Polarization: an essential tool for the study of the nucleon structure

Transcription

1 Polarization: an essential tool for the study of the nucleon structure Egle Tomasi-Gustafsson IRFU/SPhN, Saclay and IN2P3/IPN Orsay Wolfgang Pauli Niels Bohr (années 30) GDR, 7-VII

2 PLAN Part I Generalities,definitions A simple example, operative theory Basic principles : measurements, calibration Part II Formalism Hadron polarimeters Some examples: physical problems Repetita juvant. GDR, 7-VII

3 Polarization is unavoidable (M.P. Rekalo) 1) Test of symmetry properties of fundamental interactions decay of polarized 60 Co (violation of P-invariance in weak interaction) 2) Exact measurements of fundamental characteristics of elementary particles magnetic moments, hadron form factors 3) Selection of reaction mechanism 4) Multipole and partial wave analysis spin and parity of spectroscopic levels, exotics 5). GDR, 7-VII

4 The Cobalt 60 experiment In 1956, following a theoretical prediction of Lee and Yang, a young woman, Mrs. Wu, showed that electrons from beta decay of polarized Cobalt 60 nuclei are not symmetrically ejected over and under the plane perpendicular to the Cobalt nuclei spins. There are more electrons going into the direction opposite to the Cobalt nuclei spins. Phys. Rev. 105, 1413 (1957) The space symmetry, an operation called P, is violated by the beta decays, i.e by weak interaction. This experiment showed also that the particle / anti-particle symmetry (the C symmetry) was violated by weak interactions. Eight years later, J. Cronin and his team show that the product CP is also violated by weak interactions. GDR, 7-VII

5 Spin for beginners (1) Spin is a fundamental property that characterizes a particle, like mass, charge A particle of spin 1/2, as a proton, can have two quantified values of the spin projection, +1/2 and -1/2. A beam of protons is not polarized when the two directions are equally probable. Vector polarization is defined as the difference of the populations of the states up ( ) and down ( ) (normalized to the sum). P y N( N( 1/ 2) 1/ 2) N( N( 1/ 2) 1/ 2) GDR, 7-VII

6 Spin for beginners (2) The polarization a beam of particles of spin 1 as deuterons, can have three quantified values of the spin projection, +1, 0, and -1. A deuteron beam is not polarized when the three directions are equally probable. A deuteron beam can be: N( 1) N( 1) - vector polarized P V N( 1) N( 1) N(0) - tensor polarized P T N( N( 1) 1) 2N(0) N( 1) N( 1) N(0) GDR, 7-VII

7 Spin for beginners (3) In the collision of a beam on a target, one measures a cross section, i.e. the probability that a definite particle is scattered at a definite angle. If the beam is unpolarized, Nature knows only one direction: cylindrical symmetry. If the beam is polarized, the reaction looses its symmetry around the beam axis (any fundamental interaction depends on the spin of interacting particles) : Left-right asymmetry : vector polarization Up-down, left-right asymmetry, difference of flux: tensor polarization GDR, 7-VII

8 Spin for users The wave function of a particle with 0 spin, as,, is described by a (pseudo)scalar. The wave function of a particle with spin 1/2, as a proton, is described by a two-component spinor. The wave function of a particle with spin 1, as a deuteron, is described by a three-component vector. The density matrix is an average on an ensemble of particles, quadratic in the wave functions. If a beam is unpolarized it is a diagonal, unit, matrix: all projections are equiprobable. GDR, 7-VII

9 Spin for users GDR, 7-VII

10 Hadron Polarimetry Polarized beams Polarized targets Polarimeters Beam polarimeters Secondary particle polarimeters - At each energy (experiment) its own polarimeter - Polarization experiments are difficult ant time consuming. -The same physical information with polarized target or polarimeter..but polarimeters in general superior GDR, 7-VII

11 The simplest example: The complete experiment parametrization of the - spin structure of the matrix element - polarization observables GDR, 7-VII

12 The Matrix Element : n p 1 p 2 two component spinors of the initial and final nucleons 2 x 2 matrix (most general form, P-conservation) 3-momenta of the initial and final nucleons -a, b scalar amplitudes, complex functions of s and t s=(p 1 +p 2 ) 2 total energy t=(p 1 -p 3 ) 2 momentum transfer squared GDR, 7-VII

13 The Reaction Amplitude : Another representation: with: GDR, 7-VII

14 Observables: what can be measured? p+ p+ : the differential cross section p+ p+ : the analyzing power p+ p+ : the polarization of the scattered proton p+ p+ : the polarization transfer coefficients GDR, 7-VII

15 The complete experiment : Determination of the moduli of the amplitudes does not bring additional information GDR, 7-VII

16 The complete experiment : GDR, 7-VII

17 Hadron Polarimetry Low energy region: Specific reactions (calculable) Elastic scattering on light targets: p+ p+ In the GeV region: Vector polarization: inclusive scattering on light targets: p+c one charged particle +X Tensor polarization: exclusive scattering: d+p d+p (elastic scattering) d+p p+p+n (charge exchange reaction) High energy region (RHIC): Elastic pp scattering, Primakoff reactions (Coulombnuclear interference in pa-scattering) GDR, 7-VII

18 Hadron Polarimetry Working principle: measurement of the azymuthal asymmetry in a secondary scattering Choice of the reaction large cross section (statistical errors) large analyzing power (systematic errors) Precision on the track reconstruction Detector alignment: 1 mm by laser 1/10 mm under beam, with particles which do not undergo nuclear reactions Choice of the reaction GDR, 7-VII

19 HADRON POLARIMETRY The efficiency The figure of merit: The error on the polarization measurement GDR, 7-VII

20 Low energy polarimeter p+ 4 He Coincidence experiment Elastic scattering GDR, 7-VII

21 Proton polarimeter Vector polarization Inclusive reaction: p+c 1 Charged particle+x Energies : from hundreds of MeV to GeV region GDR, 7-VII

22 Proton polarimeter Inclusive reaction: p+c 1 Charged particle+x 1: Calibration Asymmetry { 2: Measurement GDR, 7-VII

23 Absolute Polarization Measurement Upolarized beam Polarized particles P A Inverse reaction =PxA=P 2 GDR, 7-VII

24 Absolute Polarization Measurement Polarized beam or Polarized target pp elastic scattering RHIC 5% FermiLab A. Bravar et al, RHIC Recoil proton detected GDR, 7-VII

25 A.Bazilevsky For the RHIC Polarimetry Group GDR, 7-VII

26 pp and pc :Interference between the EMspinflip amplitude that generates the proton anomalous magnetic moment and the hadron non spin-flip amplitude GDR, 7-VII

27 GDR, 7-VII

28 GDR, 7-VII

29 GDR, 7-VII

30 GDR, 7-VII

31 GDR, 7-VII

32 p + CH 2 one charged particle + X 2 - polarimeter GDR, 7-VII

33 Polarimetry at 4-5 GeV Pomme polarimeter......jinr -LHE synchrophasotron GDR, 7-VII

34 p + CH 2 one charged particle + X GDR, 7-VII

35 HYPOM Figure of merit Optimum thickness: 55 cm In the literature: from 3 to 100cm GDR, 7-VII

36 Current Status Current data base of analyzing power: need Ay at 1/p=0.12 GeV -1, or p=7.5 GeV/c p + CH 2 one charged particle + X Inclusive More reactions at higher energy Hadron calorimeter to reject low energy particles Analyzing power A y Pt ~P sinθ ~ 0.3 GeV/c Smaller angles at high energies GDR, 7-VII

37 Experiments Need to know the proton momentum extended focal plane polarimeter Large detector geometry Magnetic elements spin precession From the focal plane to the target GDR, 7-VII

38 Focal plane polarimeter f ε(θ, ) fpp (, ) 1 A P sin 2π y t fpp A P y n cos P t fpp and P n fpp are the physical asymmetries at the FPP GDR, 7-VII

39 Focal plane polarimeter GDR, 7-VII

40 Azymuthal distribution Q 2 =5.6 GeV/c 2 GDR, 7-VII

41 FPP Jlab Hall C GDR, 7-VII

42 Ed 3 /d 3 p, mb GeV (GeV/c) -3 sr -1 P zz ,5 Polarization transfer 1,0 Polarized proton beam P z POLARIS Deuteron fragmentation d+c->p+x d+c->d+x P d = 9 GeV/c 4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 p, GeV/c 0,5 K 0 0,0-0,5-1,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 k, GeV/c GDR, 7-VII