Apr 18, 2023 Jan Rak 1

Jet properties from dihadron and Jet properties from dihadron and photon hadron correlations at photon hadron correlations at

s=200 GeVs=200 GeV

Jet properties from dihadron and Jet properties from dihadron and photon hadron correlations at photon hadron correlations at

s=200 GeVs=200 GeV

Jan RakJan RakJyvaskyla University & HIP, Finland

for the PHENIX collaboration

Jan RakJan RakJyvaskyla University & HIP, Finland

for the PHENIX collaboration

Apr 18, 2023 Jan Rak 2

Single inclusive vs two particle Single inclusive vs two particle correlations correlations

Inclusive distributions - despite the great success in the theoretical understanding RAA there is somewhat limited sensitivity to details of parton interaction with QGP–Energy loss, surface bias - different models similarity vs p RAA quark vs gluon RAA similarity vs direct gamma RAA similarity–Light vs heavy quark RAA (non-photonic electron) similarity

Two particle correlations - more detailed view into a nature of parton interactions with QCD medium. Access to parton intrinsic momentum kT -> soft pQCD radiation, jet shape parameters jT -> induced radiation, fragmentation function -> energy loss.–Di-hadron correlations and conditional yields–Direct photons-hadron correlations in p+p @ s=200 GeV

Apr 18, 2023 Jan Rak 3

Medium tomography: T. Renk, K. Eskola hep-ph/0610059

nucl-ex/0611018 (Phys. Rev. Lett.)

Eskola et al. NPA696 (2001) 729

gluons in Pb / gluons in p

x

AntiShadowing

Shadowing

Apr 18, 2023 Jan Rak 4

Elastic vs Radiative energy lossElastic vs Radiative energy lossS. Wicks et al., nucl-th/0512076

Partonic Energy Loss

Radiative 2N processes. Final state QCD radiation as in vacuum (p+p coll) - enhanced by QCD medium.

Elastic 22 LO processes

8 LO subprocesses

q ′q → q ′q 49

s2 +u2

t2

qq→ qq 49

s2 +u2

t2+

s2 + t2

u2

⎡

⎣⎢

⎤

⎦⎥

qq→ q ′q 49

t2 +u2

s2

......

8 LO subprocesses

q ′q → q ′q 49

s2 +u2

t2

qq→ qq 49

s2 +u2

t2+

s2 + t2

u2

⎡

⎣⎢

⎤

⎦⎥

qq→ q ′q 49

t2 +u2

s2

......

Elastic E models predict stronger broadening of away-side correlation peak - not seen in the data. Also various models differ significantly in radiative/elastic fraction.

Apr 18, 2023 Jan Rak 5

ppTT broadening only in broadening only in DIS?DIS?

Pasquale Di Nezza HERMES

??

away-side widths similar for central and peripherald+Au 0.24+-0.07 radAu+Au 20-40% 0.20+-0.02 radAu+Au 0-5% 0.22+-0.02 rad

away-side widths similar for central and peripherald+Au 0.24+-0.07 radAu+Au 20-40% 0.20+-0.02 radAu+Au 0-5% 0.22+-0.02 rad

STAR Phys.Rev.Lett.97:2006

8 < pT(trig) < 15 GeV/c

Apr 18, 2023 Jan Rak 6

Inclusive nuclear suppression factor RAA is not quite sensitive to the particular dE/dx mechanism - is it due to the surface bias?

Light and heavy quarks suppression looks similar:

Quarks and gluons suppression looks similar:

Direct photon suppression at high pT looks similar:

Some of the open questions Some of the open questions

RAAc−quark ≈RAA

u,d

RAAquark ≈RAA

gluon

RAAq,g ≈RAA

gamma

It is evident that the detailed understanding of unmodified parton properties

CRUTIAL

Apr 18, 2023 Jan Rak 7

pQCD quenching - modification pQCD quenching - modification of D(z) of D(z)

1( )

1 1 1

zD z D

E E E

⎛ ⎞≈ ⎜ ⎟− −⎝ ⎠

%

Wang, X.N., Nucl. Phys. A, 702 (1) 2002

( ) / ; ( ) / ( )D z dN dz z p fragment p jet≡ =

=ln(EJet/phadron)

pThadron~2 GeV for

Ejet=100 GeV

Borghini and Wiedemann, hep-ph/0506218

• MLLA: parton splitting+coherence angle-ordered parton cascade. Theoretically controlled, experimentally verified approach

• Medium effects introduced at parton splitting

Apr 18, 2023 Jan Rak 8

Azimuthal correlation function in Azimuthal correlation function in pp++pp @ @ s=200 GeVs=200 GeV

d+Au

Phys.Rev.D74:072002,2006

N

A

N jT jet fragmentation transverse momentum

F kT parton transverse momentum

YA folding of D(z) and final state parton dist.

p + p jet + jet

Apr 18, 2023 Jan Rak 9

Jet shape evolution with trigger and Jet shape evolution with trigger and assoc. assoc. ppTTAu+Au / p+p s = 200 GeV

arXiv:0705.3238 [nucl-ex]

Per-trigger yield vs. for various trigger and partner pT (pA

T pBT), arranged by

increasing pair momentum (pAT + pB

T)

• Flat region:

celebrated b2b disappearance

• Punch through region (HR):

reappearance at high-pT

• Shoulder region (SR):

Medium induced “Mach cone”

•Low pT:

Enhancement in SR & suppression in HS

•High pT:

Reappearance of away-side jet not due to merging of side peaks

Apr 18, 2023 Jan Rak 10

Dihadron correl. AuDihadron correl. Au++AuAu @ @ s=200 GeVs=200 GeV

RHS =Yjet( )d

HR∫Yjet( )d

SR∫

RHS =Yjet( )d

HR∫Yjet( )d

SR∫

Truncated mean 1<pTa<5 GeV/cTruncated mean 1<pTa<5 GeV/c

The width and the truncated pT of the shoulder peak are more **similar to the near peak** rather to the away side one

The width and the truncated pT of the shoulder peak are more **similar to the near peak** rather to the away side one

Apr 18, 2023 Jan Rak 11

Mach cone ?Mach cone ?

Consistent with p+p

Narrower by 20%

Mach cone significantly narrower (by 20%) as compared to peripheral away peak. Is Mach cone narrower than Delta function??

Mach cone significantly narrower (by 20%) as compared to peripheral away peak. Is Mach cone narrower than Delta function??

Apr 18, 2023 Jan Rak 12

Details on two-particle Details on two-particle correlations in correlations in pp++pp

Fragmentation function D(z) and

Intrinsic momentum kT

Fragmentation function D(z) and

Intrinsic momentum kT

Apr 18, 2023 Jan Rak 13

Soft + hard QCD Soft + hard QCD radiationradiation

k kTT phenomenology phenomenology

dd

=δ( −) dd)qT

pTγ=δ()qT −pTγ )

dd

=δ( −) dd)qT

pTγ=δ()qT −pTγ )

Back-to-back balanced

Soft QCD radiationSoft QCD radiation

dd

∝Gauss( ) dd)qT

pTγ∝Gauss(pTγ )

dd

∝Gauss( ) dd)qT

pTγ∝Gauss(pTγ )

dd

∝1

−n dd)qT

pTγ∝

1pTγ

−n

dd

∝1

−n dd)qT

pTγ∝

1pTγ

−n

Hard NLO radiationHard NLO radiation

q + g→ quark( )qT ) +photon(pTγ )Compton photo-production

Apr 18, 2023 Jan Rak 14

kT2 =

2

pT ,pair2 = kT

2

intrinsic+ kT

2

soft+ kT

2

NLOkT

2 =2

pT ,pair2 = kT

2

intrinsic+ kT

2

soft+ kT

2

NLO

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Phys. Rev., 1981, D23, 604

PHENIX

Resummation techniques:D. Boer and W. Vogelsang,Phys. Rev. D69 (2004) 094025 J. Qiu and I. Vitev,Phys. Lett. B570 (2003) 161

dd)qT

pTγ∝ exp(−)qT

2 ) ⊗ )qT−n

dd)qT

pTγ∝ exp(−)qT

2 ) ⊗ )qT−n

Apr 18, 2023 Jan Rak 15

Correl. fcn width - Correl. fcn width - kkTT and and acoplanarityacoplanarity

€

pout = 2 kTy

pTa

ˆ p Ta

⇒ pout2 = zt kT

2 xh

ˆ x h

pT,pair Lorentz boost preserves

€

M inv2 = 4 ˆ p T

2 = 2 ˆ p Ttˆ p Ta − 2 ˆ

r p Tt

ˆ r p Ta

€

ˆ x h =ˆ p Ta

ˆ p Tt

xh =pTa

pTt

€

ˆ x h−1 zt kT

2 = xh−1 pout

2 − jTy2 (1+ xh

2)partonic hadronic

Jet momenta imbalance due to kT smearing

Lab frame

Hard scattering rest frame

From an analysis of associated yield

Apr 18, 2023 Jan Rak 16

Assoc. yield - “Averaged” pQCD Assoc. yield - “Averaged” pQCD approachapproach

Assumptions (Phys.Rev.D74:072002,2006 for details) :

1. Invariant mass of mass-less partons in hard-scattering CMS and in LAB is the same -> non-Gaussian kT-smearing

2. Effective FS parton distribution:

3. Effective Fragmentation function:

,,γ to be extracted from fit to gamma-h or LEP

One can then evaluate:

1. Inclusive 0 cross section

2. Trigger 0 associated dist.

1'

2

1( ) ( )

T

TQ

T T x

d dz pD z

p dp z z = ⋅ ⋅Σ∫

1'

2

1( ) ( )

T

TQ

T T x

d dz pD z

p dp z z = ⋅ ⋅Σ∫

( ) (1 ) (1 )D z z z z γ= ⋅ − ⋅ +( ) (1 ) (1 )D z z z z γ= ⋅ − ⋅ +

€

ΣQ ( ˆ p T )∝ ˆ p T−n

€

ΣQ ( ˆ p T )∝ ˆ p T−n

M inv2 =4 p̂T

2 =2 p̂Tt p̂Ta −2 ˆrpTt ˆ

rpTa M inv

2 =4 p̂T2 =2 p̂Tt p̂Ta −2 ˆ

rpTt ˆ

rpTa

Apr 18, 2023 Jan Rak 17

Trigger associated spectra are Trigger associated spectra are insensitiveinsensitive to to D(z)D(z)

LEP data MJT Approximation - Incomplete Gamma function when assumed power law for final state PDF and exp for D(z)

xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosφ≈−pTa

pTt

yield

d

dpTt

=1

pTtn−1 dztzt

n−2

xTt

1

∫ e−b.zt ≈ m (n−1)1)xh

1+xE)xh

⎛

⎝⎜⎞

⎠⎟

−n

Apr 18, 2023 Jan Rak 18

Unavoidable Unavoidable zz-bias in di-hadron -bias in di-hadron correlationscorrelations

z-bias; steeply falling/rising D(z) & PDF(1/z)

ztrig

zassoc

Varying pTassoc with pTtrigger kept fixed leads to variation of both trigger and associated jet energies.

Fixed trigger particle Fixed trigger particle momentummomentum

does notdoes not fixfix

the the jet energyjet energy!!

Angelis et al (CCOR):Nucl.Phys. B209 (1982)Angelis et al (CCOR):Nucl.Phys. B209 (1982)

Apr 18, 2023 Jan Rak 19

kkTT bias bias

pT ,γ ∝Gauss( kT

2 )⊗1)pT8

Small kT (Gauss) and large pT power law

less probable than

Large kT (Gauss) and small pT power law

Even at relatively high photon momentum (10 GeV/c) γ-h pairs still not fully in power law pQCD regime.

Apr 18, 2023 Jan Rak 20

kk22TT and and zztt in p+p @ 200 GeV from in p+p @ 200 GeV from

00-h CF-h CFPhys.Rev.D74:072002,2006

For D(z) the LEP date were used. Main contribution to the systematic errors comes from unknown ratio gluon/quark jet => D(z) slope.

Base line measurement for the kT broadening - collisional energy loss. Direct width comparison is biased.

Still, we would like to extract FF from our own data -> direct photon-h correl.

Apr 18, 2023 Jan Rak 21

High pHigh pTT: ref. for HI, : ref. for HI, resummation, detailed NLO testsresummation, detailed NLO tests

PHENIX measured pTpair=3.360.090.43GeV/c

extrapolation to LHC k2T36 GeV2/c2

G.G. Barnaföldi, P.Levai

Apr 18, 2023 Jan Rak 22

Avoidable in Direct Photons Avoidable in Direct Photons CorrelationsCorrelations

q

qg

γ q

q g

γ

Compton Annihilation

q

q

q

q

g

g

g

γγ

Bremsstrahlung

Direct Photon Processes

These two diagrams fix the jet energy scale

Up to the kT effect !

Fragmentation photons measured using isolation cut analysis

ztrig =1±kT / )pT Q2 ≈const dN/dzassoc ∝ D(z)

Apr 18, 2023 Jan Rak 23

Direct Direct γγ-h Correlations in PHENIX p+p -h Correlations in PHENIX p+p s=200 GeVs=200 GeV

Run 5 p+p @ 200 GeV

5-7 X 1-2 GeV/c 7-9 X 1-2 GeV/c

5-7 X 2-5 GeV/c 7-9 X 2-5 GeV/c 9-12 X 2-5 GeV/c

9-12 X 1-2 GeV/c

Statistical Subtraction method:

γdirect = γall - γdecay

Matthew Nguyen APS Spring Meeting, April 15,

2007

• Signature small near-side correlation signal apparent

• Yield sensitive to contribution at the near-side

• Still room for some fragmentation contribution

Apr 18, 2023 Jan Rak 24

0 Direct γ

PHENIX PHENIX s=200 GeV s=200 GeV 00 and dir- and dir-γγ assoc. assoc. distributionsdistributions

Run 5 p+p @ 200 GeVStatistical Subtraction Method

Arb

itrar

y N

orm

aliz

atio

n

Arb

itrar

y N

orm

aliz

atio

n

Matthew Nguyen APS Spring Meeting, April 15, 2007

Exponential slopes still vary with trigger γ pTγ.

If dN/dxEdN/dz then the local slope should be pTγ independent.

xE =

rpTa ⋅

rpTtr

pTt2 =−

pTa

pTt

cosφ≈−pTa

pTt

FF slope

Apr 18, 2023 Jan Rak 25

Pythia Initial/Final st. Pythia Initial/Final st. radiation & radiation & kkTT

Initial/Fina state radiation OFF, k

2T=0 GeV/c

Initial/Fina state radiation OFF, k

2T=0 GeV/c

Initial/Fina state radiation ON, k

2T=5 GeV/c

Initial/Fina state radiation ON, k

2T=5 GeV/c

Apr 18, 2023 Jan Rak 26

Photon associated yields - Photon associated yields - “averaged” pQCD“averaged” pQCD

P()pTt &

)pTa ) )

pT

)pTt +

)pTa)pTt

)pTa −)pT2

exp( )pTt +

)pTa)2 −4 )pT

2

2 kTx2

⎛

⎝⎜⎜

⎞

⎠⎟⎟

)pTt =gamma mom.

P()pTt &

)pTa ) )

pT

)pTt +

)pTa)pTt

)pTa −)pT2

exp( )pTt +

)pTa)2 −4 )pT

2

2 kTx2

⎛

⎝⎜⎜

⎞

⎠⎟⎟

)pTt =gamma mom.

dN

dpTa pTt

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ )pTt P()pTt &

)pTa) )pT

dN

dpTa pTt

=D(zt)⊗ ΣQ' (

pTt

zt

)⊗ d∫ )pTt P()pTt &

)pTa) )pT

kT bias still important, sensitivity to the D(z) shape as expected, the slope is also changing as in the data - parton imbalance.

PYTHIA

Apr 18, 2023 Jan Rak 27

LO in LO in S S and BDMPS quenching and BDMPS quenching weightweight

F. Arleo, hep-ph/0701207

Absolutely no matching between dNd/z and D(z). This is because of the important contribution of the fragmentation-photon channel, as well as the restricted kinematical z window.

Apr 18, 2023 Jan Rak 28

SummarySummaryInclusive and two-particle correlation measurement in the high-pT sector at RHIC opened a new window into a QGP physics. Inclusive measurements have limited discrimination power -> complementary multiparticle correlations are important. However, two-particle correlations are not bias-free either:

di-hadron correlations:

• kT and initial/final state QCD radiation, resummation vs NLO

• jT near-side jet shape modifications

• z-bias washes out the sensitivity of the associated xE yield to the Fragmentation Function.

direct photon-hadron correlations

• Fragmentation function can be extracted from the associated xE yield. However

• kT-bias still present - pushes the minimum photon-trigger pT above 10 GeV/c at RHIC.