studies of the transverse structure of the nucleon at jlab
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Studies of the transversestructure of the nucleon at
JLabMarco Mirazita
INFN – Laboratori Nazionali di Frascati
INPC2013 – Firenze, 2-7 June 2013 1
From PDFs to TMDsParton Distributions Functions (PDFs)- parton model in collinear approximation
xP
P
2
P
xP+kT
Transverse Momentum Dependent distributions (TMDs)- parton model with gluons and sea quarks- partons have transverse momentum angular
momentum- full decomposition of the nucleon spin
Tkxf
,1
3
TMDs in SIDISMany terms already at leading order• higher order suppressed by M/QDF
FF
• Structure Function
FFDFF Fragmentation
Functionqh
• Azimuthal modulation
• Beam and/or target polarizations
UNPOL
POL
NNNN
• Spin Asymmetries
• Cross section difference
POLNN
4
TMD measurements at JLab
• Very high luminosity• Transversely polarized He target
• Very high luminosity• precision measurements
Hall B
• High luminosity• large acceptance
• Small Collins • Larger Sivers for p+ than for p-
Hall AXeHee p' 3 Collins effect
11sin HhF shUT
Sivers effect
11sin DfF TUT
sh
Different results from the proton• non-zero Collins signal for p+• opposite behaviour for Sivers
HERMES proton data
Transverse target SSA on neutron
5
Double spin asymmetry
6
•small differences among pions•fairly flat distributions
11
111 1DfDg
NNNN
fPA
B
R=0.6
R=1
R=0.4
Comparison with gaussian model
1
1
fwidthpgwidthpA
T
T
fT
T
k
k
T exfkxf2
2
11 ,
gT
T
k
k
T exgkxg2
2
11 ,
PRELIMINARY
New CLAS data under analysis2D (x,pT) extraction
Xepe p
Extracting TMD from data
7
Phenomenological fits of asymmetries- gauss PT dependence
Monte Carlo implementation of gauss model
Distorsions due to phace space limits
f1
D1
Bessel-weighting method allows the model-independent extraction of TMDs
,...
,...
,
,
h
hw
PxW
PxWA
2
12
1
21
21
1 ,~,~,~,~
TT
TTBessel
bzDbxfbzDbxgA
Fourier-transform of TMDs in bT space- no convolution integrals- directly comparable with lattice
Double Spin Asymmetry
Di-hadron way to TMDsSingle hadron production
22 ,, TT kzDpxf
Double hadron production struck quark fragmenting in a hadron pair
8
Unpolarized cross section
Advantages- no convolutionDisadvantages- more complicated kinematics- unknown but measurable DiFF
e+e-→(pp) (pp) X
JLab at 12 GeV
9
CHL-2
Hall A - SBS
SolidHall C – HMS/SHMS
Hall B – CLAS12
RICH
beampipe
target
q DC1 DC2
DC3
CLAS12 RICH
SIDIS measurements at JLab12
10
CLAS12 p/KHall C p/K
CLAS12 p/K
CLAS12 p/KHall C p/K
CLAS12 p/K
CLAS12 p/KSolid p
PROTON
D2
3He
Hall A p/KSolid p
Solid p
• proton and neutron targets, unpolarized as well as longitudinally and transversely polarized
• complementary detectors• ID of final hadrons
flavor separation of TMDs
11
Sivers Asymmetry in CLAS12 for p
12
Transversity at JLab12 with DiHadronsMeasurements with polarized protons Measurements with polarized neutrons
CLAS12SoLID XeNe pp
13
Conclusions
Correlation of spin and transverse momentum of partons is crucial to understand the nucleon structure in terms of quark and gluon degrees of freedom
Measurements of azimuthal dependencies of single and double spin asymmetries indicate that these correlations may be significant
JLab with the 6 GeV electron beam has played a major role in these studies
Studies of the spin-structure of the nucleon is one of the main driving forces behind the upgrade of Jefferson Lab
14
Boer-Mulders effect
15
amplitudes are positive in low-z and high pT2 regions and show a strong kinematic
dependencepredicted amplitudes are very small and agree with data only in high-z and low pT
2 regions
unpolarized hydrogen target
z=0.11 z=0.17
z=0.23 z=0.30
z=0.37 z=0.49
pT2=0.004 pT
2=0.06
pT2=0.12 pT
2=0.21
pT2=0.50pT
2=0.34
21
21
2cos ,, TT kzHpxhA
Cahn effect
16
amplitudes are significantly non-zero and show a sign change (positive to negative) towards high pT
2 predicted amplitudes have similar trends but are systematically larger
z=0.11 z=0.17
z=0.23 z=0.30
z=0.37 z=0.49
pT2=0.004
pT2=0.06
pT2=0.21
pT2=0.50
pT2=0.12
pT2=0.34
1111cos DfHhA
17
PT dependence of the cross section
Hall C
transverse momentum dependence of f1
up+
dp-
Simplified analysis assuming only valence quarks and two FF
u and d quarks have different transverse momentum widths
Sivers asimmetry
....11 Df
Xeep pUnpolarized SIDIS pion production
18
Accessing HT terms at JLabBeam spin asymmetry in pion SIDIS
11 11
~~ DgeHGfEhALU
Xepe p
HT analog of Sivers
HT correction to D1 and Collins
qgq correlationforces acting on the quarks
Higher Twist TMD table- suppressed ~M/Q
• polarized quarks in unpolarized nucleon
• same asymmetry for charged and neutral pions null Collins contribution?• non-zero contribution from g
•Significantly positive K+moments•K- moments consistent with zero•K+ amplitude > p+ amplitude Unexpected from u-quark dominance
SIVERS
Sivers and Collins with kaons
),( suK ),( dup
• K+ and p+ asymmetries consistent within error bars
• K- and p- asymmetries may have opposite sign
COLLINS
proton
deuteron
Transversity PDF
20
DiFF from BELLE data
SIDIS DiHadron data- red: Hermes- blue: COMPASS
Curves from Torino parametrization (gauss)
A. Courtoy, DIS2012
model-independent extraction in collinear approximation
21
The Multi-Hall SIDIS program at JLabM. Aghasyan, K. Allada, H. Avakian, F. Benmokhtar, E. Cisbani, J-P. Chen, M. Contalbrigo, D. Dutta, R. Ent, D. Gaskell, H. Gao, K. Griffioen, K. Hafidi, J. Huang, X. Jiang, K. Joo, N. Kalantarians, Z-E. Meziani, M. Mirazita, H. Mkrtchyan, L.L. Pappalardo, A. Prokudin, A. Puckett, P. Rossi, X. Qian, Y. Qiang, B. Wojtsekhowski for the Jlab SIDIS working group
The complete mapping of the multi-dimensional SIDIS phase space will allow a comprehensive study of the TMDs and the transition to the perturbative regime.
Flavor separation will be possible by the use of different target nucleons and the detection of final state hadrons.
Measurements with pions and kaons in the final state will also provide important information on the hadronization mechanism in general and on the role of spin-orbit correlations in the fragmentation in particular.
Higher-twist effects will be present in both TMDs and fragmentation processes due to the still relatively low Q2 range accessible at JLab, and can apart from contributing to leading-twist observables also lead to observable asymmetries vanishing at leading twist. These are worth studying in themselves and provide important information on quark-gluon correlations.
22
Bessel analysis of BSAXepe p
Bessel-weighted cross section asymmetry
Boer,Gamber,Musch,Prokudin - arXiv:1107.5294
Test of the extraction of Fourier-transformed TMDs with MonteCarlo data
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