References - Bogoliubov Laboratory of Theoretical Physics - JINR

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This expression can further be arranged in a covariant form which in addition does not depend on specific representations of the Dirac matrices. To this end we introduce the additional time-like vector p =(1,�0) and write the final form of ℜas. ℜ = � mm ′ (pk + m)(pk ′ + m ′ (/p +1) ) Our trace formulation of the amplitude in the spin framework is well adapted to the computation of the dipole magnetic or electric moments of the quarks inside baryons compared to the calculation of the same quantities using the explicit spinor components [1][2]. There is however a similar trace formulation[3] but in the helicity framework .Such a formulation although competitive to our is not adequate to dipole moment calculations as the latter ones are interpreted at the end in terms of longitudinal and transverse spin structure functions. We can of course retrieve all results of the helicity formalism as particular cases of the spin formalism . 2 Application: The convection current part of the quark dipole magnetic moment. By using the Gordon decomposition we divide the dipole magnetic moment expression into two terms, one is the convection current part and the other is the spin part. In the application of our trace formalism we only compute the convection part for illustartion of the power of the formulation. The convection part has the form: � � Tr� � ∇ρ �q=0 × � k d3 k (2π) 3 In the above calculation we use the identities � ∇kk0 = � k k0 and � ∇k| � k| = � k | � k| (5) to eliminate all differentiation leading to terms proportional to �kas we have to take the cross product with�kin(5). In particular any differentiation of the spin variable is eliminated as s is function of � ξand of the boost parameterω = − tanh −1 ( |�k| ), idem for the primed spin. k0 With this remark only the variable /kand /k ′ are differentiated and we get − 1 � � 1 ( �k × Tr ( 2 (k0+m) /k+m � 1+γ5/s )( )(γ0�γ) ) 2m 2 d3k (2π) 3 = 1 � 1 ( �k × Trγ5/k/sγ0�γ) 8m (k0+m) d3k (2π) 3 = − 1 � 1 | � 2 k| �s⊥ 2m (k0+m) d3k (2π) 3 = − x � | �k| 2 (x+1) 2m2�s⊥ d3k (2π) 3 (6) Intheequationabove,weapproximatethefactork0bythe average value of the relativistic quark energy inside the nucleon and keep the notationk0 to designate the average value. Inserting the missing factors μ = Q 2m and � m for each spinor u in(5) to complete the k0 definition of the magnetic moment and define the parameter x = m we get the convection k0 current part in terms of the longitudinal spin � S and the transverse spin �δ: xμ (x+1) (� S − � δ 2x ) μ = Q 2m 96 (7)
Compare the gain of time and effort in obtaining this contribution with the lengthy method that used the components of the Dirac spinor in one of our previous work [1] 3 Conclusion. Dipole moments, electric or magnetic are naturally expressed in terms of the spin( longitudinal and transverse) of the quarks inside the parent baryons. Our trace formulation of the amplitude in the spin framework (as opposed to helicity formulation) is appropriate to such computations. On the other hand our formulation has the advantage of making the amplitudes or even the squared amplitudes easily computable either analytically or symbolically. References [1] M.Mekhfi, Correct use of the Gordon decomposition in the calculation of nucleon magnetic dipole moments, Phys.Rev.C 78 (055205) 08. [2] Di Qing, Xiang-Song Chen and Fan Wang, Is nucleon spin structure inconsistent with the constituent quark model Phys.Rev.D58 (114032 )1998 [3] R.Vega and J.Wudka, Phys. Rev. D53 (1996) 5286-5292; Erratum-ibid. D56 (1997) 6037-6038 97
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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
Page 47 and 48: TOWARDS A MODEL INDEPENDENT DETERMI
Page 49 and 50: Common for the difference cross sec
Page 51 and 52: TRANSVERSITY GPDs FROM γN → πρ
Page 53 and 54: The scattering amplitude of the pro
Page 55 and 56: INFRARED PROPERTIES OF THE SPIN STR
Page 57 and 58: 5 Acknowledgement B.I. Ermolaev is
Page 59 and 60: We shall call this model the “sec
Page 61 and 62: y f ν V = f l V = f u V = f d gz V
Page 63 and 64: 2. We remind, that the celebrated G
Page 65 and 66: of the resonance A, θV � 39 o .
Page 67 and 68: • Right-handed EW currents. The c
Page 69 and 70: pesum- (p Entries 0 + pe)-(p-pe) Me
Page 71 and 72: CROSS SECTIONS AND SPIN ASYMMETRIES
Page 73 and 74: R(ρ) 5 4 3 2 1 0 2 3 4 5 6 7 8 9 1
Page 75 and 76: TWO-PHOTON EXCHANGE IN ELASTIC ELEC
Page 77 and 78: and depend on three parameters : fN
Page 79 and 80: O(αs) SPIN EFFECTS IN e + e −
Page 81 and 82: 3 Polarization results for mq → 0
Page 83 and 84: Since one has (↑↓) pc Born =(
Page 85 and 86: Figure 1: A typical lowest order Fe
Page 87 and 88: sin φ S (π + ) A UT 1.0 0.8 0.6 0
Page 89 and 90: form the agreement with these data
Page 91 and 92: in settling this dynamical issue. G
Page 93 and 94: SPIN CORRELATIONS OF THE ELECTRON A
Page 95 and 96: the two-photon system equaling 1).
Page 97: ANOTHER NEW TRACE FORMULA FOR THE C
Page 101 and 102: where the triplet and octet axial c
Page 103 and 104: [2] Y. Prok et al. [CLAS Collaborat
Page 105 and 106: Melosh rotations which boost the re
Page 107 and 108: ky �GeV� 0.4 0.2 0.0 �0.2 �
Page 109 and 110: [2] B. Pasquini, and S. Boffi, Phys
Page 111 and 112: The appearance of both |+〉 and |
Page 113 and 114: 2.2 Intrinsic Transverse Motion Qua
Page 115 and 116: are still complex: for a given corr
Page 117 and 118: This last is required to complete t
Page 119 and 120: [16] P.G. Ratcliffe and O.V. Teryae
Page 121 and 122: Figure 1: a)[left] μpG p E /Gp M (
Page 123 and 124: 4 Conclusion We introduced a simple
Page 125 and 126: √ δΔq8 x for Δq8 and γΔGx fo
Page 127 and 128: understanding of polarized light qu
Page 129 and 130: They are inverse powers of Q 2 kine
Page 131 and 132: accounts approximately for the TM a
Page 133 and 134: POTENTIAL FOR A NEW MUON g-2 EXPERI
Page 135 and 136: When the momentum increases (p >p0)
Page 137 and 138: EVOLUTION EQUATIONS FOR TRUNCATED M
Page 139 and 140: 4 Perspectives Evolution equations
Page 141 and 142: NEW DEVELOPMENTS IN THE QUANTUM STA
Page 143 and 144: statistical approach compared to th
Page 145 and 146: POLARIZED HADRON STRUCTURE IN THE V
Page 147 and 148: 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
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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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