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TRANSVERSE SPIN AND MOMENTUM EFFECTS IN THE COMPASS EXPERIMENT Giulio Sbrizzai† (on behalf of the COMPASS collaboration) Università degliStudidiTriesteandINFN † E-mail: giulio.sbrizzai@ts.infn.it Abstract The study of the spin structure of the nucleon is part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. COMPASS investigates transverse spin and transverse momentum effects by studying the azimuthal distributions of the hadrons produced in deep inelastic scattering of naturally polarized 160 GeV/c muons on transversely polarized target. The results obtained using a 6 LiD from the data collected in 2002-2004, and new results obtained using a NH3 target, from the data collected in 2007, are presented. 1 Introduction A powerful method to access the nucleon structure is the measurement of the azimuthal modulations of the distribution of the hadrons inclusively produced in the deep inelastic scattering. On the basis of general principles of quantum field theory in the one photon exchange approximation, the semi inclusive deep inelastic scattering (SIDIS) cross section can be written in a model independent way [1]. In its expression there are 18 structure functions, 8 of them are leading order. They can be accessed measuring the corresponding modulation in different combinations of the azimuthal angle of the hadron and of the nucleon spin vector, all of them independent. Most of them have a clear interpretation in terms of the Parton Model and can be written as the convolution of a distribution function of the quarks inside the nucleon (PDF) and a function which describes the fragmentation of the struck quark into a specific hadron (FF). Recent data on single spin asymmetries in SIDIS off transversely polarized nucleon targets [2], [3] triggered a lot of interest towards the transverse momentum dependent and spin dependent distributions and fragmentation functions. Correlations between spin and transverse momentum give rise to effects, which would be zero in the absence of intrinsic motion of the quarks inside the nucleon. One of the most famous PDF is the transversity distribution which gives the difference of the number of quarks with momentum fraction x with their transverse spin parallel and anti-parallel to the nucleon spin [4]. The transversity distribution, together with the better known spin-averaged distribution and helicity distribution functions, is necessary to fully specify the nucleon structure at leading order. Since it is chiral odd it can be measured only coupled to another chiral odd function. In SIDIS one candidate is the Collins fragmentation function which is the spin dependent part of the FF of a polarized 338
quark in an unpolarized hadron. The convolution of the two functions generates the so called Collins asymmetry in the hadrons distribution. A second SIDIS channel to access the transversity distribution is in conjunction with the interference fragmentation function of the polarized quark in two hadrons giving rise to an azimuthal modulation of the plane of inclusively produced hadrons pairs with respect to the scattering plane. Of special interest among the transverse momentum dependent distribution functions are: the Sivers function [5] which describes a possible deformation of the quark intrinsic transverse momentum distribution in a transversely polarized nucleon, and the Boer- Mulders function [6] which gives the correlation of the quark transverse momentum and its transverse spin in an unpolarized nucleon. The measurements of these functions can give further insights on the connection between the transverse spin and transverse momentum and are needed to progress towards a more structured picture of the nucleon structure, beyond the collinear partonic representation. 2 The COMPASS experiment COMPASSisanhighenergyexperimentatthe CERN SPS with a wide physics program focused on the study of the nucleon spin structure and hadron spectroscopy using muon and hadron beams. The data used to investigate the transverse spin and transverse momentum structure of the nucleon have been taken with a positive muon beam of 160 GeV/c on a transversely polarized target. The scattered muon and the produced hadrons are detected in a two stage spectrometer with a wide angular acceptance and an excellent particle identification [2]. For the data taking with a transversely polarized target, in the years 2002 2003 and 2004, deep inelastic scattering data have been collected using a 6 LiD target material, while in 2007 a NH3 target material was used. The target material was placed in 2 (during 2004) or 3 (during 2007) cells oppositely transversely polarized and the direction of the target polarization has been reversed every 5 days in each target cell. Many results have been determined from these data, in this report i will only discuss the results for unpolarized asymmetries from 2004 data and the results for the Sivers and Collins asymmetries from 2002-2004 and 2007 data. 3 Unpolarized target azimuthal asymmetries The cross section for the hadron production of the lepton nucleon deep inelastic scattering off an unpolarized is [1]: d 5 σ dx dy dz dφh dp 2 T = 2πα2 � · xyQ2 1+(1−y) 2 2 cos 2φh + (1−y)cos2φhFUU FUU +(2−y) � cos φh 1 − y cos φh FUU + λl y � sin φh 1 − y sin φh FLU There are three independent modulations on the azimuthal angle of the hadron with respect to the scattering plane. The sin φh modulation is proportional to the beam polar- sin φh ization and the structure function F has no clear explanation in term of the parton LU 339 � (1)
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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
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In figure 3 the expected errors on
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[12] A. V. Efremov and O. V. Teryae
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Figure 1: The COMPASS spectrometer.
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Comparing this formula to the inclu
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Figure 5: Comparison of COMPASS inc
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[9] B. Adeva et al. (SMC Coll.), Ph
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q T sin( φ-φ ) M AUT 0.14 0.12 0.
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proton beam is planned. References
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Run Year √ s (GeV) Polarization R
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ackground fraction, and asymmetry i
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At √ s = 200 GeV, ALL(pp → π
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[6] D. de Florian, W. Vogelsang, an
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higher energies, where the cross se
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Figure 3: The experimental results
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kinematic range to low values of Bj
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3 Semi-Inclusive DIS Collins and Si
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Unpolarized target asymmetries. The
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4 Summary Since the end of data-tak
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polarization as well as a construct
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Finally the COMPASS reconstruction
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tained in the NLO QCD approximation
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with only modern NN potential are r
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(a) (b) Figure 3: (a) T20 data take
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of electroproduction from polarized
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As is seen in Fig. 1 values of the
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SEMI-INCLUSIVE DIS AND TRANSVERSE M
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The yellow band in Fig. 1 is the re
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At leading twist, a third asymmetry
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THE COMPLETION OF SINGLE-SPIN ASYMM
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A N , % 30 20 10 0 0 0.2 0.4 0.6 0.
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Unexpectedly large single spin asym
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THE GENERALIZED PARTON DISTRIBUTION
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, E) H ~ (H, I Im C 5 4 3 2 1 Q = 1
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Reducing to a common denominator (
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LAMBDA PHYSICS AT HERMES S. Belosto
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analysis was carried out reconstruc
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SPIN PHYSICS AT NICA A. Nagaytsev J
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original software packages (MC simu
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MEASUREMENTS OF TRANSVERSE SPIN EFF
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to “near-side” and “away-side
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THE FIRST STAGE OF POLARIZATION PRO
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In paper [12] the study was made of
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emphasis to increase the statistics
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Table 2: The parameters of the main
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POLARIZATION MEASUREMENTS IN PHOTOP
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With a polarized electron beam inci
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Figure 3: Preliminary helicity asym
Page 290 and 291: INVESTIGATION OF DP-ELASTIC SCATTER
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Page 294 and 295: SPIN PHYSICS WITH CLAS Y. Prok 12,
Page 296 and 297: 1.3 Flavor Decomposition of the Hel
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Page 300 and 301: The upcoming energy upgrade of Jeff
Page 302 and 303: y the nearly 1000 combined citation
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Page 306 and 307: 4 Results of GEp-III Experiment In
Page 308 and 309: 6 Theoretical Developments The earl
Page 310 and 311: lz = 0 (along the direction of the
Page 312 and 313: models have recently been challenge
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Page 320 and 321: In summary, we made measurements on
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Page 324 and 325: The sensitivity of the data to the
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Page 328 and 329: 3.1.2 Beam charge and spin asymmetr
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Page 332 and 333: References [1] D. Mueller et al, Fo
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Page 336 and 337: 3. Data selection. The data selecti
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Page 342 and 343: model. Both the cos φh and the cos
Page 344 and 345: D cos φ A 0 -0.1 -0.2 -0.3 + h -2
Page 346 and 347: 4.3 The Sivers asymmetry According
Page 348 and 349: [3] A. Airapetian et al. [HERMES co
Page 350 and 351: 2. Delta-Sigma Experimental Set-up.
Page 352 and 353: 6. Estimate of the count rate in tr
Page 354 and 355: 2 Analysis Formalism Spin-dependent
Page 356 and 357: The MC production comprises three s
Page 358 and 359: 6 High pT hadron pair analysis for
Page 360 and 361: [2] V. Y. Alexakhin et al. [COMPASS
Page 362 and 363: 2 Towards polarized Antiprotons For
Page 364 and 365: 4 Spin-Filtering Experiments at COS
Page 366 and 367: to test the theoretical models of t
Page 368 and 369: C1 C2 π CH1,2 CH3,4 CH5,6 111 000
Page 370 and 371: not even resemble the data behavior
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Page 374 and 375: The differential cross section of t
Page 376 and 377: with zero for all mass ranges, with
Page 378 and 379: more precise and dedicated measurem
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Page 382 and 383: is recorded, a good particle identi
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Page 386 and 387: 2.6 Summary and Outlook The first d
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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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References - Bogoliubov Laboratory of Theoretical Physics - JINR

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