References - Bogoliubov Laboratory of Theoretical Physics - JINR

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2 Analysis Formalism Spin-dependent effects can be measured experimentally using the helicity asymmetry ALL = Δσ 2σ = σ↑⇓ − σ↑⇑ σ↑⇓ + σ↑⇑ defined as the ratio of polarised (Δσ) and unpolarised (σ) cross sections. ↑⇑ and ↑⇓ refer to the parallel and anti-parallel spin helicity configuration of the beam lepton (↑) with respect to the target nucleon (⇑ or ⇓). According to the factorisation theorem, the (polarised) cross sections can be written as the convolution of the (polarised) parton distribution functions, (Δ)qi, the hard scattering partonic cross section, (Δ)ˆσ, and the fragmentation function Df. The gluon polarisation is measured directly via the Photon-Gluon Fusion process (PGF); which allows to probe the spin of the gluon inside the nucleon. To tag this process directly in DIS a high pT hadron pairs data sample is used to calculate the helicity asymmetry. Two other processes compete with the PGF process in leading or- (2) Figure 1: The contributing processes: a) DIS LO, b) QCD Compton and c) Photon-Gluon Fusion. der QCD approximation, namely the virtual photo-absorption leading order (LO) process and the gluon radiation (QCD Compton) process. In Fig. 1 all contributing processes are depicted. The helicity asymmetry for the high pT hadron pairs data sample can thus be schematically written as: A 2h LL (xBj) =RPGF a PGF ΔG LL G (xG)+RLO DA LO 1 (xBj)+RQCDC a QCDC LL ALO 1 (xC) (3) The Ri (the index i refers to the different processes) are the fractions of each process. ai LL represents the partonic cross section asymmetries, Δˆσi /ˆσ i , (also known as analysing power). D is the depolarisation factor 1 . The virtual photon asymmetry ALO 1 is defined as ALO 1 ≡ � i e2 i Δqi � i e2 . i qi To extract ΔG/G from eq. (3) the contribution from the physical background processes LO and QCD Compton needs to be estimated. This is done using Monte Carlo (MC) simulation to calculate Ri fractions and ai LL . The virtual photon asymmetry ALO 1 is estimated using a parametrisation based on the A1 asymmetry of the inclusive data [5]. Therefore a similar equation to (3) can be written to express the inclusive asymmetry of adatasample,A incl LL . Using eq. (3) for the high pT hadron pairs sample and a similar eq. for the inclusive sample the following expression is obtained: 1The depolarisation factor is the fraction of the muon beam polarisation transferred to the virtual photon. 352
and ΔG G (xav corr A2h LL (xBj)+A G ) = β A corr = −A1(xBj)D RLO Rincl − A1(xC)β1 + A1(x LO ′ C)β2 β1 = 1 Rincl � LO β2 = a incl,QCDC LL α1 = a PGF a QCDC LL RQCDC − a incl,QCDC R incl R incl QCDC R incl LO RQCDC R incl LO LL a QCDC LL D LL RPGF − a incl,PGF R LL RLO incl PGF Rincl LO α2 = a incl,PGF R LL RQCDC incl PGF Rincl a LO QCDC LL D β = α1 − α2. RLO QCDC Rincl LO The term Acorr comprises the correction due to the other two processes, namely the LO and the QCD Compton processes. α1, α2, β1, β2, xC, x ′ C and xav G are estimated using high pT and inclusive MC samples. 3 Data Selection Data from 2002 to 2004 years is used. The selected events have an interation vertex containing an incoming muon beam and a scattered muon. As mentioned in sec. 2 the data samples are divided into two data sets: the high pT hadron pairs and the inclusive data samples. Both data sets have the Q 2 > 1(GeV/c) 2 kinematic cut applied. Another cut is applied on the fraction of energy taken by the virtual photon, y: 0.1
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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
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
Page 316 and 317: 48 ± 3% for two beams. The proton
Page 318 and 319: is constant with cos θ∗ , as exp
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
Page 326 and 327: COMPASS could be converted into a f
Page 328 and 329: 3.1.2 Beam charge and spin asymmetr
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Page 332 and 333: References [1] D. Mueller et al, Fo
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 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
Page 380 and 381: oth types of experiment results are
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
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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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References - Bogoliubov Laboratory of Theoretical Physics - JINR

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