Duality in Semi-Inclusive DIS
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Transcript of Duality in Semi-Inclusive DIS
Duality in Semi-Inclusive DIS
P. Bosted (JLab)
First Workshop on Quark-Hadron Duality and the Transition to pQCD June 6, 2005
Semi-inclusive processes
Factorization as a test of quark-hadron duality
Factorization tests in unpolarized SIDIS
Kinematic dependences of g1/f1
PT dependence of spin and azimuthal asymmetries
Summary & Outlook
P. Bosted, Duality Workshop, June 2005
2
Semi-inclusive DIS
orbital angular momentum of quarksparton distributions at large x
X.Ji Where region I/II boundary?Can useful information come from Region II?
Main focus of SIDIS studies:
P. Bosted, Duality Workshop, June 2005
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Semi-Inclusive Deep Inelastic Scattering (SIDIS):
• Probes orbital motion of quarks through quark transverse momentum distribution• Access to new PDFs not accessible in inclusive DIS.
kT-dependent parton distributions
Sivers transversity
Mulders,This talk
Off-diagonal PDFs vanish if quarks only in s-state!
In addition T-odd PDFs require FSI (Brodsky et al., Collins, Ji et al. 2002)
This talk
P. Bosted, Duality Workshop, June 2005
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SIDIS kinematic plane and relevant variables
Ey /ν=
)/(sinEEQ ' 24 22 θ=
νMQx 2/2=
'EE −=ν
ν/Ez h=
P. Bosted, Duality Workshop, June 2005
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Missing mass of pions in ep->e’X
Duality question: is MX>1.4 GeV (approximately z<0.7 for Q2-2.5 GeV2, W=2.5 GeV) needed for SIDIS factorization to work? Note absence of Delta in 0!
-0
+n
0
++
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Factorization Test from Unpolarized Multiplicites
Multiplicity (proportional to D+
(z)) is approximately independent of x forW>3 GeV, Q2=2.5 GeV2, x<0.5, and 0.25<z<0.6
P. Bosted, Duality Workshop, June 2005
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Du+ KKP (LO)
Factorization Test from Unpolarized Multiplicites
Multiplicity (proportional to D+
(z)) is also approximately independent of x forW>2 GeV, Q2=2 GeV2, 0.1<x<0.6, and 0.45<z<0.7at E=5.5 GeV fromCLAS at JLab
P. Bosted, Duality Workshop, June 2005
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Unpolarized SIDIS: new test
Simple picture in valence region:
p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)d(+) = [u(x)+d(x)] [4D+(z) + D-(z)]d(-) = [u(x)+d(x)] [4D-(z) + D+(z)]
Rpd= [p(+) + p(-)] / [d(+) + d(-)] = [4u(x) + d(x)] / 5[u(x)+d(x)]
= p(x)/d(x)
Rpd should be independent of
z and pt
x-dependence of Rpd should be same asinclusve p(x)/d(x)in valence region
P. Bosted, Duality Workshop, June 2005
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Unpolarized SIDIS: new test
Rpd is independent of z for 0.4<z<0.7for W=2.5 GeV,
Q2=2.5 GeV2,x=0.3, low pt
Good agreementGRV (using PEPSI
MC, solid histogram)
10% level deviationsfor z>0.7
(Mx>1.4 GeV)Influence of Delta?
P. Bosted, Duality Workshop, June 2005
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Unpolarized SIDIS: new test
Rpd is independent of pt for z=0.55W=2.5 GeV, Q2=2.5 GeV2,
x=0.3
Good agreementGRV (using PEPSI
MC, solid histogram)
P. Bosted, Duality Workshop, June 2005
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Unpolarized SIDIS: new test
Rpd follows expectedx-dependence
for z=0.55W=2.5 GeV, Q2=2.5 GeV2,
low pt
Pretty good agreement with
GRV (using PEPSI MC, solid histogram)
12
CLAS Experiment Setup and Kinematics
Scattering of 5.7 GeV polarized electrons off polarized NH3, ND3
~8M + in SIDIS kinematics
x x
13
• Target polarization PT about 0.7 (0.3) for NH3 (ND3)• Beam polarization PB about 0.7• Dilution factor f varies from 0.1 to 0.3: used Lund model for n/p ratio (agrees with Hall C data) and preliminary Hall B data for A-dependence• Depolarization factor DLL(y) evaluated assuming R=L/T same as for inclusive.• Assumed Aperp=0 (not measured)• No radiative corrections applied• “+” and “-” include some K+, K- for P>1.5 GeV • 0 events cleanly identified with two photons
Determination of g1/F1 (approximately A1)
++−+
++−+
+−
≈NN
NN
)y(fDPPA
LLTB
p 11
P. Bosted, Duality Workshop, June 2005
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x-depenence of SIDIS proton g1/F1
• Good agreement with HERMES + data at higher W.
• x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO)
• Magnitude also in good agreement with simulation
W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7
P. Bosted, Duality Workshop, June 2005
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Simple picture in valence region:
p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)p(+) = 4u(x)D+(z) + d(x)D-(z)p(-) = 4u(x)D-(z) + d(x)D+(z)
(g1/F1)+-=[p(+)+p(-)]/[p(+)+p(-)] = [4u(x) + d(x)] / [4u(x) + d(x)]
= (g1/F1)inclusive
Similarly for 0 (g1/F1)0= (g1/F1)inclusive
Polarized SIDIS: factorization tests
(g1/F1)+- and (g1/F1)0
should be independent of
z and pt,and equal to
inclusive (g1/F1)
P. Bosted, Duality Workshop, June 2005
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SIDIS: factorization studies
g1/F1 for inclusive, for the sum of , and for are fairly consistent with each other in the range 0.4<z<0.7, as expected in LO if factorization works. Cuts used: Mx>1.4 GeV, Q2>1.1 GeV2, W>2 GeV
GRVS Significant ?
P. Bosted, Duality Workshop, June 2005
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z-depenence of SIDIS proton g1/F1
CLAS 5.7 GeV
PRELIMINARY
No significant z-dependence seen for 0 and ++ - for 0.3<z<0.7, as expected if factorization holds
Good agreement with PEPSI predictions including dropoff at high z for -, due to increasing importance of d(x)]
P. Bosted, Duality Workshop, June 2005
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pt-depenence of SIDIS proton g1/F1
No pt dependence for 0 (green), as expected if factorization works
+ (red) and - (blue) individually showpt dependence, but the sum of the two (not shown)is almost independent ofpt, as expected if factorization works
Reasonable agreement with PEPSI predictions.
PRELIMINARY
CLAS 5.7 GeV
P. Bosted, Duality Workshop, June 2005
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Q2-depenence of SIDIS proton g1/F1
PRELIMINARY
CLAS 5.7 GeV
No Q2 dependence
for Q2>1.1 GeV2. Evidence
of HT for Q2<1.1 GeV2
W>2 GeV 0.4<z<0.7
20
SIDIS g1/F1 for Deuteron
Results don’t agree as well with PEPSI using GRSV, more sensitive to un-favored fragmentation functionand NLO corrections than proton (although errorsare about a factor of two larger)
NLO QCD fits including new SIDIS CLAS data canhelp constrain polarized PDFs in valence region
PRELIMINARYCLAS 5.7 GeV
P. Bosted, Duality Workshop, June 2005
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Longitudinally Polarized Target SSA
Clear dependence seen for proton target and +, 0
Fit A*sin() + B*sin(2) for Twist-3 and Twist-2 respectively
P. Bosted, Duality Workshop, June 2005
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)()( 12
,
sin zHxxheQ
MS q
Lqqq
LUL⊥
−Σ∝φ
SSA: x-dependence
∑∑ ⊥⊥
=
q
q
qqL
ULTUL zDxf
zHxh
DPA)()(
)()(
11
112sin φ
Twist-2 Higher Twist
T The hL functions depend on both x and pt, so no simple factorization tests aren’t possible. However, cancheck if (x,pt,z) dependence follows model expectations
P. Bosted, Duality Workshop, June 2005
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)()( 12
,
sin zHxxheQ
MS q
Lqqq
LUL⊥
−Σ∝φ
SSA: x-dependence
∑∑ ⊥⊥
=
q
q
qqL
ULTUL zDxf
zHxh
DPA)()(
)()(
11
112sin φ
PRELIMINARY 5.7 GeV
Twist-2 Higher Twist
Data in rough agreement with Efremov et al.predictions, exceptfor 0 sin() term(evidence for termsnot involving Collinsfragmentation?)
P. Bosted, Duality Workshop, June 2005
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SSA: PT-dependence of sin moment
sinLU(UL) ~FLU(UL)~ 1/Q (Twist-3)
CLAS @4.3 GeV
Beam and target SSA for + (not sensitive to MX-cut) are consistent with increase with PT
CLAS @5.7 GeV
P. Bosted, Duality Workshop, June 2005
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Summary•Factorization tests with both unpolarized and polarized data work surprisingly well for W>2 GeV, Q2>1.1 GeV2, 0.3<z<0.7, pt<1 GeV, even for Mx<2 GeV (another evidence of quark-hadron duality)
• Breakdown of factorization at high z: may be due to Delta excitation or diffraction vector meson production (ongoing analysis)
•Target fragmentation may come into play at lower z than naively expected (ongoing analysis)
•Data may be used even with 6 GeV electrons to study PDFs, at least in limited kinematic region
•More data planned all final states at 6 GeV and with 11 GeV at Jlab. High statistical accuracy tests will better quantify the useful kinematic range of SIDIS
P. Bosted, Duality Workshop, June 2005
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QUESTIONS
•Factorization W<2 GeV?
• Factorization for kaons at low energy?
•NLO tretment
•TM corrections
•Electroweak current?
•… we’re just in the beginning!
P. Bosted, Duality Workshop, June 2005
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support slides…..
For Collins fragmentation function use HERMES data
Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H1
d→/H1u→), band
correspond to -2.5<R<0
CLAS-5.7GeV
First glimpse of Twist-2 TMD h1L┴
PRELIMINARY
•More data required with - & 0 •Exclusive 2 pion background may be important
Distribution functions fromQSM from Efremov et al
P. Bosted, Duality Workshop, June 2005
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SIDIS (*p->X) x-section at leading twist:
The structure functions depend on Q2, xB, z, PhT 1) Unpolarized target2) Longitudinally pol. target 3) Transversely pol. target
Studies of PDFs require three experiments
f1
h┴1T
g1T
f┴1T
h1
h┴1
g1h┴
1L
kT-even kT-odd
TMD PDFs
T-odd
P. Bosted, Duality Workshop, June 2005
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Future: more 0 data in SIDIS
1) SIDIS0 production is not contaminated by diffractive
2) HT effects and exclusive 0 suppressed3) Simple PID by 0-mass (no kaon contamination)4) Provides complementary to +/- information on
PDFs
disadvantages: reconstruction efficiency (requires detection of 2)
advantages:
P. Bosted, Duality Workshop, June 2005
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CLAS+Inner Calorimeter (IC)
IC at CLAS opens new avenue for studies of spin and azimuthal
asymmetries of exclusive and semi-inclusive
CLAS
CLAS+IC
CLAS
IC
424 PbWO4 ……..crystals
Reconstruction efficiency of high energy 0 with IC increases ~ 4 times due to small angle coverage
IC E/E=0.0034/E+0.038/√E+0.022
32
UL ~KM
Longitudinally polarized target SSA using CLAS+IC
•Provide measurement of SSA for all 3 pions, extract the Mulders TMD and study Collins fragmentation with longitudinally polarized target•Allows also measurements of 2 pion asymmetries
Hunf=-1.2Hfav
Hunf=-5Hfav
Hunf=0
50 days of CLAS+IC
curves, QSM from Efremov et al
P. Bosted, Duality Workshop, June 2005
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SIDIS factorizationStructure functions FUU,FLL… factorize into TMD distribution and fragmentation:
P┴ has contributions from distribution, fragmentation and soft gluon radiation
QCD Factorization (Ji and col.)QCD Factorization (Ji and col.)Naïve Factorization (Mulders and col.)Naïve Factorization (Mulders and col.)
TMD PDF
TMD FF
soft factorsoft factor
hard scatteringhard scattering
SIDIS Factorization proved for low PT !!!
P. Bosted, Duality Workshop, June 2005
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ALU x-dependence: CLAS @ 4.3 and 5.7 GeV
0.5<z<0.8
Separation of different HT contribution will require independent measurements of separate contributions
Beam SSA analyzed in terms of the Collins effect by Schweitzer et al. using e(x) from QSM
Photon Sivers Effect Afanasev & Carlson, Metz & Schlegel
Beam SSA analyzed in terms of the Sivers effect by F.Yuan using h1
┴ from MIT bag model
P. Bosted, Duality Workshop, June 2005
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double spin asymmetry A1p
1
11
1
F
g
NN
NN
)y(fDPPA
'TB
p ≈+−
= ++−+
++−+
( )( )( ) ,
Ry
y)y(D'
ε
ε
+
−−=
1
21 ,4
2
2222
Q
yxM=
P. Bosted, Duality Workshop, June 2005
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NH3 dilution
p
n..f
344974
1+=
Dilution function extracted from PEPSI-MC is consistent with data