Parton-Hadron Transition in Nuclear Physics

Haiyan Gao1,2

1. Duke University2. Massachusetts Institute of Technology

Nuclear Particle Physics Colloquium MIT

March 10, 2003

Two “Realms” of Nuclear Physics

Static potential between (lattice)

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qq

• Nucleon-meson degrees of freedom effective at low energies

• Quark-gluon degrees of freedom at high energies• Where is the transition?

Parton-Hadron Transition in Nuclear Physics

Simplest systems: pion, nucleon, deuteron– Form factors– Deuteron photodisintegration – Photopion production from nucleon

Photopion production from nuclei

Signatures for the transition?• Constituent quark counting rule (Brodsky-Farrar)

– Dimensional analysis– pQCD analysis– Support by experiments

• Hadron helicity conservation– Quark orbital angular momentum?

• What else (nuclei as laboratories)?– Nuclear filtering – Color transparency– Others….

Constituent Quark Counting

• Based on dimensional analysis, confirmed by short-distance pQCD analysis– Power law predictions for form factors:pion, nucleon,

deuteron ……

– Two-body exclusive process A+B -> C+D

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dσ

dt∝

1

sn−2f (θcm )

Charged Pion Elastic Form Factor

• Simplest valence quark structure

• pQCD is expected to manifest at relatively low momentum transfer

• Reputable pQCD and non-pQCD calculations exist

• The asymptotic pion form factor

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fπ (Q2) =12 fπ

2πCFα s(Q2)

Q2

Ratio for the Reaction

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π−/π +

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γ+ N → π + N

Huang and Kroll, Euro. Phys. J. C17 (2000)

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dσ (γn → π − p)

dσ (γp → π +n)≈ (

ued + seu

ueu + sed

)2

Charged Pion Ratio from Photoproduction

900 c.m.

900 c.m.

Nucleon Electromagnetic Form Factor

Spin-1/2 objectF1 (Dirac), 1/Q4 F2 (Pauli), 1/Q6

GE, GM: linearCombination ofF1 and F2

pQCD Analysis

Belitsky, Ji and Yuan carried out pQCD analysis (hep-0212351):

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Q2

ln2+

8

9β Q2

Λ2

F2(Q2)

F1(Q2)

→ const

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8

9β<<1

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β =11− 2n f /3

pQCD?

How far can one go?

11 GeV Proj.

Deuteron StructureSpin-1 nucleus, three form factors: GC, GQ, GM

Quark-gluon description

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A(Q2) = GC2 (Q2) +

8

9τ 2GQ

2 (Q2) +2

3τGM

2 (Q2)

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Fd = A ≈1

(Q2)5

Deuteron Form Factor

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dσ

dt∝

1

s10

Constituent quark countingpredicts for proton-protonelastic scattering

Deuteron Photodisintegration

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dσ

dt∝

1

s11

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γ+ d → p + n

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dσ

dt∝

1

s11

Data seem to show scaling at70 and 90 degree, onset ofscaling at higher energies issuggested at 36 and 52 degree

Simplest nuclear reaction

With MAD, deuteronPhotodisintegration cross-section can be extended to 7 GeVat forward angles (less than one month)

Hadron Helicity Conservation???

Recent data on protonform factor ratio frompolarization transfer measurements

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rγ + d →

r p + n

r γ + p →

r p + π o

e + d → e +r d

Orbital angular momentum

Virtual photon asymmetry:

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A1 =σ 1/ 2 −σ 3 / 2

σ 1/ 2 + σ 3 / 2

Data in disagreement with pQCD HHC based parameterization

Zheng et al, to be submitted to PRL

Polarization measurements in deuteron photodisintegration

Oscillatory Scaling (QCD oscillation)Proton-proton elastic scattering

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s10 dσ

dt

Interference picture

• Left: Born diagram (short-distance)

• Right: independent scattering amplitude (Landshoff)

• Interference between the two gives rise to oscillation, spin correlation anomaly, nuclear transparency bump

27Al(p,2p)

Origin of the oscillation?

• Interference between short-distance and long-distance amplitudes

• New resonance states associated with crossing a new quark flavor threshold

• Intriguing momentum transfer dependence

in nuclear transparency T from A(p,2p)

suggests nuclear filtering effect?

(suppression of long-distance amplitude in nuclear medium)

Generalized counting rule

Ji, Ma, Yuan (hep-ph/0301141) derived the following generalized counting rule involving parton orbital angular momentum:

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dσ

dΩ≈ s

−1− (n H + lzH −1)H

∑

When and minimal n, reduces to the counting Rule of Brodsky-Farrar, and Matveev-Muradian-Tavkhelidze

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lzH = 0

Why photopion production from nucleon?

• Pion has the simplest valence quark structure• Photopion production cross-section decreases

relatively slower with the increase of energy

Advantageous for the study of QCD oscillation

and the test of the generalized counting rule prediction by Ji, Ma and Yuan

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dσ

dt∝

1

s7

Jlab Experiment E94-104

• Three unique measurements:– Coincidence measurement

from deuterium target to investigate quark counting rule, from hydrogen

– Singles ratio over a large t range to test various predictions

– Coincidence measurement from 4He to form nuclear transparency

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γ+ n → π − + p

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π−

π +

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γ+ n → π − + p

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γp → π +n

E94-104 Experiment Layout

Fermi Momentum

Black:simulation

Red: data

Reconstructed Photon Energy Spectrum

E94-104 Results

Hints of oscillation?

• E94-104 data show global scaling behavior• Hints of oscillatory scaling?

JLab 12 GeV Projection

HRS (100 hrs)

HMS+SHMS (600 hrs)

JLab 12 GeV Projection

HRS+calorimeter (360 hrs)

Color transparency

A novel QCD effect based on:– Point like configuration (PLC) state is produced

in exclusive process at large momentum transfer

– PLC state experience reduced interactions inside the nuclear medium

– PLC state remains small while it propagates out of the nucleus

27Al(p,2p)

BNL A(p,2p) Experiments

JLab & SLAC results A(e,e’p)

FNAL A(π, dijet) Data

• Coherent π+ diffractive dissociation at 500 GeV/c

• using 12C and 195Pt nuclei (Q2>4kt2)

• from inclusive pion-nucleus scattering

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σ(A) = σ oAα

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α > 0.76

1.2

1.8

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α

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kT

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kT(GeV/c)

Incoherent Meson Production

0

HERMES (e,e’ ) with E = 27 GeV, A = Noe

14

A. Airapetian et al. , PRL 90, 052501 (2003)

T as a function of Q for fixed l has a slopeconsistent with CT.

2

C

Q ( GeV/c) 2 2

2.5σ deviation fromtraditional calculations

Nuclear Filtering (NF)• NF refers to the

suppression of large-distance quark separation in nuclear medium

• NF predicts oscillation in nuclear transparency 180o out-of-phase with free cross-section oscillation

• NF is an QCD effect complementary to CT

The interference picture and nuclear filtering effect is not the only explanation

New charm resonance state by Brodsky et al

Photopion production from nuclear targets

Transition in the nuclear medium– Color transparency effect

• Pion simple valence quark structure, more likely for point-like configuration

• Light nuclei more amenable to theoretical calculations

– Nuclear filtering effect • Relatively large photopion production cross-section

allows detailed study of the nuclear transparency

Nuclear Transparency from 4He

pn +→+ πγ≈T

E94-104

Results70 C.M. angle 90 C.M. angle

0 0

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γ+ n → π − p

More theoretical calculations of CT is needed

Preliminary E94-104results are interesting

Exact wave functionconfigurations can be used for 4He

HMS +SHMS (600 hrs)

Jain, Kundu, RalstonPhys. Rev. D 65 (2002) 094027

HMS +SHMS (600 hrs)

Summary

• Studies with the simplest nuclear systems are essential in understanding the transition region

• 12 GeV upgrade would provide an outstanding opportunity for this study

• The planned new detection systems are crucial for this study

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rγ + p → π o r

p

Short-distance pQCD is not the full picture!

Quark orbital angular momentum!

Important to look at the details of the scaling agreement!