γ*q

e

Michel Garçon – SPhN/Saclay Bates Symposium, MIT, Cambridge, September 2006

Tensor Polarizationin

Elastic electron-deuteron scattering

Tensor Polarizationin

Elastic electron-deuteron scattering

e’- Why polarization ?

- Experimental techniques(t20 vs T20)

- Results and separation of form factors

- First measurement of iT11(e)

- Physical interpretation (not a review !)

- One interesting finding: the deuteron and χET

- Conclusion

When polarization reveals the shape of thingsWhen polarization reveals the shape of things

The deuteron, as a spin 1 nucleus,

has 3 electromagnetic form factors,

determined through

the measurement of 3 observables;

at least one of them must be

a polarization measurement

0=M

1±=M

Elastic electron-deuteron scatteringElastic electron-deuteron scattering

⎟⎠⎞

⎜⎝⎛ +×

Ω=

Ω 2tan2 θσσ BA

dd

dd

P

Cross section

Spin 1

GCGQGM

Polarization observables

⎟⎠⎞

⎜⎝⎛ +×∝

∝∝

∝∝

∝

⎟⎟⎠

⎞⎜⎜⎝

⎛≈

QCMe

Me

M

QM

C

Q

GGGt

BGt

BGt

GGtGG

ft

η31

11

210

222

21

20

What are t20 and T20 ?What are t20 and T20 ?

011

01120

2

21

=−=+=

=−=+=

⎟⎠⎞

⎜⎝⎛Ω

+⎟⎠⎞

⎜⎝⎛Ω

+⎟⎠⎞

⎜⎝⎛Ω

⎟⎠⎞

⎜⎝⎛Ω

−⎟⎠⎞

⎜⎝⎛Ω

+⎟⎠⎞

⎜⎝⎛Ω

=

MMM

MMM

dd

dd

dd

dd

dd

dd

tσσσ

σσσ

measures the alignment of the deuterons, along their direction of motion, after the e-d scattering

→ recoil polarization measurement

Likewise T20 measures the relative probability of scattering from a polarized deuteron in different spin states

→ polarized target measurement

T20 = t20, and they are bounded between and )1pure(2/2

)0pure(2

±=+

=−

M

M

ExperimentsExperiments

1980 1985 1990 1995 2000 2005

t20

T20

Bates/Argonne

Bates/AHEAD

Bates/BLASTBates/BLASTVEPP-2

VEPP-3

VEPP-3

JLab/POLDER

NIKHEF

NIKHEF

(Bonn)

The necessary measurement of polarization observables

The necessary measurement of polarization observables

Polarized target (T20) Recoil polarization (t20)

Atomic gasin storage ring

Novosibirsk

NIKHEF

Bates/BLAST

Cryogenic solid targetin extracted beam

Bonn

Background under e-d events (not true for BLAST)Target polarization measurement tricky

Data analysis “straightforward”

e-d events cleanExternal calibration requiredPolarimeter analysis tricky

Bates/Argonne 3He(d,p)

Bates/AHEAD H(d,p)

JLab/POLDER H(d,pp)

e

e’e

e’

d

d

Double scattering experimentsDouble scattering experiments

Very low counting rates imply- Very high intensity beam 10-100 µA

- Primary deuterium target as thick as possible, 5-12 cm LD2

capable of coping with the heat deposited by the beam up to 400 W

- Large acceptance magnetic channel for recoil deuterons,

focusing them on the (secondary) polarimeter target 6-12 msr

- High efficiency of the polarimeter ~ 1/1000

Deuteron (tensor) polarimetersDeuteron (tensor) polarimeters

3He+p→d+XA(.01)0.3(10-3)1-2 GeVH(d,p) HYPOM

C(d,d’) pp→dπed JLab

R+A.013-0.24.10-3160-520H(d,pp) POLDER

ed BatesR.018-0.42.10-3100-200H(d,p) AHEAD

ed Bates πd→πdA.008-0.810

-420-503He(d,p)

ExperimentsAbsolute or

relative norm.

Figure of merit

ε½

Analyzing power

Efficiencyε

d energy range (MeV)

)2( 2 ddTmQ =

Deuteron magnetic channels (1)Deuteron magnetic channels (1)

Bates/Argonne experiment

Deuteron magnetic channels (2)Deuteron magnetic channels (2)

Bates/AHEAD experiment

Deuteron magnetic channels (3)Deuteron magnetic channels (3)

JLab/POLDER experiment

Polarized deuterium targetsPolarized deuterium targets

Atomic beam…(across circulating electron beam)

Novosibirsk 1012 d/cm2

…. stored in a cellNovosibirsk

NIKHEF 2-8 1013 d/cm2

Bates

PT ~ 0.65 - 0.85

L ~ 1031-1032 cm-2s-1

Cryogenic solid target

deuterated butanol

ND3 Bonn < 1nA

(could be improved ND3 or LiD 100 nA)

PT ~ 0.2

L ~ 1032 cm-2s-1

Polarized deuterium targets (2)Polarized deuterium targets (2)

Beam

D2 Gas

Target Cell

Polarized atomic beam

+ storage cell

e

D

(NIKHEF)

Target density up to 1014 atoms/cm3

PZZ fromSextupoles +

RF transitions in- Medium Field - Strong Field (Bates/BLAST)

Experimental figure of meritExperimental figure of merit

?

?

Kinematics of different experimentsKinematics of different experiments

Results: t2q until 2001Results: t2q until 2001

Results: t2q in 2006Results: t2q in 2006

VEPP-3:

Nikolenko et al., PRL 90

Bates/BLAST (preliminary):

C. Zhang, PhD thesis, MIT 2006

GC nodeGC node

2/2~0

21)2(2~

432

20

220

2

2

−=⇒=

++

−=

=

tG

xxxt

GG

MQx

C

C

Q

d

Results (form factors)

Results (form factors)

Results (form factors)

Results (form factors)

GC nodeGC node

What about vector polarization ?What about vector polarization ?

⎟⎠⎞

⎜⎝⎛ +×

Ω=

Ω 2tan2 θσσ BA

dd

dd

P

Cross section

Spin 1

GCGQGM

Polarization observables

⎟⎠⎞

⎜⎝⎛ +×∝

∝∝

∝∝

∝

⎟⎟⎠

⎞⎜⎜⎝

⎛≈

QCMe

Me

M

QM

C

Q

GGGt

BGt

BGt

GGtGG

ft

η31

11

210

222

21

20

Can extract GMindependently of

back angles measurements (B)

First measurement of T11(e)(BLAST)

First measurement of T11(e)(BLAST)

P.J. Karpius, Ph.D. thesis, UNH, Dec. 2005

Physical interpretationPhysical interpretation

e

e’

π,ρ,ω

p

n

e

e’

e

e’

p

n

e’

e

Nucleon-nucleon potential:from one-pion exchange to short-range repulsion

Isoscalar meson-exchange currents

Beyond nucleons and mesons:Isobar configurations,

6-quarks cluster (hidden color)?

Asymptotic regime: perturbative QCD

Low Q Intermediate Q High Q

Non-relativistic potential modelsNon-relativistic potential models

From

the impulse approximation (NRIA)

to the inclusion of

meson-exchange currents

Spectator nucleon on-shell

Gross, Van Orden…

Hummel, Tjon…

Devine, Phillips, Wallace

Carbonell, Karmanov... Cooke, Miller…

Chung…, Strikman… Lev, Pace, Salme

Allen, Klink, Polyzou…

Forest, Schiavilla

Quantum Mechanics(equation of motion from different representations of Poincaré group)

Instant form Point form

2 nucleons equally off mass shell

Integration over relative energy (ET)

Relativistic calculationsRelativistic calculations

Bethe-Salpeter (4D)

3D-reductionsLight-front dynamics

Light-front form

Quantum Field Theory(explicitly covariant)

Relativistic calculationsRelativistic calculations

Phillips, Wallace & Devine, PRC 72 (2005)(ET calculation now includes MEC)

t20 is quite sensitive to relativistic effects

Gilman & Gross,JPG 28 (2002):

t20 is insensitive to relativistic effects

Relativistic calculationsRelativistic calculations

The very techniques

developed for the study of the deuteron

were in some cases applied to

quark-antiquark wave functions

Exemple: semi-leptonic decays such as need proper relativistic treatment

↔ precise determination of CKM matrix elements

F. Bissey & J.-F. Mathiot, EPJC 16 (2000) 131

lDlB ν→

t20 & helicity amplitudes:high Q2 behaviour

t20 & helicity amplitudes:high Q2 behaviour

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

Λ

Λ≈⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧↔

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

=Δ

=Δ

=Δ

=Δ

20

2

1

0

)/()/(

1

QbQaG

GGG

G

GG

h

h

h

h

M

Q

C

BB node node impliesimpliesnonnon--zero zero helicityhelicity flip amplitudeflip amplitude

tt2020 andand tt2121 implyimply large large doubledouble--helicityhelicity flip amplitudeflip amplitude

Chiral effective theory (χEFT)Chiral effective theory (χEFT)

NN wave functions calculated from NN potential

expanded up to a given order in P=(p,mπ)/Λ :

O(P2)=NLO, O(P3)=NNLO, O(P4)=N3LO.

Short-range physics integrated out as contact terms in the

Lagrangian with increasing numbers of derivatives in the field.

Likewise for deuteron current operator Jµ (up to NNLO).

Low Q2 and χETLow Q2 and χET

GC/GE(s) has much better converging properties in this expansion than GC itself (D. Phillips)

- that amounts to avoid difficulties in the theory associated with the nucleon structure.

Since t20 is given mostly by GQ/GC at low Q2, and since the (isoscalar) nucleon form factor GE(s) cancels in this ratio,

tensor polarization is a good testing ground for chiral effective theories (χET) !

D. P. was also led to introduce a O(P5) term to remedy the long standing problem that NN potentials underestimate Qd by 2-3%. The physical significance of this term in still unclear, but, if interpreted in terms of

meson exchange, the first current that would contribute would be ρa1γ ! In any case, a very short-range ingredient is needed to describe Qd

and … t20 .

Tensor polarization and χEFTTensor polarization and χEFT

202d

20

2d20

2

~Q23~ define

Q, lowAt

tQ

t

QtQ

R −=⇒

∝ D. Phillips, nucl-th/0608036, (+ M.G.)

BLAST

M. G. & Van Orden, Adv. Nucl. Phys. (2001)

Some conclusionsSome conclusions

- ~ 25 years of t20/T20 measurements have led to the separate determination of the deuteron charge monopole and quadrupole form factors.

- Two competing techniques used successfully(double scattering vs polarized target)

- Bates/BLAST increased significantly the precision in the determination of GC around its node position- Stimulated significant theoretical progress in (arduous) relativistic calculations

- Intermediate to high Q2: no manifest evidence for the role of quarks in nuclei.

- Low Q2: Bates/BLAST results on t20 and recent development in χEFT in the NN sector meet interestingly.

Some conclusionsSome conclusions

Next experimental stepsNext experimental steps:

• Precise measurement of A(Q2) at low Q2 (JLab).• GM node and secondary maximum need to be measured.

• An absolute and high precision low Q2 measurement of T20 highly desirable (but where ?)• t20/T20 (or t11(e)) at high Q2 (but how ?)