References - Bogoliubov Laboratory of Theoretical Physics - JINR

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References [1] S. Weinberg, Gravitation and Cosmology, p. 239 ff, Wiley (1972) [2] E.P. Wigner, Ann. Math. 40, 149 (1939) [3] L.H. Ryder, Gen. Rel. Grav. 31, 775 (1999) [4] L.L. Foldy & S.A. Wouthuysen, Phys. Rev. 78, 29 (1950) 454
DYNAMICS OF SPIN IN NONSTATIC SPACETIMES Yu.N. Obukhov 1 , A.J. Silenko 2 † and O.V. Teryaev 3 (1) Department of Mathematics, University College London, London, UK (2) Research Institute of Nuclear Problems, Belarusian State University, Minsk, Belarus (3) Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia † E-mail: silenko@inp.minsk.by Abstract The quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source is discussed. A relativistic equation describing the motion of classical spin in curved spacetimes is derived. The precession of the classical spin is in a perfect agreement with the motion of the quantum spin obtained from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. It is shown that the precession effect depends crucially on the choice of a tetrad. In this paper, we consider two important problems. One aim is to generalize the methods of the Foldy-Wouthuysen transformations, that we previously used for the analysis of the spin in static gravitational fields, to the case of the stationary gravitational configurations. Another aim is to systematically investigate the dependence of the spin dynamics on the choice of a tetrad. We denote world coordinate indices by Latin letters and reserve first letters of the Greek alphabet for tetrad indices. Spatial indices 1, 2, 3 are labeled by Latin letters from the beginning of the alphabet. The separate tetrad indices are distinguished by hats. The line element for the Lense-Thirring (LT) metric [1] is given by with V = ds 2 = V 2 c 2 dt 2 − W 2 δab (dx a − K a cdt)(dx b − K b cdt), (1) � 1 − GM 2c2 �� 1+ r GM 2c2 �−1 � , W = 1+ r GM 2c2 �2 , K r a = 1 c ɛabc ωb xc. (2) The non-diagonal components of the metric (that reflect the rotation of the source) are described by the so-called Kerr field K that is given by Eq. (2) with ω = 2G c2 � 2GM a J = 0, 0, r3 cr3 � , (3) where J = Mcaez is the total angular momentum of the source. The exact metric of the flat spacetime seen by an accelerating and rotating observer also has form (1) where V =1+ a · r c 2 , W =1, Ka = − 1 c (ω × r)a . (4) 455
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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
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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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Page 410 and 411: 3 The conditions for transparent sp
Page 412 and 413: where angles α and β are defined
Page 414 and 415: forward angles, where vector Ay and
Page 416 and 417: espectively. The open symbols repre
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Page 420 and 421: i PV / PV i PV / PV 1 0.5 0 -0.5 -1
Page 422 and 423: The energies of the states Ψ1 −
Page 424 and 425: field P ≈ +1. If we add the trans
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Page 428 and 429: y detector saturation from pC colli
Page 430 and 431: 2 �p+ 8 He analyzing power measur
Page 432 and 433: 3.3 Effect of valence neutrons on s
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Page 438 and 439: 436
Page 441 and 442: REGULARIZATION OF SOURCE OF THE KER
Page 443 and 444: The corresponding phase transition
Page 445 and 446: ABOUT SPIN PARTICLE SOLUTION IN BOR
Page 447 and 448: where the functions fi(s, η) must
Page 449 and 450: SPINDYNAMICS I.B. Pestov JINR, 1419
Page 451 and 452: State of hadron matter is defined t
Page 453 and 454: REMARK ON SPIN PRECESSION FORMULAE
Page 455: It is easy to see that for a (massi
Page 459 and 460: Schwinger gauge. Probably for the f
Page 461 and 462: DSPIN-09 WORKSHOP SUMMARY Jacques S
Page 463 and 464: to some preliminary results reporte
Page 465 and 466: A new measurement of the polarizati
Page 467 and 468: new NLO QCD parametrization of the
Page 469: Name (Institution, Town, Country) E
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