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SEMI-INCLUSIVE DIS AND TRANSVERSE MOMENTUM DEPENDENT DISTRIBUTION STUDIES AT CLAS M. Mirazita (for the CLAS Collaboration) INFN - Laboratori Nazionali di Frascati Abstract Transverse Momentum Dependent parton distribution functions were introduced to describe both longitudinal and transverse momentum distributions of partons inside a nucleon. Great progress has been made in recent years in understanding these distributions measuring different spin asymmetries in semi-inclusive processes. Here we present an overview of the ongoing studies at CLAS and programs planned for the 6 and 12 GeV activity. 1 Introduction The spin structure of the nucleon has been of particular interest since the EMC [1] measurements, subsequently confirmed by a number of other experiments [2–7], showed that the helicity of the constituent quarks account for only a fraction of the nucleon spin. Possible interpretations of this result include significant polarization of either the strange sea (negatively polarized) or gluons (positively polarized) and the contribution of the orbital momentum of quarks. The semi-inclusive deep inelastic scattering (SIDIS) experiments, when a hadron is detected in coincidence with the scattered lepton provide access to spin-orbit correlations. Observables are spin azimuthal asymmetries, and in particular single spin azimuthal asymmetries (SSAs), of the detected hadron, which are due to the correlation between the quark transverse momentum and the spin of the quark/nucleon. 2 Transverse Momentum Distributions Significant progress has been made recently in understanding the role of partonic initial and final state interactions [8–10, 2]. The interaction between the active parton in the hadron and the spectators leads to gauge-invariant transverse momentum dependent (TMD) parton distributions [8,10–13]. Furthermore, QCD factorization for semi-inclusive deep inelastic scattering at low transverse momentum in the current-fragmentation region has been established in Refs. [14, 15]. This new framework provides a rigorous basis to study the TMD parton distributions from SIDIS data using different spin-dependent and independent observables. TMDs are probability densities for finding a (polarized) parton with a longitudinal momentum fraction x and transverse momentum � kT in a (polarized) nucleon (see Tab. 1). The diagonal elements of the table are the partonic momentum, longitudinal and transverse spin distribution functions, and are the only ones surviving after 244
Table 1: Leading-twist transverse momentum-dependent distribution functions. U, L, andT stand for transitions of unpolarized, longitudinally polarized, and transversely polarized nucleons (rows) to corresponding quarks (columns). N/q U L T U f1 h ⊥ 1 L g1 h ⊥ 1L T f ⊥ 1T g1T h1 h ⊥ 1T � kT -integration. Off-diagonal elements require non-zero orbital angular momentum and are related to the wave function overlap of L=0 and L=1 Fock states of the nucleon [16]. Similar quantities arise in the hadronization process, where a set of fragmentation functions can be introduced, describing the probability that a (polarized) parton fragment into a (polarized) hadron. For unpolarized hadrons, like for example pions and kaons, only two leading twist fragmentation functions are accessible: the usual unpolarized fragmentation function D1 and the Collins T -odd fragmentation function H ⊥ 1 [9] describing fragmentation of transversely polarized quarks into unpolarized hadrons. 3 TMDsmeasurementswithCLASat6GeV Measurements of SSAs in SIDIS kinematics have been performed with CLAS at the Jefferson Laboratory using a 5.7 GeV energy electron beam. Scattering of unpolarized or longitudinally polarized electron beams off an unpolarized H2 or longitudinally polarized NH3 target has been studied in a wide range of kinematics. The average beam polarization was ≈ 75% and the average target polarization was ≈ 70%. The scattered electron and charged or neutral pions were detected in the CLAS with DIS cuts Q 2 > 1GeV 2 and W>2GeV. 3.1 Single Spin Asymmetry with longitudinally polarized target As was first discussed by Kotzinian and Mulders in 1996 [17], the spin-orbit correlation in a longitudinally polarized nucleon gives rise to a Single Spin Asymmetry which involves the leading twist distribution function h ⊥ 1L and the Collins fragmentation function H⊥ 1 sin 2φ σUL ∝ SL(1 − y)sin2φ � e 2 qh ⊥ 1L(x)H ⊥ 1 (z) (1) where φ is the azimuthal angle of the hadron with respect to the lepton plane and x, y, z are the fraction of the nucleon momentum carried by the struck quark, the fraction of the electron energy carried by the virtual photon and the fraction of the virtual photon momentum carried by the detected hadron, respectively. A recent measurement of the sin 2φ asymmetry for charged pions has been performed by Hermes [18] and is consistent with zero, as shown by the empty squares in Fig. 1. Non-zero asymmetries are predicted at large x (x >0.2), a region well covered by CLAS. Indeed, the preliminary CLAS results at 6 GeV for charged pions, reported with full triangles in Fig. 1, show significant negative SSAs, while the results for neutral pions are consitent with zero. 245 q,¯q
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XIII Advanced Research Workshop on
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ã�� [539.12.01 + 539.12 ... 14
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Analytic perturbation theory and pr
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Measurements of GEp/GMp to high Q 2
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WELCOME ADDRESS Alexei Sissakian Di
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he joined the group of prof. Przemy
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proton. Dividing these 90 ◦ cm p-
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p-p scattering angle fixed at exact
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tuning for each ring. The Workshop
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was only about 10 5 per second, but
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[10] E.F. Parker et al., Phys. Rev.
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MICROSCOPIC STERN-GERLACH EFFECT AN
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DeGrand-Miettinen model predicted P
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TOWARDS STUDY OF LIGHT SCALAR MESON
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104xdBR(φ--> π η 0 -1 γ )/dm, G
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RECURSIVE FRAGMENTATION MODEL WITH
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Figure 2: String decaying into pseu
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pT -distributions in the quark frag
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4 Inclusion of spin-1 mesons For a
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CONSTITUENT QUARK REST ENERGY AND W
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〈r 2 ch 〉≈1fm2 . Now with Eqs
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TOWARDS A MODEL INDEPENDENT DETERMI
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Common for the difference cross sec
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TRANSVERSITY GPDs FROM γN → πρ
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The scattering amplitude of the pro
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INFRARED PROPERTIES OF THE SPIN STR
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5 Acknowledgement B.I. Ermolaev is
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We shall call this model the “sec
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y f ν V = f l V = f u V = f d gz V
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2. We remind, that the celebrated G
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of the resonance A, θV � 39 o .
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• Right-handed EW currents. The c
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pesum- (p Entries 0 + pe)-(p-pe) Me
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CROSS SECTIONS AND SPIN ASYMMETRIES
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R(ρ) 5 4 3 2 1 0 2 3 4 5 6 7 8 9 1
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TWO-PHOTON EXCHANGE IN ELASTIC ELEC
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and depend on three parameters : fN
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O(αs) SPIN EFFECTS IN e + e −
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3 Polarization results for mq → 0
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Since one has (↑↓) pc Born =(
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Figure 1: A typical lowest order Fe
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sin φ S (π + ) A UT 1.0 0.8 0.6 0
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form the agreement with these data
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in settling this dynamical issue. G
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SPIN CORRELATIONS OF THE ELECTRON A
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the two-photon system equaling 1).
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ANOTHER NEW TRACE FORMULA FOR THE C
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Compare the gain of time and effort
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where the triplet and octet axial c
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[2] Y. Prok et al. [CLAS Collaborat
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Melosh rotations which boost the re
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ky �GeV� 0.4 0.2 0.0 �0.2 �
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[2] B. Pasquini, and S. Boffi, Phys
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The appearance of both |+〉 and |
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2.2 Intrinsic Transverse Motion Qua
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are still complex: for a given corr
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This last is required to complete t
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[16] P.G. Ratcliffe and O.V. Teryae
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Figure 1: a)[left] μpG p E /Gp M (
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4 Conclusion We introduced a simple
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√ δΔq8 x for Δq8 and γΔGx fo
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understanding of polarized light qu
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They are inverse powers of Q 2 kine
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accounts approximately for the TM a
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POTENTIAL FOR A NEW MUON g-2 EXPERI
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When the momentum increases (p >p0)
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EVOLUTION EQUATIONS FOR TRUNCATED M
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4 Perspectives Evolution equations
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NEW DEVELOPMENTS IN THE QUANTUM STA
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statistical approach compared to th
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POLARIZED HADRON STRUCTURE IN THE V
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g 3 A =Δuv(Q 2 ) − Δdv(Q 2 ), g
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AXIAL ANOMALIES, NUCLEON SPIN STRUC
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3. Vector current of strange quarks
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ORBITAL MOMENTUM EFFECTS DUE TO A L
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The elastic scattering S-matrix in
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IDENTIFICATION OF EXTRA NEUTRAL GAU
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for final l + l − events (l = μ,
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QUARK INTRINSIC MOTION AND THE LINK
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where wP = − m 2M 2 −p1 cos ω
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where g q 2x − ξ 1(x, pT )= πM2
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EXPERIMENTAL RESULTS
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01 00 11 01 01 01 00 11 01 01 01 00
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where C1, C2 and A1 - signals from
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Figure 1: Layout of experiment targ
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According to requirements of the de
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Electron energy is measured at ATLA
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Fig. 2 shows the results of the lon
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e γ* e’ x+ ξ x− ξ A A’ e e
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cos 0φ C A φ cos C A cos 2φ C A
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5 Summary HERMES has measured signi
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(1.205 ± 0.0012) GeV/c, 10 10 p/s,
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was done in the interval ”−t”
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If we admit a non-zero quark transv
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which is trivial in collinear LO ap
Page 196 and 197: In figure 3 the expected errors on
Page 198 and 199: [12] A. V. Efremov and O. V. Teryae
Page 200 and 201: Figure 1: The COMPASS spectrometer.
Page 202 and 203: Comparing this formula to the inclu
Page 204 and 205: Figure 5: Comparison of COMPASS inc
Page 206 and 207: [9] B. Adeva et al. (SMC Coll.), Ph
Page 208 and 209: q T sin( φ-φ ) M AUT 0.14 0.12 0.
Page 210 and 211: proton beam is planned. References
Page 212 and 213: Run Year √ s (GeV) Polarization R
Page 214 and 215: ackground fraction, and asymmetry i
Page 216 and 217: At √ s = 200 GeV, ALL(pp → π
Page 218 and 219: [6] D. de Florian, W. Vogelsang, an
Page 220 and 221: higher energies, where the cross se
Page 222 and 223: Figure 3: The experimental results
Page 224 and 225: kinematic range to low values of Bj
Page 226 and 227: 3 Semi-Inclusive DIS Collins and Si
Page 228 and 229: Unpolarized target asymmetries. The
Page 230 and 231: 4 Summary Since the end of data-tak
Page 232 and 233: polarization as well as a construct
Page 234 and 235: Finally the COMPASS reconstruction
Page 236 and 237: tained in the NLO QCD approximation
Page 238 and 239: with only modern NN potential are r
Page 240 and 241: (a) (b) Figure 3: (a) T20 data take
Page 242 and 243: of electroproduction from polarized
Page 244 and 245: As is seen in Fig. 1 values of the
Page 248 and 249: The yellow band in Fig. 1 is the re
Page 250 and 251: At leading twist, a third asymmetry
Page 252 and 253: THE COMPLETION OF SINGLE-SPIN ASYMM
Page 254 and 255: A N , % 30 20 10 0 0 0.2 0.4 0.6 0.
Page 256 and 257: Unexpectedly large single spin asym
Page 258 and 259: THE GENERALIZED PARTON DISTRIBUTION
Page 260 and 261: , E) H ~ (H, I Im C 5 4 3 2 1 Q = 1
Page 262 and 263: Reducing to a common denominator (
Page 264 and 265: LAMBDA PHYSICS AT HERMES S. Belosto
Page 266 and 267: analysis was carried out reconstruc
Page 268 and 269: SPIN PHYSICS AT NICA A. Nagaytsev J
Page 270 and 271: original software packages (MC simu
Page 272 and 273: MEASUREMENTS OF TRANSVERSE SPIN EFF
Page 274 and 275: to “near-side” and “away-side
Page 276 and 277: THE FIRST STAGE OF POLARIZATION PRO
Page 278 and 279: In paper [12] the study was made of
Page 280 and 281: emphasis to increase the statistics
Page 282 and 283: Table 2: The parameters of the main
Page 284 and 285: POLARIZATION MEASUREMENTS IN PHOTOP
Page 286 and 287: With a polarized electron beam inci
Page 288 and 289: Figure 3: Preliminary helicity asym
Page 290 and 291: INVESTIGATION OF DP-ELASTIC SCATTER
Page 292 and 293: framework with the use of deuteron
Page 294 and 295: SPIN PHYSICS WITH CLAS Y. Prok 12,
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1.3 Flavor Decomposition of the Hel
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Γ p 1 0.15 0.125 0.1 0.075 0.05 0.
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The upcoming energy upgrade of Jeff
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y the nearly 1000 combined citation
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� R = −Pt/Pl τ(1 + ε)/2ε; he
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4 Results of GEp-III Experiment In
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6 Theoretical Developments The earl
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lz = 0 (along the direction of the
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models have recently been challenge
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[32] Chung P. L. and F. Coester, Ph
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48 ± 3% for two beams. The proton
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is constant with cos θ∗ , as exp
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In summary, we made measurements on
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angle between the direction of the
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The sensitivity of the data to the
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COMPASS could be converted into a f
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3.1.2 Beam charge and spin asymmetr
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contributions enter only beyond lea
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References [1] D. Mueller et al, Fo
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l’ l p q p h H (z) 1 h (x) 1 l l
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3. Data selection. The data selecti
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φ sin3 a 0.06 0.04 0.02 0 -0.02 -0
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TRANSVERSE SPIN AND MOMENTUM EFFECT
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model. Both the cos φh and the cos
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D cos φ A 0 -0.1 -0.2 -0.3 + h -2
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4.3 The Sivers asymmetry According
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[3] A. Airapetian et al. [HERMES co
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2. Delta-Sigma Experimental Set-up.
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6. Estimate of the count rate in tr
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2 Analysis Formalism Spin-dependent
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The MC production comprises three s
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6 High pT hadron pair analysis for
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[2] V. Y. Alexakhin et al. [COMPASS
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2 Towards polarized Antiprotons For
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4 Spin-Filtering Experiments at COS
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to test the theoretical models of t
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C1 C2 π CH1,2 CH3,4 CH5,6 111 000
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not even resemble the data behavior
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to the slope of the Rosenbluth plot
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The differential cross section of t
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with zero for all mass ranges, with
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more precise and dedicated measurem
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oth types of experiment results are
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is recorded, a good particle identi
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error of the extracted asymmetries
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2.6 Summary and Outlook The first d
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386
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PROTON BEAM POLARIZATION MEASUREMEN
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N A 0.06 0.05 0.04 0.03 0.02 0.01 0
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Intensity profile (arb. units) 1 0.
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[4] H. Okada et al., Proc. of the 1
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The amplitudes of the signals and t
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The following results has been obta
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interaction vanishes and a single Z
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an amorphous NH3 for low and high,
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and depends on a choice of � ℓ1
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3 The conditions for transparent sp
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where angles α and β are defined
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forward angles, where vector Ay and
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espectively. The open symbols repre
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RF dipole (transverse B): εBdl = 1
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i PV / PV i PV / PV 1 0.5 0 -0.5 -1
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The energies of the states Ψ1 −
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field P ≈ +1. If we add the trans
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econstruction provide more accurate
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y detector saturation from pC colli
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2 �p+ 8 He analyzing power measur
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3.3 Effect of valence neutrons on s
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i.e. n0(θ +2π) =n0(θ) . There ar
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w and ˙ɛ. For example, we use par
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436
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REGULARIZATION OF SOURCE OF THE KER
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The corresponding phase transition
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ABOUT SPIN PARTICLE SOLUTION IN BOR
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where the functions fi(s, η) must
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SPINDYNAMICS I.B. Pestov JINR, 1419
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State of hadron matter is defined t
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REMARK ON SPIN PRECESSION FORMULAE
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It is easy to see that for a (massi
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DYNAMICS OF SPIN IN NONSTATIC SPACE
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Schwinger gauge. Probably for the f
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DSPIN-09 WORKSHOP SUMMARY Jacques S
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to some preliminary results reporte
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A new measurement of the polarizati
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new NLO QCD parametrization of the
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Name (Institution, Town, Country) E
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