References - Bogoliubov Laboratory of Theoretical Physics - JINR

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oth types of experiment results are available [2–4]. The results from SIDIS are indicating a non-zero IFF while the first analysis of the IFF effect at PHENIX [4] opens a way to disentangle transverse spin effects in proton proton collisions. Because the IFF is not a TMD function, extraction of transversity times IFF is not dependent on a model of the transverse momentum dependence, which is the case in the measurement of the Collins effect [6]. Here transverse momentum in the final state originates from a convolution of quark distribution and fragmentation function. This leads also to the Sudakov suppression of the effect [8]. Technically, the extraction of the IFF from electron colliders is also easier, as the signal is not competing with asymmetries from QCD radiation. Also acceptance effects are smaller for the relative azimuthal angles of hadron pairs. 2 Observables in e + e − collisions The transverse polarization of the fragmenting quark leads to a cosine modulation of the azimuthal angle of the plane spanned by the two hadrons h1, h2 which is described by the vector R = Ph1 − Ph2 lying in the plane. Since the electron beams are unpolarized any effect that one would measure in one hemisphere of an event would average out. Instead one can make use of the fact that the spins of quark and anti quark in electron-positron annihilation are 100% correlated. Thus the correlation of the azimuthal angles of the vectors R α in the hemispheres α ∈{1, 2} around the thrust axis with regard to the event plane is sensitive to the IFF. The measurement uses the center of mass system and defines the event plane as the plane which contains the beam axis ˆz and thrust axis ˆn. Figure 1 shows the coordinate system with the relevant quantities. With these the angles φα between Rα and the event plane can be expressed as φ2 − π Ph3 e + Ph4 e − Ph1 Ph1 + Ph2 Ph2 π − φ1 Thrust axis ˆn Figure 1: Azimuthal angle definition. Azimuthal angles φ1 and φ2 are defined relative to the thrust axis. φ{1,2} = sgn[ˆn · (ˆz × ˆn × (ˆn × R1,2)}] � � ˆz × ˆn ˆn × R1,2 × arccos · |ˆz × ˆn| |ˆn × R1,2| . (1) The product of the quark and anti quark interference fragmentation functions H ∢ 1 · ¯ H ∢ 1 is then proportional to the amplitude a12 of the modulation cos(φ1 + φ2) of the di-hadron 378
pair yields [9]. The di-hadron fragmentation functions are dependent on the kinematic variables mInv, the invariant mass of the hadron pair, and z = 2Eh the normalized energy Q of the hadron pair. Here Eh is the energy of the hadron and Q the absolute energy transferred by the virtual photon. Therefore the normalized azimuthal yield of di-hadron pairs can be described as with N(y, z1,z2,m1,m2,φ1 + φ2) ∝ a12(y, z1,z2,m1,m2) · cos(φ1 + φ2) (2) � a12(y, z1,z2,m1,m2) ∼ B(y) · Here the sum goes over all quark flavors q and B(y) = y(1−y) 1 2 −y+y2 q e2qH ∢ 1 (z1,m1) ¯ H∢ 1 (z2,m2) � q e2q D1(z1,m1) ¯ . (3) D1(z2,m2) CM = sin 2 θ 1+cos 2 θ is the kinematic factor describing the transverse polarization of the quark-anti quark with regard to its momentum. The polar angle θ is defined between the electron axis and the thrust axis as shown in fig. 1. The yields are dependent on z1, z2, m1, m2, the fractional energies and invariant masses of the hadron pairs in the first and second hemisphere, and y. In the following the yields are integrated over y in the limits of the fiducial cuts introduced in section 2.3. The labeling of the hemisphere is at random, and it is experimentally not possible to distinguish between quark and anti quark fragmentation. Further information about the IFF can be learned from the dependence on the decay angle θh in the CMS of the two hadrons produced. Using a partial wave decomposition to isolate components that contain the interference between waves with one unit difference in angular momentum, one expects a dependence on sin θh which gives the interference term between s and p waves. This term is expected to dominate at Belle kinematics and is favored by the acceptance. Since the acceptance is symmetric around θh = π the p-p contribution proportional to 2 cos θh should average out. Table 3 shows that this is approximately the case. 2.1 Models As described in the previous section the IFF is an interference effect between hadrons, here pions, created in partial waves with a relative angular momentum difference of one. The dominant contribution being from the s-p interference term [10,11]. Therefore information about the IFF can be gained from a partial wave analysis for di-pion production [12]. Here the data from [13] suggest a phase shift around the ρ mass, leading to a sign change in the fragmentation function. In some models [14] the location of the phase shift around the mass of the ρ meson is caused by the interference of pion pairs produced in a p wave coming from the decay of the spin one ρ which interferes with the non-resonant background. Based on this model and estimation of particle yields from simulations, Bacchetta, Ceccopieri, Mukherjee and Radici [15] made model predictions for the magnitude of IFF Asymmetries at Belle. Again, a strong dependence on the invariant mass is predicted, with a maximum around the rho mass. The asymmetries are expected to rise with z due to the preservation of spin information early in the fragmentation. 2.2 The Belle experiment The Belle detector, located at the KEKB asymmetric energy e + e − collider is described in detail in [16]. For the purpose of this study it is important that a high number of events 379
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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
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INVESTIGATION OF DP-ELASTIC SCATTER
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framework with the use of deuteron
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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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Page 336 and 337: 3. Data selection. The data selecti
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Page 340 and 341: TRANSVERSE SPIN AND MOMENTUM EFFECT
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
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Page 386 and 387: 2.6 Summary and Outlook The first d
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Page 391 and 392: PROTON BEAM POLARIZATION MEASUREMEN
Page 393: N A 0.06 0.05 0.04 0.03 0.02 0.01 0
Page 396 and 397: Intensity profile (arb. units) 1 0.
Page 398 and 399: [4] H. Okada et al., Proc. of the 1
Page 400 and 401: The amplitudes of the signals and t
Page 402 and 403: The following results has been obta
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Page 406 and 407: an amorphous NH3 for low and high,
Page 408 and 409: and depends on a choice of � ℓ1
Page 410 and 411: 3 The conditions for transparent sp
Page 412 and 413: where angles α and β are defined
Page 414 and 415: forward angles, where vector Ay and
Page 416 and 417: espectively. The open symbols repre
Page 418 and 419: RF dipole (transverse B): εBdl = 1
Page 420 and 421: i PV / PV i PV / PV 1 0.5 0 -0.5 -1
Page 422 and 423: The energies of the states Ψ1 −
Page 424 and 425: field P ≈ +1. If we add the trans
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Page 428 and 429: 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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