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References [1] D. Mueller et al, Fortsch.Phys.42 (1994) 101. [2] X. Ji, Phys. Rev. Lett. 78 (1997) 610; Phys. Rev. D55(1997) 7114. [3] A.V. Radyushkin, Phys. Lett. B 385 (1996) 333; Phys. Rev. D56(1997) 5524. [4] M. Burkardt, Phys. Rev. D62(2000) 071503; erratum-ibid. D66(2002) 119903; Int. J. Mod. Phys. A18(2003) 173; Phys. Lett. B 595 (2004) 245. [5] K. Goeke, M.V. Polyakov and M. Vanderhaegen, Prog. Part. in Nucl. Phys. 47 (2001) 401. [6] M. Diehl, Generalized Parton Distributions, DESY-thesis-2003-018, hep-ph/0307382. [7] A.V. Belitsky and A.V.Radyushkin, Phys. Rep. 418 (2005) 1. [8] The COMPASS Collaboration, COMPASS Medium and Long Term Plans, CERN- SPSC-2009-003, SPSC-I-238, January 21, 2009. [9] A.V. Belitsky, D. Müller and A. Kirchner, Nucl. Phys. B 629 (2002) 323. [10] M. Strikman and C. Weiss, Phys. Rev. D69 (2004) 054012. [11] M. Vanderhaeghen, P.A.M. Guichon and M. Guidal, Phys. Rev. Lett. 80 (1998) 5064; Phys. Rev. D 60 (1999) 094017; [12] K. Kumericki and D. Mueller, hep-ph/0904.0458. [13] A. Airapetian et al, JHEP06 (2008) 066. [14] F. Ellinghaus, W.-D. Nowak, A.V. Vinnikov, and Z. Ye, Eur. Phys. J. C46 729 (2006), hep-ph/0506264. [15] A. Sandacz, Exclusive processes in leptoproduction at COMPASS, presentedatInternational Conference on the Structure and the Interactions of the Photon, PHO- TON09, Hamburg (2009), http://photon09.desy.de. [16] G. Jegou, Exclusive ρ 0 production at COMPASS, presented at the XVII International Workshop on Deep-Inelastic Scattering and Related Topics, DIS2009, Madrid (2009), http://www.ft.uam.es/DIS2009. [17] S.V. Goloskokov, P. Kroll, Eur. Phys. J. C42 281 (2005), hep-ph/0501242; S.V. Goloskokov, P. Kroll, Eur. Phys. J. C53 367 (2008), hep-ph/0708.3569; S.V. Goloskokov, P. Kroll, Eur. Phys. J. C59 809 (2009), hep-ph/0809.4126. 330
AZIMUTHAL ASYMMETRIES IN PRODUCTION OF CHARGED HADRONS BY HIGH ENERGY MUONS ON POLARIZED DEUTERIUM TARGETS 1 I.A. Savin on behalf of the COMPASS collaboration Joint Institute for Nuclear Research, Dubna Abstract Search for azimuthal asymmetries in semi-inclusive production of charged hadrons by 160 GeV muons on the longitudinally polarized deuterium target, has been performed using the 2002- 2004 COMPASS data. The observed asymmetries integrated over the kinematical variables do not depend on the azimuthal angle of produced hadrons and are consistent with the ratio gd 1 (x)/f d 1 (x). The asymmetries are parameterized taking into account possible contributions from different parton distribution functions and parton fragmentation functions depending on the transverse spin of quarks.They can be modulated (either/or/and) with sin(φ), sin(2φ), sin(3φ) and cos(φ). The x-, z- andpT h -dependencies of these amplitudes are studied. 1. Introduction. Although the longitudinal spin structure of nucleons has been investigated for more than 20 years and results are very well known, the studies of the transverse spin structure of nucleons have been started recently. Since the pioneering HERMES [1] and CLAS [2] experiments it is known that the signature of the transverse spin effects is an appearance of azimuthal asymmetries (AA) of the hadrons produced in Semi-Inclusive Deep Inelastic Scattering (SIDIS) of leptons on polarized targets. These asymmetries are related with new Parton Distribution Functions (PDF) and new polarized Parton Fragmentation Functions (PFF), depending on the transverse spin of quarks [3]. AAs on the transversally polarized targets have been already reported by HERMES [4] and COMPASS [5, 6], and on the longitudinally polarized targets - by HERMES [7, 8]. The search for the AA using the COMPASS spectrometer [9] with the longitudinally polarized deuterium target is described below. In the framework of the parton model of nucleons, the squared modulus of the matrix element of the SIDIS is represented by the type of the diagram in Fig.1a, where an example of one of the new PDF, transversity, h1(x) and new Collins PFF, H ⊥ 1 (z), is shown. New PDFs and PFFs, due to their chiral odd structure, always appear in pairs. The kinematics of the SIDIS is shown in Fig.1b, where ℓ (ℓ ′ ) is the 4-momentum of incident (scattered) lepton, q = ℓ − ℓ ′ , Q 2 = −q 2 , θγ is the angle of the virtual photon momentum �q with respect to the beam, PL(PT ) is a longitudinal (transversal) component of the target polarization, PII, with respect to the virtual photon momentum in the laboratory frame, ph is the hadron momentum with the transverse component pT h , φ is the azimuthal angle between the scattering plane and hadron production plane, φS is the angle of the target polarization vector with respect to the lepton scattering 1 Supported by the RFFI grant 08-02-91013 CERN a 331
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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
Page 282 and 283: Table 2: The parameters of the main
Page 284 and 285: POLARIZATION MEASUREMENTS IN PHOTOP
Page 286 and 287: With a polarized electron beam inci
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Page 290 and 291: INVESTIGATION OF DP-ELASTIC SCATTER
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Page 294 and 295: SPIN PHYSICS WITH CLAS Y. Prok 12,
Page 296 and 297: 1.3 Flavor Decomposition of the Hel
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Page 300 and 301: The upcoming energy upgrade of Jeff
Page 302 and 303: y the nearly 1000 combined citation
Page 304 and 305: � R = −Pt/Pl τ(1 + ε)/2ε; he
Page 306 and 307: 4 Results of GEp-III Experiment In
Page 308 and 309: 6 Theoretical Developments The earl
Page 310 and 311: lz = 0 (along the direction of the
Page 312 and 313: models have recently been challenge
Page 314 and 315: [32] Chung P. L. and F. Coester, Ph
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Page 320 and 321: In summary, we made measurements on
Page 322 and 323: angle between the direction of the
Page 324 and 325: The sensitivity of the data to the
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Page 328 and 329: 3.1.2 Beam charge and spin asymmetr
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Page 334 and 335: l’ l p q p h H (z) 1 h (x) 1 l l
Page 336 and 337: 3. Data selection. The data selecti
Page 338 and 339: φ sin3 a 0.06 0.04 0.02 0 -0.02 -0
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
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
Page 378 and 379: more precise and dedicated measurem
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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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