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contributions to the spin of nucleon and, what is particularly important, estimation of the polarised gluon contribution ΔG from COMPASS and RHIC data. • Determination of Higher Twist (HT) effects from moments of g2, which will be measured at JLab. This is possible via generalization of Wandzura-Wilczek relation [10] for truncated moments and test of Burkhardt-Cottingham [11] and Efremov- Leader-Teryaev [12] sum rules. HT corrections can provide information on the quark-hadron duality. • Predictions for generalized parton distributions (GPDs). Moments of GPDs can be related to the total angular momentum (spin and orbital) carried by various quark flavors. Measurements of DVCS, sensitive to GPDs, will be done at JLab. This would be an important step towards a full accounting of the nucleon spin. Concluding, in light of the recent progress in experimental program, the comprehensive theoretical analysis of the structure functions and their moments is of a great importance. I thank Anatoly Efremov for inviting me to this meeting and warm hospitality. References [1] V.N. Gribov, L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438; Sov. J. Nucl. Phys. 15 (1972) 675; Yu.L. Dokshitzer, Sov. Phys. JETP 46 (1977) 641; G. Altarelli, G. Parisi, Nucl. Phys. B126 (1977) 298. [2] S.Forte,L.Magnea,Phys.Lett.B448 (1999) 295 [hep-ph/9812479]; S. Forte, L. Magnea, A. Piccione, G. Ridolfi, Nucl. Phys. B594 (2001) 46 [hepph/0006273]. [3] D. Kotlorz, A. Kotlorz, Acta Phys. Pol. B35 (2004) 705 [hep-ph/0403061]. [4] A.N. Sissakian, O.Yu. Shevchenko, O.N. Ivanov, JETP Lett. 82 (2005) 53 [hepph/0505012]; Phys. Rev. D73 (2006) 094026 [hep-ph/0603236]. [5] D. Kotlorz, A. Kotlorz, Phys. Lett. B644 (2007) 284 [hep-ph/0610282]. [6] D. Kotlorz, A. Kotlorz, Acta Phys. Pol. B40 (2009) 1661 [arXiv:0906.0879]. [7] B.I. Ermolaev, M. Greco, S.I. Troyan [arXiv:0905.2841]. [8] J. Blümlein, H. Böttcher, Nucl. Phys. B636 (2002) 225 [hep-ph/0203155]. [9] HERMES Collaboration, A. Airapetian et al., Phys. Rev. D75 (2007) 012007. [10] S. Wandzura, F. Wilczek, Phys. Lett. B72 (1977) 195. [11] H. Burkhardt, W.N. Cottingham, Ann. Phys. 56 (1970) 453. [12] A.V. Efremov, O.V. Teryaev, E. Leader, Phys. Rev. D55 (1997) 4307. 138
NEW DEVELOPMENTS IN THE QUANTUM STATISTICAL APPROACH OF THE PARTON DISTRIBUTIONS Jacques Soffer Department of Physics, Temple University Philadelphia, Pennsylvania 19122-6082, USA E-mail: jacques.soffer@gmail.com Abstract We briefly recall the main physical features of the parton distributions in the quantum statistical picture of the nucleon. Some predictions from a next-to-leading order QCD analysis are compared to recent experimental results. A new set of parton distribution functions (PDF) was constructed in the framework of a statistical approach of the nucleon [1], which has the following characteristic features: • For quarks (antiquarks), the building blocks are the helicity dependent distributions q±(x) (¯q±(x)) and we define q(x) = q+(x) +q−(x) andΔq(x) = q+(x) − q−(x) (similarly for antiquarks). • At the initial energy scale taken at Q 2 0 =4GeV 2 , these distributions are given by the sum of two terms, a quasi Fermi-Dirac function and a helicity independent diffractive contribution, which leads to a universal behavior at very low x for all flavors. • The flavor asymmetry for the light sea, i.e. ¯ d(x) > ū(x), observed in the data is built in. This is clearly understood in terms of the Pauli exclusion principle, based on the fact that the proton contains two u quarks and only one d quark. • The chiral properties of QCD lead to strong relations between q(x) and¯q(x). For example, it is found that the well established result Δu(x) > 0 implies Δū(x) > 0 and similarly Δd(x) < 0leadstoΔ ¯ d(x) < 0. • Concerning the gluon, the unpolarized distribution G(x, Q 2 0) is given in terms of a quasi Bose-Einstein function, with only one free parameter, and for simplicity, one assumes zero gluon polarization, i.e. ΔG(x, Q 2 0 ) = 0, at the initial energy scale Q2 0 . • All unpolarized and polarized light quark distributions depend upon eight free parameters, which were determined in 2002 (see Ref. [1]), from an NLO fit of a selected set of accurate DIS data. More recently, new tests against experimental (unpolarized and polarized) data turned out to be very satisfactory, in particular in hadronic reactions, as reported in Refs. [2–4]. The statistical approach has been extended [5] to the interesting sitution where the PDF have, in addition to the usual Bjorken x dependence, an explicit kT transverse momentum 139
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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
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
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: 4 Perspectives Evolution equations
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
Page 149 and 150: AXIAL ANOMALIES, NUCLEON SPIN STRUC
Page 151 and 152: 3. Vector current of strange quarks
Page 153 and 154: ORBITAL MOMENTUM EFFECTS DUE TO A L
Page 155 and 156: The elastic scattering S-matrix in
Page 157 and 158: IDENTIFICATION OF EXTRA NEUTRAL GAU
Page 159 and 160: for final l + l − events (l = μ,
Page 161 and 162: QUARK INTRINSIC MOTION AND THE LINK
Page 163 and 164: where wP = − m 2M 2 −p1 cos ω
Page 165 and 166: where g q 2x − ξ 1(x, pT )= πM2
Page 167: EXPERIMENTAL RESULTS
Page 170 and 171: 01 00 11 01 01 01 00 11 01 01 01 00
Page 172 and 173: where C1, C2 and A1 - signals from
Page 174 and 175: Figure 1: Layout of experiment targ
Page 176 and 177: According to requirements of the de
Page 178 and 179: Electron energy is measured at ATLA
Page 180 and 181: Fig. 2 shows the results of the lon
Page 182 and 183: e γ* e’ x+ ξ x− ξ A A’ e e
Page 184 and 185: cos 0φ C A φ cos C A cos 2φ C A
Page 186 and 187: 5 Summary HERMES has measured signi
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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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