in p+p collisions,
we expect jets in Au+Au to be different from those in
p+p.
Consider dihadron correlation in the same jet on the near side.
Anomaly #3 Jet structure in Au+Au different from that in p+p
collisions
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Trigger at 4 < pT < 6 GeV/c
p+p: mainly SS fragmentation Au+Au: mainly TS
Associated particle
p1 (trigger)
p2 (associated)
kq1
q2
q3
q4
ξ∑i ∫dkkfi(k)S(q1)T(q3)R(q1,q3,p1) trigger
S(q2)T(q4)R(q2,q4,p2) associated
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There are other contributions as well.
(TS) + [SS]
(SS) + [TS]
(SS) + [SS] too small for Au+Au
but the only term for p+p
trigger associated
(TS) + [TS]
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Associated particle distribution in p2 with trigger at p1
dNπ
dp2 p1
=
∑ i ∫dkkfi (k)dNππ
dp1dp2
(k)
∑ i ∫dkkfi(k)dNπ
dp1(k)
trigger at p1 integrated over 4 < p1 < 6 GeV/c
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
(TS)[TS]
(TS)[SS]+(SS)[TS]
(SS)[SS] for p+p collisions much lower
Central Au+Au collisions
+
42
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Central Au+Au collisions
Hwa & Yang, nucl-th/0407081
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Centrality dependence of associated-particle dist.
Distributions Ratios
Au+Au centrald+Au peripheral
d+Au centrald+Au peripheral
Jets in Au+Au and in p+p are very different.
Anomaly #3
p+p
resolved
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Azimuthal anisotropy
Anomaly #4
v2(p) > v2() at pT > 2.5
GeV/c
v2: coeff. of 2nd harmonic of distribution
PHENIX, PRL 91 (2003)
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Molnar and Voloshin, PRL 91, 092301 (2003).
Parton coalescence implies that v2(pT)
scales with the number of constituents
STAR data
46
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Anomaly #5 Forward-backward asymmetry at intermed. pT
backwardforward
in d+Au collisions
STAR preliminary data
47
More interesting behavior found in large pT and large pL region.
It is natural for parton recombination to result in forward-backward asymmetry
Less soft partons in forward (d) direction than in backward (Au) direction.
Less TS recombination in forward than in backward direction.
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Summary
Traditional picture
pT0 2 4 6 8 10
hardsoft
pQCD + FF
More realistic picture
pT0 2 4 6 8 10
hardsoft semi-hard
(low) (intermediate)
thermal-thermal thermal-shower
(high)shower-shower
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All anomalies at intermediate pT can be understood in terms of recombination of
thermal and shower partons
Recombination is the hadronization process.
At pT > 9 GeV/c fragmentation dominates, but it can still be expressed as shower-shower recombination.
Thus we need not consider fragmentation separately any more.
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Rapidity dependence of RCP in d+Au
collisions BRAHMS nucl-ex/0403005
RCP < 1 at
=3.2
Central more suppressed than peripheral collisions
Interpreted as possible signature of Color Glass Condensate.
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=0 RCP > 1
=3.2 RCP < 1
At forward rapidity, parton x is degraded (stopping) more for central than for peripheral
x distributions at various b accounted for by recombination
central < peripheral
RCP < 1 at large
BRAHMS data
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Forward RCP in d+Au collisions
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Forward pT spectra in d+Au collisions
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At very high pT and very high energy like at LHC, then the density of hard partons produced will be so high as to make jet-jet recombination very important .
The effect should be dramatic.
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Thermal partons
No prediction from our model (without hydro input) Fit data on spectrum for pT < 2GeV/c
C = 23.2 GeV-1 , T = 0.317 GeV
Shower partons
= 0.07
ξ fraction of hard partons that can get out of the dense medium to produce shower
Au+Au: adjusted to fit the data at intermediate pT.
ξ
d+Au: = 1ξ