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3 The conditions for transparent spin resonance crossing Taking into account the above conception one can get a complete compensation of depolarization degree at resonance crossing. The conditions for transparent crossing are given by J(λ−) =±J(λ+) . (4) where λ− and λ+ are λ values before (θ = θ−) andafter(θ = θ+) resonance crossing. Let us consider the simple example of circular accelerator with only one Fourier harmonic of the field � W due to vertical betatron oscillations for the purposes of illustration: where �e1(Ψz) =�ex cos Ψz+�ey sin Ψz, Ψz is the phase, νz =Ψ ′ z �W = ν0 �ez + w�e1(Ψz) (5) is the vertical betatron tune, �ex, �ey, �ez denote the corresponding radial, longitudinal and vertical orts of “accelerator” basis, ν0 = γG = γ(g − 2)/2 is spin tune in ideal accelerator at w =0. Thus, the “natural” spin basis is: �ℓ1 = − w ε �ez+ h h �e1(Ψz) � , �ℓ2 = �n × � � ℓ1 = �ey cos Ψz−�ex sin Ψz , �n(Ψz) = ε w �ez+ h h �e1(Ψz) , here are h = √ ε 2 + w 2 , ε = ν0 − νz — spin detuning. The general spin tune ν is equal to h in this natural basis { � ℓ1, � ℓ2,�n}, near the isolated spin resonance. Ν Ν0�Νk Ν0�ΓG Figure 1: The general spin tune dependence vs tune ν0 (vs the energy) 1 �1 � � n�e z Ν0�Νk Ν0 Figure 2: The vertical component of precession axis plotted vs the tune ν0 1 �1 � � n�e 1 Ν0�Νk Figure 3: The transverse component of precession axis plotted vs the tune ν0 The dependencies of general spin tune as well as vertical and transverse �n axis projections on “energy” are shown in Fig. 1-3. The mirror-reflected decision {�n, ν} →{−�n, −ν} is shown by a dashed line. The variable λ coincide with the ν0 = γG value at the particles accelerations. The condition (3) can be fulfilled at any moment of adiabatic crossing if (ν − νk = h, w = const) |dν0/dθ| ≪w 2 . (6) The condition (6) can be violated for very small resonance strength (at w → 0 ). Spin action variable J(λ) can be changed only in the resonance region. The beam’s polarization is decrease in this case. The condition for transparent crossing is the restoration of the spin action variable value after spin resonance crossing. 408 Ν0
4 Examples of transparent crossing Examples of transparent resonance crossing is given in papers [1–3]. The condition (3) can be fulfilled only if detuning changed in spin resonance region. The SAI dependence is shown schematically in Fig. 4 and Fig. 5. SAI changing is plotted symbolic by the dashed line inside spin resonance region. The detuning shape defines SAI changing in resonance region. When condition (3) is violated the width of resonance region is defined by crossing speed and is equal approximately to θres ∼ 1/ � dε/dθ. 1 �1 Ji a Resonance region J f ��Ji Figure 4: Transparent resonance crossing in the case of SAI-flip Θ 1 �1 Ji a J f �Ji Figure 5: Transparent resonance crossing in the case of SAI keeps sign Another possibility to restore SAI appears, if one uses multiple resonance crossing [4]. At single crossing with constant speed ε ′ = dε/dθ the SAI values before and after resonance crossing are connected by general FS formulae [7]: Jf = � 1 − 2exp � − w2 2|ε ′ a | �� Ji =cos2αJi , sin α =exp � − w2 4|ε ′ a | � where angle α is defined by speed of detuning changing at resonance crossing moment θ = a. It should be noted that it is impossible to restore SAI after single crossing with constant speed. The restoration of SAI after resonance crossing can be obtained due to detuning of changing in outside resonance region. The SAI dependence is shown schematically in Fig. 6 and Fig. 7 for the cases of two times transparent crossing. 1 �1 Ji a b Jab J f ��Ji Figure 6: Two times transparent resonance crossing in the case of SAI-flip Θ 1 �1 Ji a b Jab J f �Ji Figure 7: Two times transparent resonance crossing in the case of SAI keeps sign Two times transparent crossing can be used for spin-flip equipment in the accelerator ring directly before beam is extracted to external target. The conditions of two times transparent resonance crossing are the following: a) in the case of SAI-flip (Fig. 6): α = β, Ψab =2πm; b) in the case of SAI keeps sign (Fig. 7): α = π/2 − β, Ψab =2πm + π, 409 Θ Θ
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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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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
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
Page 372 and 373: to the slope of the Rosenbluth plot
Page 374 and 375: The differential cross section of t
Page 376 and 377: with zero for all mass ranges, with
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Page 382 and 383: is recorded, a good particle identi
Page 384 and 385: error of the extracted asymmetries
Page 386 and 387: 2.6 Summary and Outlook The first d
Page 388 and 389: 386
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
Page 404 and 405: interaction vanishes and a single Z
Page 406 and 407: an amorphous NH3 for low and high,
Page 408 and 409: and depends on a choice of � ℓ1
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
Page 426 and 427: econstruction provide more accurate
Page 428 and 429: y detector saturation from pC colli
Page 430 and 431: 2 �p+ 8 He analyzing power measur
Page 432 and 433: 3.3 Effect of valence neutrons on s
Page 434 and 435: i.e. n0(θ +2π) =n0(θ) . There ar
Page 436 and 437: w and ˙ɛ. For example, we use par
Page 438 and 439: 436
Page 441 and 442: REGULARIZATION OF SOURCE OF THE KER
Page 443 and 444: The corresponding phase transition
Page 445 and 446: ABOUT SPIN PARTICLE SOLUTION IN BOR
Page 447 and 448: where the functions fi(s, η) must
Page 449 and 450: SPINDYNAMICS I.B. Pestov JINR, 1419
Page 451 and 452: State of hadron matter is defined t
Page 453 and 454: REMARK ON SPIN PRECESSION FORMULAE
Page 455 and 456: It is easy to see that for a (massi
Page 457 and 458: DYNAMICS OF SPIN IN NONSTATIC SPACE
Page 459 and 460: 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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