Overview of nucleon form factor measurements Mark Jones Jefferson - PowerPoint PPT Presentation

Overview of nucleon form factor measurements Mark Jones Jefferson Lab HUGS 2009

Overview of nucleon form factor measurements Review articles C. F. Perdrisat, V. Punjabi, M. Vanderhaeghen Prog.Part.Nucl.Phys.59:694,2007 J. Arrington, C. D. Roberts, J. M. Zanotti, J.Phys.G34:S23-S52,2007 Mark Jones Jefferson Lab HUGS 2009

In the beginning ... • 1918, Rutherford discovers the proton • 1932, Chadwick discovers the neutron and measures the mass as 938 +/- 1.8 MeV • 1933, Frisch and Stern measure the proton’s magnetic moment = 2.6 +/- 0.3 µ B = 1 + κ p magnetic moment = 2.6 +/- 0.3 µ B = 1 + κ p • 1940, Alvarez and Bloch measure the neutron’s magnetic moment = 1.93 +/- 0.02 µ B = κ n

In the beginning ... • 1918, Rutherford discovers the proton • 1932, Chadwick discovers the neutron and measures the mass as 938 +/- 1.8 MeV • 1933, Frisch and Stern measure the proton’s magnetic moment = 2.6 +/- 0.3 µ B = 1 + κ p magnetic moment = 2.6 +/- 0.3 µ B = 1 + κ p • 1940, Alvarez and Bloch measure the neutron’s magnetic moment = 1.93 +/- 0.02 µ B = κ n Proton and neutron have anomalous magnetic moments a finite size.

Electron as probe of nucleon elastic form factors Known QED coupling

Electron as probe of nucleon elastic form factors Unknown γ ∗ Ν Known QED coupling coupling

Electron as probe of nucleon elastic form factors Unknown γ ∗ Ν Known QED coupling coupling Nucleon vertex: γ � + iκ � Γ � ( p ′ , p ) = F 1 ( Q 2 ) 2 M � F 2 ( Q 2 ) σ �ν q ν � �� � � �� � Dirac P auli Elastic form factors F 1 is the helicity conserving(non spin�flip) F 2 is helicity non�conserving(spin�flip)

Electron-Nucleon Scattering kinematics Scattered electron e , � P ′ e = ( E ′ k ′ ) Θ e Incident Electron beam P e = ( E e ,� k ) γ ∗ γ Fixed nucleon target with mass M Ν Virtual photon kinematics Q 2 = − ( P e − P ′ e ) 2 = 4 E e E ′ e sin 2 ( θ e / 2) � �� � �� ν = E e − E ′ e

Electron-Nucleon Scattering kinematics Scattered electron e , � P ′ e = ( E ′ k ′ ) Θ e Incident Electron beam P e = ( E e ,� k ) γ ∗ γ Fixed nucleon target with mass M Ν Virtual photon kinematics Q 2 = − ( P e − P ′ e ) 2 = 4 E e E ′ e sin 2 ( θ e / 2) � �� � �� ν = E e − E ′ e � M 2 + 2 Mν − Q 2 γ ∗ Ν center of mass energy W =

Electron-Nucleon Scattering kinematics Scattered electron e , � P ′ e = ( E ′ k ′ ) Θ e Incident Electron beam Elastic W = M P e = ( E e ,� W scattering k ) Final Inelastic scattering W > M + m π W > M + m π scattering States Resonance W = M R scattering Virtual photon kinematics Q 2 = − ( P e − P ′ e ) 2 = 4 E e E ′ e sin 2 ( θ e / 2) � �� � �� ν = E e − E ′ e � M 2 + 2 Mν − Q 2 γ ∗ Ν center of mass energy W =

Electron-Nucleon cross section Single photon exchange (Born) approximation E ′ dσ ( dσ e { F 2 1 ( Q 2 ) d = d ) ���� E e � � 2 ( Q 2 ) + 2( F 1 ( Q 2 ) + κF 2 ( Q 2 )) 2 tan 2 θ e κ 2 F 2 + τ } 2 τ = Q 2 / 4 M 2 τ = Q / 4 M E ′ d � = ( dσ dσ E � F 2 1 ( Q 2 ) Low Q 2 d � ) ���� �

Early Form factor measurements � Proton is an extended q � � r ) e i� r d 3 � r | 2 σ = σ ���� | ρ ( � ρ ( � r ) charge potential σ σ ���� q ) | 2 σ = σ ���� | F ( � Proton has a Proton has a radius of 0.80 x 10 -13 cm √ 3 ae a � � r ρ ( � r ) = q ) = (1 + q � a � ) − 2 F ( � “Dipole” shape fm -2 Q 2 = 0.5 GeV 2

Sach’s Electric and Magnetic Elastic Form Factors In center of mass of the eN system ( Breit frame), no energy transfer ν CM = 0 so | � | 2 = | � q | 2 ρ ( � r ) � ( � r ) = charge distribution = magnetization distribution � � q � � q � � r ) e i� r d 3 � r ) e i� r d 3 � G E = ρ ( � r G M = � ( � r At Q 2 = 0 G Mp = 2 . 79 G Mn = − 1 . 91 G Ep = 1 G En = 0

Electron-Nucleon cross section τ = Q 2 / 4 M 2 Single photon exchange (Born) approximation E ′ dσ ( dσ e { F 2 1 ( Q 2 ) d = d ) ���� E e � � 2 ( Q 2 ) + 2( F 1 ( Q 2 ) + κF 2 ( Q 2 )) 2 tan 2 θ e κ 2 F 2 + τ } 2 G E ( Q 2 ) G E ( Q 2 ) F 1 ( Q 2 ) − κ N τ F 2 ( Q 2 ) F 1 ( Q 2 ) − κ N τ F 2 ( Q 2 ) = = G M ( Q 2 ) F 1 ( Q 2 ) + κ N F 2 ( Q 2 ) =

Elastic cross section in G E and G M Q 2 = 2.5 Q 2 = 5 Q = 5 Q 2 = 7 Slope Intercept

Proton Form Factors: G Mp and G Ep Experiments from the 1960s to 1990s gave a cumulative data set G E /G D ≈ G M / ( � p G D ) ≈ 1 � � � � �� � − � �� � �� �

Proton Form Factors: G Mp and G Ep G E contribution to σ is Experiments from the 1960s to 1990s small then large error bars gave a cumulative data set G E /G D ≈ G M / ( � p G D ) ≈ 1 � � � � �� � − � �� � �� � At large Q 2 , G E contribution is smaller so difficult to extract

Proton Form Factors: G Mp and G Ep GE > 1 then large error Experiments from the 1960s to 1990s bars and spread in data. gave a cumulative data set G E /G D ≈ G M / ( � p G D ) ≈ 1 � � � � �� � − � �� � �� � At large Q 2 , G E contribution is smaller so difficult to extract G M measured to Q 2 = 30 G E measured well only to Q 2 = 1

Q 2 dependence of elastic and inelastic cross sections As Q 2 increases σ elastic / σ Mott drops dramatically

Q 2 dependence of elastic and inelastic cross sections As Q 2 increases σ elastic / σ Mott drops dramatically At W = 2 GeV σ inel / σ Mott drops less steeply

Q 2 dependence of elastic and inelastic cross sections As Q 2 increases σ elastic / σ Mott drops dramatically At W = 2 GeV σ inel / σ Mott drops less steeply At W=3 and 3.5 At W=3 and 3.5 σ inel / σ Mott almost constant

Q 2 dependence of elastic and inelastic cross sections As Q 2 increases σ elastic / σ Mott drops dramatically At W = 2 GeV σ inel / σ Mott drops less steeply At W=3 and 3.5 At W=3 and 3.5 σ inel / σ Mott almost constant Point object inside the proton

Asymptotic freedom to confinement • “point-like” objects in the nucleon are eventually identified as quarks • Theory of Quantum Chromodynamics (QCD) with gluons mediating the strong force. • At high energies , the quarks are asymptotically free and perturbative QCD approaches can be used . perturbative QCD approaches can be used .

Asymptotic freedom to confinement • “point-like” objects in the nucleon are eventually identified as quarks • Theory of Quantum Chromodynamics (QCD) with gluons mediating the strong force. • At high energies , the quarks are asymptotically free and perturbative QCD approaches can be used. �������� �������� ����������� ������� • The QCD strong coupling increases as the quarks separate from each other • Quantatitive QCD description of nucleon’s properties remains a puzzle • Study of nucleon elastic form factors is a window see how the QCD strong coupling changes

Elastic FF in perturbative QCD Infinite momentum frame γ ∗ � Nucleon looks like three massless quarks � Energy shared by two hard gluon exchanges u u � Gluon coupling is 1/Q 2 gluon u u F 1 ( Q 2 ) ∝ 1 /Q 4 F 1 ( Q ) ∝ 1 /Q gluon d d d d Proton Proton

Elastic FF in perturbative QCD Infinite momentum frame γ ∗ � Nucleon looks like three massless quarks � Energy shared by two hard gluon exchanges u u � Gluon coupling is 1/Q 2 gluon u u F 1 ( Q 2 ) ∝ 1 /Q 4 F 1 ( Q ) ∝ 1 /Q gluon d d d d � F 2 requires an helicity flip the spin of the quark. Proton Assuming the L = 0 Proton F 2 ( Q 2 ) ∝ 1 /Q 6

Electron as probe of nucleon structure