Duality in Meson Electroproduction
(E00-108)
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Introduction
E00-108 Experiment
Analysis
Results
First efforts to study cos(φ) terms
Summary
( Hamlet Mkrtchyan, for the E00-108 Collaboration )
Hall C Meeting, January 25, 2007
Introduction
• At high energies: QCD allows for an efficient
description in terms of quarks-gluons
• At low energies: more efficient description in
terms of mesons-baryons
• Quark-hadron duality: relationship between the
strong and week interaction limits of QCD
• The early observation of quark-hadron duality
(Bloom-Gilman) was unexpected
W2 versus ξ for JLab resonance data
(e,e’x)
0.3
NMC 5
0.2
Q2 =0.45 GeV2
• Resonance peaks
averaging to the NMC
scaling curve
0.3
NMC 5
• DIS probes only the sum
of quarks and anti-quarks
0.2
Q2 =1.5 GeV2
0.4
0.1
νW 2
0
• The origin of quarkhadron duality poorly
understood
0.1
0
0.3
NMC 5
0.2
Q2 =3.30 GeV2
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ξ
1
• Small or cancelling High
Twist contribution (In Operator
Product Expansion framework)
z=Eπ/ν
• At low energies, this factorization ansatz is expected to
brake down, due to effects of FSI, resonant excitations.
(What will be at W’2 < 2 GeV2 ?)
• At high energies SIDIS can be decomposed into part
dependent on the quark hadronization, D(z), and on the
quark-photon interaction, q(x,Q2).
} W´
W´2=Mx2=Mp2+Q2(1/x-1)(1-z)
σ~D(z)·q(x,Q2)
Meson electroproduction in SIDIS
• We mapped z-dependence at fixed x, x-dependence
at fixed z and Pt at fixed z and x.
• We took data on 1H, 2H and Al (dummy target).
• Electron beam: I = 20-60 μA and energy ~5.5 GeV,
Q2~2.3 GeV2/c2 and W~2.5 GeV
• The experiment ran in the summer of 2003 in Hall C.
SOS was used for e- and HMS for π± detection
• Goal: to study the duality concept to the unknown
region of semi-inclusive pion electroproduction
E00-108 Experiment
D+ is favoured (D- is unfavoured) fragmentation function
or probability for the struck quark u (d) rise to a π+
• Used CTEQ5M parametrization for q(x,Q2),
average D+(z)+D-(z) from Binnewies and D-/D+
from HERMES
σSIDIS=σDIS·∑ei2[qi(x)Di(z)]·be-bpt2 {1+Acos(φ)+Bcos(2φ)}
• The meson yield arises in term of a fit to the
normalized (e,e’x) DIS cross section:
• Acceptance, radiative corrections and the bin
centering in cross-section is done using SIMC
Analysis
• Subtracted pions from decay of diffractive ρ,
using PYTHIA to estimate σρ ( similar to HERMES )
.
• We estimated Rad. Corrections in two steps:
- using peaking approximation in SIMC, and
- exclusive π, from interpolation MAID & DESY.
• We used parameter b≈4.66 from HERMES
(our own best estimate is b=4.0±0.4 for π±)
• Took in MC: σSIDIS=σDIS·∑ei2[qi(x)Di(z)]·be-bpt2
• In x-scan and z-scan data the φ-dependence
was effectively integrated out ( pions at Pt~0 )
Analysis
1
10
0.3
4.0
0.4
3.5
0.5
3.0
0.6
Z
2.5
0.7
2.0
0.8
0.9
1.5
Mx
2
• Large excess in the
data at Z>0.8 with
respect to the
prediction reflects the
N–Δ region.
(m∆2≈1.5 GeV2)
(using CTEQ5M for PDFs and
Binnewies for Fragmentation)
• Good agreement
between data and
high energy
prediction at Z<0.65
σ~D(z)·q(x,Q2)
Z-Dependence of cross section
for any z, x !
Rp d- = [σp(π+) - σp(π-)] / [σd(π+) - σd(π-)]
= [4uv(x,pt) - dv(x,pt)] / 3[uv(x,pt) + dv(x,pt)]
for any z, x, pt (if d & u have same pt dependence)
• Simple Leading Order picture in valence region:
Rpd+ = [σp(π+) + σp(π-)] / [σd(π+) + σd(π-)]
= [4u(x,pt) + d(x,pt)] / 5[u(x,pt) + d(x,pt)]
• To quantify factorization of SIDIS we formed the
ratios insensitive to the fragmentation process.
Super-Ratios
0.4
0.5
Z
0.6
0.7
0.8
Duality brakes down at z>0.7 (low Mx !)
Our data are close to the near-independence of z
The ratios agree PDF models predictions for z<0.7
0
0.5
1
1.5
2
2.5
3
0.8
1
1.2
1.4
1.6
Our data are close to the near-independence of z
The ratios agree PDF models predictions for z<0.7
At low Mx (z>0.75) duality brakes down.
Both ratios independent of pt (to 0.3 GeV) for z=0.55
• Both ratios agree PDF models 0.2<x<0.5 for z=0.55
• Will our results verify duality and this
factorization assumption ?
• At high energy the ratio depend on z & Q2
• Assuming factorization & using the deuterium
data only, the ratio D-/D+ can be extracted:
σd(π+) = [u + d] [4D+ + D-]
σd(π-) = [u + d] [4D- + D+]
D-/D+ = (4 – r) / (4r – 1)
were
r = σd(π+)/σd(π-)
(The Ratio unfavoured & favoured Fragmentation Functions)
Ratio D-/D+
• Near-independence from x, as expected
• Our results agree with HERMES and EMC
• The resonant contribution at z>0.8 cancel out !
D-/D+ from Deuteron π+ to π- ratio
• For the analysis of cos(φ) terms in Monte Carlo we
will use σSIDIS with this correction
• We did fine binning in Q2, fitted the ratios of the
yields with: F(Q2)=1+ C1ln(Q2)+C2/Q2+C3/Q4
• We found: Q2-dependence in our data differs from
the factorized high-energy expectation
• In MC semi-inclusive cross in a simplest form:
σSIDIS ~ σDIS (dN/dz) b exp(-bPt2)
First efforts to study cos(φ) terms
• As a weights of cos(φ) and cos(2φ) terms
cross section one can use the the value:
A=P1/P3 and B=P2/P3
• We did fine binning in φ and fitted the ratios of
the normalized yields Ydata/YMC with function
F(φ)=P3+P1cos(φ)+P2cos(2φ)
• We assume that all remaining difference data
and MC can be addressed to the cos(φ) terms
in
First efforts to study cos(φ) terms
0.4
0.4
0.6
0.6
0.8
0.8
1
1
Our very preliminary results: A≈B~0
A~σLT, B~σTT
σSIDIS=σDIS·∑ei2[qi(x)Di(z)]·be-bpt2 {1+Acos(φ)+Bcos(2φ)}
-1
-1
1
-0.5
-0.5
0.8
0
0
0.6
0.5
0.5
0.4
1
1
-1
-1
1
-0.5
-0.5
0.8
0
0
0.6
0.5
0.5
0.4
1
1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
Our very preliminary results: A≈B~0
A~σLT, B~σTT
σSIDIS=σDIS·∑ei2[qi(x)Di(z)]·be-bpt2 {1+Acos(φ)+Bcos(2φ)}
-0.4
0.6
-0.4
0.5
-0.2
-0.2
0.4
0
0
0.3
0.2
0.2
0.2
0.4
0.4
-0.4
0.6
-0.4
0.5
-0.2
-0.2
0.4
0
0
0.3
0.2
0.2
0.2
0.4
0.4
• Detailed study effects of Radiation Corrections &
physics background on φ terms of σSIDIS needed
• First approach to study cos(φ) term implemented
Preliminary results are: A≈B~0 for z-scan x-scan
• Factorization and duality brakes down at z>0.7
• Our data verify the onset of quark-hadron duality
and factorization for Mx2>2 (z<0.7) as predicted
for high-energy.
Summary