Polarization: an essential tool for the study of the ... · Polarization: an essential tool for the study of the nucleon structure Egle Tomasi-Gustafsson ... Ballade, épitaphe et

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)


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


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) ……….


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)


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



• 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



• 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


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.


Spin for users


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


The simplest example:

• The complete experiment

parametrization of the - spin structure of the matrix element- polarization observables


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


The Reaction Amplitude :

Another representation:

with:


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


The complete experiment :

Determination of the moduli of the amplitudes

does not bring additional information


The complete experiment :


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)


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


HADRON POLARIMETRY

• The efficiency

• The figure of merit:

• The error on the polarization measurement


Low energy polarimeter p+4He

Coincidence experiment

Elastic scattering


Proton polarimeter

Inclusive reaction: p+C 1 Charged particle+X

Vector polarization

Energies : from hundreds of MeV to GeV region


Proton polarimeter

1: Calibration

2: Measurement

Inclusive reaction: p+C 1 Charged particle+X

Asymmetry{


Absolute Polarization Measurement

=PxA=P2

Upolarized beam Polarized particles

Inverse reactionP A


Absolute Polarization Measurement

A. Bravar et al, RHIC

Polarized beam or

Polarized target

pp elastic scattering

Recoil proton detected

RHIC

FermiLab5%


A.Bazilevsky

For the RHIC Polarimetry Group


pp and pC :Interference between the EMspin-flip amplitude that generates theproton anomalous magnetic moment and the hadron non spin-flip amplitude







p + CH2 → one charged particle + X

2 - polarimeter


Polarimetry at 4-5 GeV

• Pomme polarimeter ...

...JINR -LHE synchrophasotron




Figure of merit

Optimum thickness: 55 cm

In the literature: from 3 to 100cm

HYPOM


Current data base of analyzing power: need Ay at 1/p=0.12 GeV-1, or p=7.5 GeV/c


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


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


Focal plane polarimeter

cosfppn

Py

Asinfppt

Py

A12π

)ε(θ,),( f

Ptfpp and Pn

fpp are the physical asymmetries at the FPP


Focal plane polarimeter


Azymuthal distribution

Q2=5.6 GeV/c2


FPP –Jlab Hall C


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

Polarization: an essential tool for the study of the ... · Polarization: an essential tool for the study of the nucleon structure Egle Tomasi-Gustafsson ... Ballade, épitaphe et

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