Compton Scattering from Low to High Energies

Home , Compton scattering

Marc Vanderhaeghen College of William & Mary / JLab

HUGS 2004 @ JLab, June 1-18 2004 Outline

Lecture 1 : Real Compton scattering on the nucleon and sum rules

Lecture 2 : Forward virtual Compton scattering & nucleon structure functions

Lecture 3 : Deeply virtual Compton scattering & generalized parton distributions

Lecture 4 : Two-photon exchange physics in elastic electron-nucleon scattering …if you want to read more details

in preparing these lectures, I have primarily used some review papers :

Lecture 1, 2 : Drechsel, Pasquini, Vdh : Physics Reports 378 (2003) 99 - 205

Lecture 3 : Guichon, Vdh : Prog. Part. Nucl. Phys. 41 (1998) 125 – 190 Goeke, Polyakov, Vdh : Prog. Part. Nucl. Phys. 47 (2001) 401 - 515

Lecture 4 : research papers , field in rapid development since 2002 1st lecture :

Real Compton scattering on the nucleon & sum rules IntroductionIntroduction :: thethe realreal ComptonCompton scatteringscattering (RCS)(RCS) processprocess

ε, ε’ : photon polarization vectors σ, σ’ : nucleon spin projections

Kinematics in LAB system :

shift in wavelength of scattered photon Compton (1923) ComptonCompton scatteringscattering onon pointpoint particlesparticles

Compton scattering on spin 1/2 point particle (Dirac) e.g. e-

Klein-Nishina (1929) : Thomson term ΘL = 0 Compton scattering on spin 1/2 particle with anomalous magnetic moment Stern (1933)

Powell (1949) LowLow energyenergy expansionexpansion ofof RCSRCS processprocess Spin-independent RCS amplitude note : transverse photons :

Low energy expansion of RCS amplitude : small

Low energy theorem (LET) : terms parametrizing the internal based on gauge invariance, structure of particle : Lorentz covariance, crossing and discrete symmetries Electric ( α ) and Magnetic ( β ) dipole polarizabilities of Low, Gell-Mann, Goldberger nucleon (1954) ElectricElectric andand MagneticMagnetic polarizabilitiespolarizabilities ofof aa compositecomposite systemsystem

the polarizability is a measure for the rigidity (stiffness) of a system LowLow energyenergy expansionexpansion ofof RCSRCS crosscross sectionsection inin termsterms ofof polarizabilitiespolarizabilities

Polarizability term : quadratic in the photon energy Angular dependence : disentangle α and β

Higher terms in photon energy : can be treated in a dispersion relation formalism (see later) LowLow energyenergy RCSRCS onon protonproton

+ higher order terms in energy Powell (nucleon with Κ ) + π0 pole

+ in low energy exp.

point nucleon (Κ = 0) Klein- Nishina LowLow energyenergy RCSRCS onon protonproton :: globalglobal fitfit

in units 10-4 fm3 !

Olmos de Leon (2001) ForwardForward realreal ComptonCompton scatteringscattering (RCS)(RCS)

forward scattering k = k’, p = p’ photon crossing: low energy expansion: ν !0

Low Energy Theorem dipole higher order polarizabilities polarizab. Low, Gell-Mann, Goldberger (1954) DispersionDispersion relationsrelations forfor forwardforward RCSRCS

unsubtracted DR : if circle at ∞ vanishes

branch cuts : πΝ, ππN, … thresholds analyticity in ν, causality Cauchy integral formula crossing symmetry SumSum rulesrules forfor forwardforward RCSRCS

Unitarity Optical Theorem

make a low energy expansion of both left and right sides of DRs SUM RULES SpinSpin independentindependent sumsum rulesrules forfor RCSRCS

term in ν0

600 ∆ (1232) M1/E2 0.08 for ν!1, σTOT = (σ1/2+σ3/2)/2 » ν µ

( b ) ) NO convergence

300 * N (1520) E1/M2 term in ν2 N*(1680) E2/M3 Total cross section Total cross

S wave Baldin sum rule (1960) 0 020.51 1.5 ν (GeV) DigressionDigression :: ultraultra--highhigh energyenergy cosmiccosmic raysrays andand thethe totaltotal photoabsorptionphotoabsorption crosscross sectionsection onon thethe protonproton

energy spectrum of ultra-high energy cosmic rays (protons)

P. Lipari (ISVHECRI 2002) ultraultra--highhigh energyenergy cosmiccosmic raysrays :: GZKGZK cutcut--offoff andand thethe totaltotal photoabsorptionphotoabsorption crosscross sectionsection onon thethe protonproton Protons scatter from Cosmic Microwave Background (CMB)

dominant processes :

GZK cut-off Greisen (1966) Zatsepin & Kuzmin (1966) Puzzle to see protons with Ep > GZK cut-off “exotic” sources near our galaxy ?

24 decay of very large mass particles MX ~ MGUT ~ 10 eV ? SpinSpin dependentdependent sumsum rulesrules forfor RCSRCS

term in ν consequence of : gauge invariance, analyticity (DR), unitarity, Gerasimov-Drell-Hearn (GDH) sum rule (1966) + convergence assumption (no-subtraction) GDHGDH sumsum rulerule inin QEDQED

Compute both sides of the sum rule in perturbation theory. Is the GDH sum rule verified? for Dirac particle : electron anomalous magnetic moment (loop effect) to 1-loop accuracy :

Schwinger

experiment electron : g = 2.002319304374 ± 8 . 10-12 ! GDHGDH sumsum rulerule inin QEDQED :: O(eO(e4)) 2 +

at O(e4) :

Altarelli, Cabibbo, Maiani (1972) GDHGDH sumsum rulerule inin QEDQED :: O(eO(e6))

+ + ... tree level 1-loop diagrams 2 + + ...

Dicus, Vega (2001)

GDH sum rule is satisfied in QED to order O(e6) SpinSpin dependentdependent sumsum rulesrules forfor RCSRCS onon protonproton

GDH sum rule (1966) :

600 b) µ (

1/2 500

σ π - sum rule for proton : 3/2

σ 400 lhs = 205 µb 300 MAMI [200, 800] MeV 200 ELSA [0.7, 3.1] GeV

100 π π π + π π + η π MAID2000 Drechsel, Kamalov, Tiator (`00) 0 ππ Holvoet, Vdh (`01) η -100 η ETA- MAID2000 0 200 400 600 800 1000 1200 1400 1600 1800 π + ππ + η ν (MeV) SpinSpin dependentdependent sumsum rulesrules forfor RCSRCS onon protonproton

term in ν : GDH sum rule

Forward Spin Polarizability (FSP) term in ν3 :

PROTON Eγ GDH FSP results [GeV] [µb] [10-4 fm4] MAID2000 estimate < 0.2 -28.5 ± 2 0.95 ± 0.05 MAMI experiment 0.2 - 0.8 226 ± 5 ± 12 -1.87 ± 0.08 ± 0.10 ELSA experiment 0.8 - 2.9 27.5 ± 2.0 ± 1.2 -0.03 Bianchi-Thomas / > 2.9 -14 ± 2 +0.01 Simula et al. : estimate Total 211 ± 15 -0.94 ± 0.15 GDH sum rule 205