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Study of Color Transparency in Exclusive Vector Meson
Electroproduction off Nuclei
Kawtar Hafidi
Hall C Summer WorkshopFriday August 25th, 2006
2K. Hafidi Friday August 25th, 2006 Hall C Summer Workshop
COLLABORATION
J. Arrington , D. F. Geesaman, R. J. Holt, B. Mustapha, D. H. Potterveld, P. E. Reimer
Argonne National Laboratory
Graduate Students:Lamiaa El Fassi (ANL)Lorenzo Zana (UNH)
Spokespersons:K. Hafidi and B. Mustapha (ANL)
M. Holtrop (UNH)
And CLAS Collaboration
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Overview
Physics Motivation
EG2 Experiment
Preliminary Results
Summary and Outlook
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Origin of CT
Discovery by Perkins (1955) of the(Dalitz) decays in emulsion of π0 (∼ 200 GeV) produced in cosmic rays π0 → e+ e- γ
The ionization produced by the pair was small near the decay point, increasing with distance from vertex
This surprising observation was quickly interpreted by Chudakov (1955) in the framework of QED: A pair of oppositely charged particles interacts in the medium with a dipole cross-section
⇒ this cross-section (σ ≅ l2) vanishes near the creation point
le+
e-γ
γ
π0
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Color Transparency is a spectacular prediction of QCD:
Under the right conditions, the nuclear matter will allow the
transmission of hadrons with reduced attenuation. Such a
phenomenon is totally unexpected in a hadronic picture
of
strongly interacting matter, but straightforward in
quark
gluon basis, this is one of the features which makes it so
interesting.
In early 80’s, Brodsky and Mueller applied the notionof transparency to QCD and to color charge
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Unless the struck quark shares the momentum transfer with the other quark, the pion fragments and the reaction is inelastic
As Q increases, the exchange of the gluon has to be fast.Causality (no interaction is faster than speed of light) ⇒ the quark’s pair has to be localized within a transverse size of
1/Q
Right Conditions ⇒ Selection of Point LikeConfigurations (PLC) via hard exclusiveprocesses γ(Q2)
π
π
Electromagnetic form factor of the pion in the Breit frame
Hard: high momentum transfer
Exclusive: completely determined initial and final states. Elastic processes are special cases
q
q-bar
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In QCD the color field of a color neutral object vanishes as the size of the objectis reduced
BecauseThe field of individual quarks and gluons cancel each other as the size is reduced by analogy to QED
ThereforeThe interaction cross-section has a dipole form
σ ≅ l2
l is the separation between the constituents
Color screening: PLC experiences reduced interaction in the nucleus
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Hadronic point of view of CT & PLC formation time
The point like aspect is seen as a consequence of coherent superposition of large number of resonances with specific weights
CT is understood as a coherence of the scattering of these resonances inside the nucleus
The formation of PLC is a function of the typical excitation energy of the system
222*21 MEME hhf
+−+≅τ
Assuming ν ≅ Eh ≅ p
22*
2MMf −
≅ντ
|i⟩ |i⟩ |i⟩ |i⟩ |i⟩ |l⟩ |k⟩ |i⟩
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What can we learn from studying CT ?
|Meson⟩ = Z0 |q q-bar⟩ + Z1 |q q-bar q q-bar⟩ + …..PLC is by definition a product of short distances: it can only come fromvalence component (higher order are reduced by a factor αs)
CT mechanism selects the simplest component of the hadron wave-funBy analogy to lattice QCD, we are in the “quenched approximation”
All the physics programs build around CT idea would allow us not onlyto access special configurations of the hadron wave-function but also tstudy how this configuration dresses with time to form the asymptotic wave-function of the hadron with all its complexity
We are here in the heart of the dynamics of confinement !
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The nucleus, a unique laboratory of quark dynamics
Characteristic proper time scale is τ0 ∼ 1 fm
τ0 is the time needed by a quark to travel distances typical of the confined systems
Taking into account Lorentz dilation, the proper time scales in
the Lab frame become τ = (Ε/Μ) τ0 ∼ few fm
The only medium available for these scales is the nucleus !
The nucleus is playing the role of the bubble chamber !
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ρ0 electroproduction on nuclei
Finite propagation distance lc(lifetime) of the (q,q-bar) virtual state
lc = 2ν/(M2 + Q2 )
Detected particles are : scattered electron and theπ+ and π- from ρ0 decay
e + N → e’ + N + ρ0
M is the mass of the vector mesonν is the energy transferred by the electron
lc
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Coherence Lengthlc = 2ν/(Mv
2 + Q2 )
Coherence length effect (CL): Q2 increases ⇒ TAincreases
Coherence Length effect canmimic CT signal
To be safe, one should keep lc fixed and measures the Q2
dependence of TA
What Could mimic CT signal ?
HERMES
Small lc Large lc
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FNAL E665 experiment
Adams et al. PRL74 (1995) 1525
Eμ = 470 GeV
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ρ0 electroproduction at fixed CL
HERMES Nitrogen data : TA=P0 + P2Q2
P2 = (0.097 ± 0.048stat ± 0.008syst) GeV-2
JLab-CLAS E02-110 projected uncertainties
Phys. Rev. Lett. 90 (2003) 052501
Data taken in 2004
Cu
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Targets
Al +emptytarget
Beam
Reference foil
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Vertex cut
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W ≥ 2 GeV⇒ avoid resonance region
-t ≤ 0.45 GeV2
⇒ select diffractive process
|ΔE| ≤ 0.1GeV⇒ select exclusive channel
ΔE = ν - Eρ + t/2Mp is the missing energy from π+π- pair due to the creation of any additional final state particles
e + Fe → e’ + ρ0 + X e + D → e’ + ρ0 + X
π+π-π+π-
EE’
vμqμ
A X}
ν = E – E’Q2 = -(qμ)2 ≅ 4 E E’ sin2(θ/2)t = (qμ - vμ)2W2 = (pμ + qμ)2 = -Q2 + Mp
2 + 2Mpν
γ*
pμ
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Before kinematic cuts
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Mπ+π− (GeV) )(GeVM −+ππ
Two pions invariant mass
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Mπ+π− (GeV)
After w, t and ΔE cutsHydrogenDeuteriumIron Fe
)(GeVM −+ππ
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D2: w > 2, -0.45 ≤ t and |ΔE| ≤ 0.1
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Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)
e + p → e + Δ++ + π-
e + p → e + Δ0 + π+
e + p → e + p + π+ + π-
e + p → e + p + ρ0: Simple Breit Wigner
π+π- Invariant mass (GeV)
D2: w > 2, t ≥ -0.45 and |ΔE| ≤ 0.1
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Fe: w > 2, -0.45 ≤ t and |ΔE| ≤ 0.1
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Entries 8994
Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)Mπ+π−(GeV)
e + p → e + Δ++ + π-
e + p → e + Δ0 + π+
e + p → e + p + π+ + π-
e + p → e + p + ρ0: Simple Breit Wigner
π+π- Invariant mass (GeV)
Fe: w > 2, t ≥ -0.45 and |ΔE| ≤ 0.1
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Radiative corrections
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Q2 (GeV2)
TFe With radiative corrections
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Acceptance correction
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Q2 (GeV2)
TFe After acceptance corrections
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Pion absorption (Continued)
Q2 (GeV2)
TFe
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Preliminary CLAS Data (Radiative + acceptance)Model calculations by Mustapha & Lee
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CT Signal after Pion Absorption Correction
Before correction
After correction
Q2 (GeV2)
TFe CLAS Preliminary
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Coherence Lengthlc = 2ν/(Mv
2 + Q2 )
Coherence length effect (CL): Q2 increases ⇒ TAincreases
Coherence Length effect can mimic CT signal
To be safe, one should keep lc fixed and measures the Q2
dependence of TA
What Could mimic CT signal ?
HERMES
Small lc Large lc
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lc
TFe CLAS Preliminary
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Preliminary Results from CLAS EG2 data
TFe
Q2 (GeV2)
CLAS Preliminary
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Summary and Outlook
Preliminary results from CLAS EG2 data show a strong Q2 dependence of the nuclear transparency for Fe as predicted by the theory (B. Kopeliovich et al., Phys. Rev C 65 (2002) 035201)
Results for 4 GeV iron and 5 GeV carbon are coming soon
Work on systematic uncertainties is underway