Nucleon structure study by polarized virtual compton scattering $(\gamma^* p\rightarrow \gamma p)$

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HAL Id: in2p3-00022234

http://hal.in2p3.fr/in2p3-00022234

Submitted on 9 Sep 2004

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Nucleon structure study by polarized virtual compton scattering (γ∗p → γp)

I.K. Bensafa

To cite this version:

I.K. Bensafa. Nucleon structure study by polarized virtual compton scattering (γ∗p → γp). The

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Nucleon Structure Study

By Polarized Virtual

Compton Scattering (γ

∗

p → γp)

I.K.Bensafa

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The VCS COLLABORATION at MAINZ

Institut fur Kernphysik, Johannes Gutenberg-Universitat Mainz, Germany

Patrick Achenbach, Carlos Ayerbe, Dagmar Baumann, Jan Bernauer, Matthias Ding, Michael O. Distler, Luca Doria, Jorg Friedrich, Jordi Garcia Llongo, Iouri Goussev, Werner Heil,

Peter Jennewein, Klaus Werner Krygier, Arnd Liesenfeld, Marcus Lloyd, Harald Merkel, Klaus Merle, Pascal Merle, Ulrich Muller, Reiner Neuhausen, Lars Nungesser,

Roberto Perez Benito, Josef Pochodzalla, Alexander Piegsa, Salvador Sanchez Majos, Thomas Walcher DAPNIA/SPhN CEN Saclay, F91191 Gif sur Yvette, France

Etienne Burtin, Nicole D’Hose, Michel Garcon, P.A.M. Guichon, Jacques Marroncle, Michael Seimetz LPC Clermont-Fd, IN2P3-CNRS, Universite Blaise Pascal, 63177 Aubiere, France

Imad Bensafa, Helene Fonvieille, Geraud Laveissiere

Institut fur Kernphysik, Johannes Gutenberg-Universitat Mainz, Germany Gabriel Tamas, Marc Vanderhaeghen

Physik-Department, Technische Universitat Munchen, D-85748 Garching, Germany Jan M. Friedrich

SSF, Universiteit Gent, Belgium

Peter Janssens, Dirk Ryckbosch, Robert Van de Vyver, Luc Van Hoorebeke ECT, Villazzano, I38050 Trento, Italy

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Schematic view of A1 Collaboration, MAMI (Mainz, Germany)

The reaction is :

ep

epγ

E (Beam Energy) = 0.88 GeV

P (Beam Polarisation) ~ 80

Detection in coincidence of

- The scattered electron

A

- The final proton

B

(High Resolution Spectrometers

(Final γ = missing particl

in Spectrometer

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Kinematic of electroprodution of photon (ep → epγ) and Feynman diagrams

ϕ

γ

p

p’

*

e

e’

Hadronic plane in CM frame Hadronic plane in CM frame Leptonic plane in Lab frame

Leptonic plane in Lab frame

θγγ* (k ) (k ) (-q ) (-q ) (q ) (q ) (k’ ) (k’ ) (q’ )(q’ ) (-q’ ) (-q’ ) lab cm cm cm cm lab lab

γ*

(q )(q )cm

ep

e’p’

γ

γ _γ

+

+ +

VCS

e

p’ p’ γ γ γ γ

p

e’

p

Bethe-Heitler (BH)

Kinematic variables :

Q2 = 0.34GeV 2 = Four-momentum transfer of Virtual Photon

q = 0.23GeV = CM momentum of final photon

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Polarizabilities in Real Compton Scattering

applied E

αE βB

applied B

• World Data:

V.Olmos de Leon et al,Eur.Phys. J. A 10 (2001) 207 [Global Fit, Table 3].

Electric polarizability

_α

¯

_E

= ( 12.1 ±0.3

_stat

∓ 0.4

_syst

) 10

−4

fm

3

Magnetic polarizability

_β

¯

_M

= ( 1.6 ±0.4

_stat

± 0.4

_syst

) 10

−4

fm

3

• Proton: very rigid object

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Nucleon Generalized Polarisabilities (GPs).

• The (GPs) are the Polarisabilities of the nucleon for Q2 = 0

• The (GPs) have been measured up to now by (ep → epγ) unpolarized

1. Below pion threshold : √_{s < (mN} + mπ), q = 126MeV/c

• Low energy Theorem (LET)

[P.Guichon et al, Nucl.Phys. A591(1995) 606] :

d5σ(epγ) = d5σ(BH+Born) + (P haseSpaceF actor).q_cm.([...] + O(q_cm2 ))

[...] = 2K2{v1[PLL(q) −PT T(q)] + (v2 − _q˜qv3)2(1 + )PLT(q)}

VCS Structure functions: contain the GPs

PLL = −2√6MGEP(L1,L1)0, PT T = −3MGMq_˜q₀2(P(M1,M1)1 −√2˜q0P(L1,M2)1), PLT = 3 2M qQ GEP(M1,M1)0 + 32M q˜q0 GMP (L1,L1)1_), Where :

- _P_LL proportional to the electric generalized polarisability _α_E(Q2) ∼ _P(L1,L1)0

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the Dispersion Relations (DR) method

• above pion threshold:

The Low Energy Theorem does not hold (T

_{V CS}

becomes complex)

Dispersion Relation Model, B.Pasquini et al., Eur.Phys.J.A 11 (2001) 185

D.Drechsel et al., Phys.Rept.378 (2003) 99

Im ₌ + ... Ν γ∗ Ν γ Ν γ∗ Ν γ π N

2

_/

_Λ

α2

)

2

,

same for

β

M

.

• model valid until ππ threshold → √s ∼ m∆(1232) = good region

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SSA. Theoretical formula of Single Spin Asymmetry (SSA).

- The SSA is defined by :

SSA = σ(he = +

1

2)− σ(he = −12)

σ(he = +1₂) +σ(he = +1₂)

1) SSA in (ep → epγ) above pion threshold:

dσ(γ∗p → γp) = dσT + dσL+2(1 + )dσLTcosΦ + dσT Tcos2Φ + h

(1−)dσLTsinΦ

SSA(γ∗p → γp) ∼ ₍₁₋₎ dσLTsinΦ ∼ (T_{V CS})

SSA measures the imaginary part of the VCS Amplitude

In electroproduction of photon: (Interference with the Bethe-Heitler process)

2) SSA in (ep → epπ0):

dσ(γ∗p → pπ0) = dσT + dσL +2(1 + )dσLTcosΦ + dσT Tcos2Φ

+h2(1 − )dσLTsinΦ

SSA(ep → epπ0) ∼ 2(1 − )dσLTsinΦ

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Experimental methods to determine the SSA.

• Likelihood method:

- We make an assumption that the Φ-dependence

of the SSA is a pure sinΦ (Φ = Φ_γγcm) :

SSA = SSA(qcm¯ , ¯q_cm , ¯, ¯θ, Φ) = K(q¯cm, ¯q_cm , ¯, ¯θ) × sinΦ

- fit the K factor and its error ∆K by the likelihood method.

• Binphi method:

- The asymmetry is given classically from the number of counts in Bins in Φ:

SSA =

σ_σ++−₊_σσ−−

=

N+ L+∆Ω+− N− L−∆Ω− N+ L+∆Ω++ N− L−∆Ω−

×

_{|BeamP ol|}1 (+,-)=(_h_e = +1₂_,_h_e = −1₂).

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-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0 5 0 100 150 200 250 300 350

Single Spin Asym. and Non-Born terms

Azimuthal angle, deg.

Single spin asymmetry

Bethe-Heitler + Born terms

All terms

Non-Born terms

polar angle = 10 deg

q-cm = 0.60 GeV/c

epsilon = 0.48

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Conclusions.