future measurements to test recombination rudolph c. hwa university of oregon workshop on future...

Future Measurements to Test Recombination

Rudolph C. HwaUniversity of Oregon

Workshop on Future Prospects in QCD at High

Energy

BNL, July 20, 2006

2

Outline

• Introduction

• Recombination model

• Shower partons

• Hadron production at low pT

• Hadron production at large

• Hadron production at large pT

• Summary

1xF

pT

3

I. Introduction

What are the properties of recombination that we want to know and test?

What partons?

q1,q2

p0 dNπ

dp=

dq1q1∫

dq2q2

Fqq(q1,q2 )Rπ (q1,q2 , p)

Fqq (q1,q2 ) probability of finding partons at

Rπ (q1,q2 , p) probability for recombination to form a pion at pSame partons? What is that

probability?

4

Usual strong evidences for recombination

number of constituent quarks scaling

v2

partons CQ ↔

What about gluons?

Rp /π of order 1 or higher

impossible by fragmentation

Useful to remember in future measurements

5

dNππ

p1dp1p2dp2=

1(p1p2 )

2

dqi

qii∏⎡

⎣⎢

⎤

⎦⎥∫ F4 (q1,q2 ,q3,q4 )R(q1,q3, p1)R(q2 ,q4 , p2 )

Two-particle correlation

q1,q2 ,q3,q4

Where are the partons from? Are they independent? Are they from 1 jet, 2 jets, or thermal medium?

Quantitative questions about recombination eventually always become questions about the nature of partons that are to recombine.

6

Multiparton distributions in terms of the thermal and shower parton distributions

Fqq (q1,q2 )=TT +TS+ SS

Fuud (q1,q2 ,q3)=TTT +TTS+TSS+SSS

F4 (q1,q2 ,q3,q4 )=(TT +TS+SS)13(TT +TS+SS)24

7

II. Recombination ModelRecombination depends on the wave function of the hadron.

Constituent quark model describes the bound-state problem of a static hadron.

What good is it to help us to know about the distribution of partons in a hadron (proton)?

Valons

Valons are to the scattering problem what CQs are to the bound-state problem.

8

Deep inelastic scattering

ee

p

Fq

We need a model to relate to the wave function of the proton

Fq

Valon modelp

U

U

Dvalons

Hwa, PRD 22, 759 (1981)

9

p

U

U

D

Basic assumptions

• valon distribution is independent

of probe

• parton distribution in a valon is independent of the host hadron

xuv (x,Q2 )= dy2GUx

1

∫ (y)KNS(xy,Q2 )

xdv (x,Q2 )= dyGDx

1

∫ (y)KNS(xy,Q2 )

valence quark distr in proton

valon distr in proton, independent of Q

valance quark distribution in valon, whether in proton or in pion

10

Hwa & CB Yang, PRC66(2002) using CTEQ4LQ

11

Recombination function

It is the time-reversed process of the valon distributions

pU

U

D

proton Rp(x1,x2,x3,x) =x1x2x3

x3 GUUDp (

x1

x,x2

x,x3

x)=g(

x1x2

x2 )2.76(x3

x)2.05δ(

x1

x+

x2

x+

x3

x−1)

pion Rπ (x1,x2,x) =x1x2

x2 GUD π (

x1

x,x2

x)=

x1x2

x2 δ(x1

x+

x2

x−1)

From π initiated Drell-Yan process

xqvπ(x) =Ax0.64(1−x)1.11 valon

model Gπ (y1,y2) =δ(y1 +y2 −1)

pU

U

Drecombination function

valon distribution

12

In a pp or AA collision process

U

D_

π+

Is entropy reduced in recombination?

The number of degrees of freedom seems to be reduced.

Soft gluon radiation --- color mutation

without significant change in momentum

The number of degrees of freedom is not reduced.

13

How do gluons hadronize?

In a proton the parton distributions are

Gluons carry ~1/2 momentum of proton but cannot hadronize directly.

Sea quark dist. Fq ~ c (1-x)7

Saturated sea quark dist. F’q ~ c’

(1-x)7

Gluon conversion to q-qbarq

q

g

Recombination of with saturated sea gives pion distribution in agreement with data.

qq

x2u(x)

x2g(x)

x [log]

14

III. Shower Partons from Fragmentation Functions

The black box of fragmentation

πq

A QCD process from quark to pion, not calculable in pQCD

z1

Momentum fraction z < 1

15

Description of fragmentation by recombination

known from data (e+e-, p, … )

can be determined

hard partonmeson

fragmentationshower partons recombination

xD(x) =dx1x1

∫dx2

x2Fq,q (x1,x2)Rπ (x1,x2,x)

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xDM (x)=dx1x1∫

dx2x2

Fq,q(x1,x2 )RM (x1,x2 ,x)

xDB (x)=dx1x1∫

dx2x2

dx3x3

Fqqq(x1,x2 ,x3)RB(x1,x2 ,x3,x)

Meson fragmentation function

Baryon fragmentation function

S(xi)

DGp DG

Λand can be calculated in the RM

17

DGM → DG

B Has never been done before in the 30 years of studying FF.

This is done in the RM with gluon conversion shower partons valons hadrons.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.



Hwa & CB Yang, PRC 73, 064904 (2006)

18

IV. Hadron production at low pT

EdNπ

dpL

≡H(x) =dx1x1

∫dx2

x2

Fqq (x1,x2)Rπ (x1,x2,x)

.

p p

x

H(x)

First studied in pp collision.

Fu x1( )Fd x2( )Parton distributions at low Q2

Hwa, PRD (1980)

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Hadronic collisions Hwa & CB Yang, PRC 66, 025205

(2002) h + p h’ +X

h h’

p π π π

K+ ππ+ K

+_

Suggested future measurement

Better data at higher energy for p π, K, p, Y

FNAL PL=100 GeV/c (1982)

20

Leading and non-leading D production

π±+ p→ D±(m) + X

Leading (same valence quark)

non-leading (sea quark)

A =σ(leading)−σ(nonleading)σ(leading)+σ(nonleading)

Asymmetry

Hwa, PRD 51, 85

(1995)

Suggested future measurement:xdN

dx(p→ D±)

21

pA collisions

p + A→ h+ Xh bears the effect of momentum degradation --- “baryon stopping”.

NA49 has good data, but never published.

p + Pb→ (p−p) + X p + Pb→ (n−n) + X

(no target fragmentation, only projectile fragmentation)

Hwa & CB Yang, PRC 65, 034905 (2002)

Shape depends on degradation. Normalization not adjustable.Suggested future

measurement:Measure

dN

dx(p + A→ h±+ X)

Need to know well the momentum degradation effect.

for all x at higher energy

22

Transfragmentation Region (TFR)

A + A→ h+ X

Theoretically, can hadrons be produced at xF > 1?It seems to violate momentum conservation, pL > √s/2.

In pB collision the partons that recombine must satisfy

xii∑ <1

p

B

But in AB collision the partons can come from different nucleons

BA

xii∑ >1

(TFR)

In the recombination model the produced p and π can have smooth distributions across the xF = 1 boundary.

23

proton-to-pion ratio is very large. QuickTime™ and a

TIFF (LZW) decompressorare needed to see this picture.



proton

pion

Hwa & Yang, PRC 73,044913 (2006)

: momentum degradation factor

Regeneration of soft parton has not been considered.


Determine the xF distribution in the TFR

Particles at xF>1 can be produced only by recombination.

24

V. Large BRAHMS data show that in d+Au collisions there is suppression at larger . QuickTime™ and a

TIFF (LZW) decompressorare needed to see this picture.

BRAHMS, PRL 93, 242303 (2004)

Hwa, Yang, Fries, PRC 71, 024902 (2005).

No change in physics from =0 to 3.2

In the RM the soft parton density decreases, as is increased (faster for more central coll).


dN

dpTdpTfor π and p

25

BRAHMS, nucl-ex/0602018

AuAu collisions

26

TT

TS

TTT

xF = 0.9

xF = 0.8 TFR

xF = 1.0

?

27

No jet => no associated particles

pT distribution fitted well by recombination of thermal partons


• Focus on xF>1 region.• Determine p/π ratio.• Look for associated particles





Hwa & Yang (2006)

28

VI. Hadron production at large pT, small pL

A. Cronin Effect

Cronin et al, Phys.Rev.D (1975)

α >1dN

dpT(pA→ hX) ∝ Aα , for h= both π and p

This is an exp’tal phenomenon. Not synonymous to initial-

state kT broadening.In the RM we have shown that final-state recombination alone (without initial-state broadening) is enough to account for CE.

We obtained it for both π and p -- impossible by fragmentation. Hwa & Yang, PRL 93, 082302 (2004); PRC 70, 037901 (2004).


Measure and ratios in d+Au collisions at all , both backward and forward.

Λ / Kp /π

29

Backward-forward Asymmetry

If hadrons at high pT are due to initial transverse broadening of parton, then

• backward has no broadening

• forward has more transverse broadening

RM has B/F>1, since dN/d of soft partons decrease as increases.


Measure p and π separately at larger range of , and for different centralities.

Expects more forward particles at high pT than backward particles



B

F

30

is larger than

Aud

associated yield in this case

x=0.7x=0.05

Correlation shapes are the same, yields differ by x2.

Aud

x=0.05x=0.7

associated yieldin that case

Degrading of the d valence q?

STAR (F.Wang, Hard Probes 06)

Soft partons -- less in forward, more in backward

RM => less particles produced forward, more backward

31

B. p/π Ratio


are needed to see this picture.All in recombination/ coalescence model

Success of the recombination model

Measure the ratio to higher pT

If it disagrees with prediction, it is not a breakdown of the RM. On the contrary the RM can be used to learn about the distributions of partons that recombine.

32

C. Strange particles







642

Hwa & CB Yang, nucl-th/0602024

Data from STAR nucl-ex/0601042

This is not a breakdown of the RM. We have not taken into account the different hyperon channels in competition for the s quark in the shower.

40% lower

30% higher

33

production





130 GeV

production

smallmore suppressed



34

We need to do more work to understand the upbending of .

It is significant to note that thermal partons can account for the ratio up to pT=4 GeV/c.

QGP: s quarks enhanced & are thermalized.

We have assumed RFs for & that may have to be modified.

35

If and are produced mainly by the recombination of thermal s quarks, then no jets are involved.

Select events with or in the 3<pT<5 region, and treat them as trigger particles. Look for associated particles in the 1<pT<3 region.

Predict: no associated particles giving rise to peaks in , near-side or away-side.


Verify or falsify that prediction

36

2. Correlation of pions in jetsTwo-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

q1

q4

q2

C2(1,2)=ρ2(1,2)−ρ1(1)ρ1(2)

ρ2(1,2)=dNπ1π2

p1dp1p2dp2

ρ1(1) =dNπ1

p1dp1



This can be measured.

G2(1,2)=C2(1,2)

ρ1(1)ρ1(2)[ ]1/ 2

Hwa & Tan, PRC 72, 024908 (2005)

D. Jet Correlations1. Correlation of partons in jets is negative

but not directly measurable

37

3. D(zT)Trigger-normalized fragmentation

functionTrigger-normalized momentum fraction

zT =pT (assoc)pT (trig)

X.-N. Wang, Phys. Lett. B 595, 165 (2004) J. Adams et al., nucl-ex/0604018

STAR claims universal behavior in D(zT)

fragmentation

Focus on this region

violation of universal behavior due to medium effect ---- thermal-shower recombination

38


Study zT ~ 0.5 with pT(trigger) ~ 8-10

GeV/c pT(assoc) ~ 4-5 GeV/c Measure p/π ratio of associated particles.

My guess: R(p/π) >> 0.1

if so, it can only be explained by recombination.

Do this for both near and away sides.

39

4. Three-particle correlation

Conical Flow vs Deflected Jets

Mediumaway

near

deflected jets

away

near

Medium

mach cone

Medium

away

near

di-jets

0

0π

π

Ulery’s talk at Hard Probes 06

40

Signal Strengths

Au+Au Central 0-12% Triggered

Δ1

Δ2

d+Au

Δ1

Δ2

• Evaluate signals by calculating average signals in the boxes.• Near Side, Away Side, Cone, and Deflected.

41

• What is the multiplicity distribution (above background) on the away side?

• If n=2 is much lower than n=1 events (on away side), then the Mach-cone type of events is not the

dominant feature on the away side.

• What is the p/π ratio (above background) on the away side?

• Evolution with higher trigger momentum should settle the question whether cone events are realistic.

• Whatever the mechanism is, hadronization would be by recombination for pT<6 GeV/c.

More studies are needed.

42

5. Using Factorial Moments to suppress statistical background event by event.

Factorial moment for 1 event

fq =1M

njj=1

M

∑ (nj −1)⋅⋅⋅(nj −q+1)

Normalized factorial moment

Fq = fq / f1q

Event averaged NFM Fq

(a) background only (b) bg + 1jet

(c) bg + 2jets

Try it out, but it is not a way to test recombination.

Chiu & Hwa, nucl-th/0605054

43

VII. Two-jet Recombinationπ and p production at high pT at LHCNew feature at LHC: density of hard partons is high.

High pT jets may be so dense that neighboring jet cones may overlap.

If so, then the shower partons in two nearby jets may recombine.

2 hard partons

1 shower parton from each

π p

44





Proton-to-pion ratio at LHC -- probability of overlap of 2 jet cones

Hwa & Yang, PRL (to appear),

nucl-th/0603053

single jet

If (pT)~pT-7,

then we get

45

The particle detected has some associated partners.

There should be no observable jet structure distinguishable from the

background.

10 < pT < 20 GeV/c

That is very different from a super-high pT jet.

But they are part of the background of an ocean of hadrons from other jets.

A jet at 30-40 GeV/c would have lots of observable associated

particles.

46

We predict for 10<pT<20 Gev/c at LHC• Large p/π ratio

• NO associated particles above the

background


Verify or falsify these two predictions

47

Summary

In general, all hadrons produced with pT<6 GeV/c are by recombination.

Specifically, many measurements have been suggested.

Good signatures: large Rp/π

in some regions no particles associated with high pT trigger.

After recombination is firmly established,the hadron spectra can be used to probe the

distributions of partons that recombine.

48

Backup slides

49

Let’s look inside the black box of fragmentation.

πq

fragmentation

z1

gluon radiation

quark pair creation

50

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 DπSea

KNS L DπV

G G DπG L

Ls DKSea

G Gs DKG

Rπ

RK

5 SPDs are determined from 5 FFs.

assume factorizable, but constrained kinematically.

No gluon column

51

Shower Parton Distributions

Hwa & CB Yang, PRC 70, 024904 (04)

52

D. Jet Correlations

1. 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)

r2(1,2) =ρ2(1,2)

ρ1(1)ρ1(2)x1 +x2 ≤1

ρ2 (1,2) = Sij (x1),Si

j '(x2

1− x1

)⎧⎨⎩

⎫⎬⎭

0

The two shower partons are correlated.



C2 (1,2)=[r2 (1,2)−1]ρ1(1)ρ1(2)

no correlation

Hwa & Tan, PRC 72, 024908 (2005)

No way to measure this directly.

53

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%



Also, cannot be measured directly.

future measurements to test recombination rudolph c. hwa university of oregon workshop on future...

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