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Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 2
Part I
• Generalities,definitions
• A simple example, ‘operative theory’
• Basic principles : measurements, calibration
PLAN
Repetita juvant ….
Part II
• Formalism
• Hadron polarimeters
• Some examples: physical problems
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 3
Polarization is unavoidable…
(M.P. Rekalo)1) Test of symmetry properties of fundamental
interactionsdecay of polarized 60Co
(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 analysisspin and parity of spectroscopic levels, exotics
5) ……….
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 4
The Cobalt 60 experiment
• 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.
• 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)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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).
)2/1()2/1(
)2/1()2/1(
NN
NNPy
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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:
)0()1()1(
)1()1(
NNN
NNPV
)0()1()1(
)1()0(2)1(
NNN
NNNPT
- tensor polarized
- vector polarized
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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.
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 11
The simplest example:
• The complete experiment
parametrization of the - spin structure of the matrix element- polarization observables
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 12
The Matrix Element :
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=(p1+p2)2 total energy
t=(p1-p3)2 momentum transfer squared
np1 p2
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 13
The Reaction Amplitude :
Another representation:
with:
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 14
Observables: what can be measured?
• p+ →p+ : the differential cross section
• p+ →p+ : the polarization of the scattered proton
• p+ →p+ : the analyzing power
• p+ →p+ : the polarization transfer coefficients
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 15
The complete experiment :
Determination of the moduli of the amplitudes
does not bring additional information
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 16
The complete experiment :
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 17
Hadron Polarimetry
In the GeV region:Vector polarization: inclusive scattering on light targets:
p+C → one charged particle +XTensor polarization: exclusive scattering:
d+p → d+p (elastic scattering) d+p → p+p+n (charge exchange reaction)
Low energy region:Specific reactions (calculable)Elastic scattering on light targets: p+ → p+
High energy region (RHIC):Elastic pp scattering, Primakoff reactions (Coulomb-nuclear interference in pA-scattering)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 18
Hadron Polarimetry
Working principle: measurement of the azymuthal asymmetry in a secondary scattering
Choice of the reaction
Choice of the reactionlarge cross section (statistical errors)large analyzing power (systematic errors)
Precision on the track reconstructionDetector alignment:
1 mm by laser1/10 mm under beam, with particles
which do not undergo nuclear reactions
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 19
HADRON POLARIMETRY
• The efficiency
• The figure of merit:
• The error on the polarization measurement
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 20
Low energy polarimeter p+4He
Coincidence experiment
Elastic scattering
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 21
Proton polarimeter
Inclusive reaction: p+C 1 Charged particle+X
Vector polarization
Energies : from hundreds of MeV to GeV region
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 22
Proton polarimeter
1: Calibration
2: Measurement
Inclusive reaction: p+C 1 Charged particle+X
Asymmetry{
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 23
Absolute Polarization Measurement
=PxA=P2
Upolarized beam Polarized particles
Inverse reactionP A
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 24
Absolute Polarization Measurement
A. Bravar et al, RHIC
Polarized beam or
Polarized target
pp elastic scattering
Recoil proton detected
RHIC
FermiLab5%
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 25
A.Bazilevsky
For the RHIC Polarimetry Group
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 26
pp and pC :Interference between the EMspin-flip amplitude that generates theproton anomalous magnetic moment and the hadron non spin-flip amplitude
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 32
p + CH2 → one charged particle + X
2 - polarimeter
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 33
Polarimetry at 4-5 GeV
• Pomme polarimeter ...
...JINR -LHE synchrophasotron
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 34
p + CH2 → one charged particle + X
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 35
Figure of merit
Optimum thickness: 55 cm
In the literature: from 3 to 100cm
HYPOM
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 36
Current data base of analyzing power: need Ay at 1/p=0.12 GeV-1, or p=7.5 GeV/c
p + CH2 → one charged particle + X
InclusiveMore reactions at higher energy
Analyzing power Ay
Pt ~P sinθ ~ 0.3 GeV/c
Smaller angles at high energies
Hadron calorimeter to rejectlow energy particles
Current Status
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 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
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 38
Focal plane polarimeter
cosfppn
Py
Asinfppt
Py
A12π
)ε(θ,),( f
Ptfpp and Pn
fpp are the physical asymmetries at the FPP
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 39
Focal plane polarimeter
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 40
Azymuthal distribution
Q2=5.6 GeV/c2
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNOGDR, 7-VII-2009 42
Polarization transfer4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0
10-2
10-1
100
101
102
103
104
105
106
Pd= 9 GeV/c
d+C->p+X
d+C->d+X
Ed
3/d
3p,
mb G
eV
(G
eV
/c)
-3 s
r-1
p, GeV/c
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
-1,0
-0,5
0,0
0,5
1,0
1,5
K0
k, GeV/c
-1 0 1
-2
-1
0
1
Pzz
Pz
POLARIS
2•109
Polarized proton beamDeuteron fragmentation
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