References - Bogoliubov Laboratory of Theoretical Physics - JINR

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Using the small (m 2 q/E 2 )–approximation one finds that σ[hf] has fallen to 50% of its forward peak value at cos θ =1− ( √ 2 − 1)m 2 q/(2E 2 ). Integrating Eq.(6) over cos θ, weobtain dσ[hf] dx = σBorn(s)CF αs 2π x ≡ σBorn(s)D[hf](x) (7) where D[hf] = CF (αs/2π)x is called the helicity flip splitting function [11]. The integrated helicity flip contribution survives in the mq → 0 limit since the integral of the last factor in Eq.(6) is proportional to 1/m2 q which cancels the overall m2 q factor in Eq.(6). It is for this reason that the survival of the helicity flip contribution is sometimes called an m/m-effect. For the helicity non-flip contribution one finds dσnf dx dcosθ = σBorn(s) αs 1+(1−x) CF 2π 2 (1 − cos θ) � � �2 (8) x 1 − cos θ 1 − m 2 q /E2 The helicity non-flip splitting function dσnf/d cos θ vanishes in the forward direction but is strongly peaked in the near-forward direction. Using again the small (m 2 q/E 2 ) approximation σnf can be seen to peak at cos θ =1− m 2 q /(2E2 ). Integrating Eq.(8) one obtains dσnf dx = σBorn(s)CF αs π 1+(1− x) 2 x ln E mq ≡ σBorn(s)Dnf(x) (9) where we have retained only the leading-log contribution. Dnf(x) can be seen to be the usual non-flip splitting function. We now turn to the anomalous helicity non-flip contribution. Let us rewrite the nonflip contribution in the form σnf = σnf + σ[hf] −σ[hf] � �� σtotal By explicit calculation we have seen that the total unpolarized rate σtotal has no anomalous contribution. The conclusion is that there is an anomalous contribution also to the nonflip transition with the strength −D[hf] = −CF (αs/2π)x. We conjecture that the same pattern holds true for other processes, i.e. that there are no anomalous contributions to unpolarized rates but that there are anomalous contributions to both helicity flip and non-flip contributions in polarized rates. Taking into account the anomalous helicity flip σ[hf] and non-flip σ[nf] contributions the pattern of the anomalous helicity contributions to the various spin configurations can then be obtained in terms of the Born term contributions and the universal flip and non- flip contributions ± � 1 0 D[hf](x)dx = ±CF αs/(4π) =± αs/(3π). Using a rather suggestive notation for the anomalous contributions one has � [↑↑] = (↑↓[hf])+(↓[hf]↑) = (↑↓)Born +(↓↑)Born [↑↓] = (↑↓[nf])+(↑[nf]↓) = −2(↑↓)Born � [↓↑] = (↓↑[nf])+(↓[nf]↑) = −2(↓↑)Born � [↓↓] = (↓↑[hf])+(↑[hf]↓) = 80 � αs CF CF �� , 4π � αs , 4π �� (↓↑)Born +(↑↓)Born CF CF � αs 4π � αs 4π (10) (11)
Since one has (↑↓) pc Born =(↓↑)pc Born =2Ncq 2 and (↑↓) pv Born = −(↓↑)pv Born =2Ncq 2 one obtains the anomalous contributions in Eq.(5) using the factorizing relations (11). In particular one sees that anomalous contribution to the single-spin polarization P (ℓ1) results to 100% from the universal helicity non-flip contribution whereas the anomalous contributions to the spin-spin correlation function P (ℓ1ℓ2) is 50% helicity flip and 50% helicity non-flip. We conclude that the anomalous non-flip contribution are unavoidable in the O(αs) description of mq → 0 spin phenomena in e + e − → q¯q (g). The normal contributions in Eq.(5) require an explicit calculation. The result H =4Ncq 2 (1 + αs/π) is, of course, well known since many years. In this talk we did not discuss physics aspects of the anomalous helicity flip contribution. We refer the interested reader to the papers [10–13] which contain a discussion of various aspects of the physics of the anomalous helicity flip contributions in QED and QCD. Acknowledgements: The work of S. G. is supported by the Estonian target financed project No. 0180056s09, by the Estonian Science Foundation under grant No. 8402 and by the Deutsche Forschungsgemeinschaft (DFG) under grant 436 EST 17/1/06. References [1] J. G. Körner, A. Pilaftsis and M. M. Tung, Z. Phys. C63 (1994) 575 [2] S. Groote, J.G. Körner and M.M. Tung, Z. Phys. C70 (1996) 281 [3] S. Groote, J.G. Körner and M.M. Tung, Z. Phys. C74 (1997) 615 [4] S. Groote, J.G. Körner and J.A. Leyva, Phys. Lett. B418 (1998) 192 [5] S. Groote, J.G. Körner and J.A. Leyva, Eur. Phys. J. C63 (2009) 391 [6] A. Brandenburg, M. Flesch and P. Uwer, Phys. Rev. D 59 (1999) 014001 [7] A.D. Dolgov and V.I. Zakharov, Nucl. Phys. B27 (1971) 525; J. Hoˇrejˇsi, Phys. Rev. D32 (1985) 1029; J. Hoˇrejˇsi and O. Teryaev, Z. Phys. C65 (1995) 691 [8] S. Groote, J.G. Körner, to be published [9] T.D.LeeandM.Nauenberg,Phys.Rev.133 (1964) B1549. [10] A.V. Smilga, Comments Nucl. Part. Phys. 20 (1991) 69. [11] B. Falk and L.M. Sehgal, Phys. Lett. B325 (1994) 509 [12] O. V. Teryaev, arXiv:hep-ph/9508374. [13] O. V. Teryaev and O. L. Veretin, arXiv:hep-ph/9602362. 81
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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
Page 31 and 32: TOWARDS STUDY OF LIGHT SCALAR MESON
Page 33 and 34: 104xdBR(φ--> π η 0 -1 γ )/dm, G
Page 35 and 36: RECURSIVE FRAGMENTATION MODEL WITH
Page 37 and 38: Figure 2: String decaying into pseu
Page 39 and 40: pT -distributions in the quark frag
Page 41 and 42: 4 Inclusion of spin-1 mesons For a
Page 43 and 44: CONSTITUENT QUARK REST ENERGY AND W
Page 45 and 46: 〈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: 3 Polarization results for mq → 0
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 and 98: ANOTHER NEW TRACE FORMULA FOR THE C
Page 99 and 100: Compare the gain of time and effort
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
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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
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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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