Beyond the Born Approximation Measuring the Two-Photon Exchange - PowerPoint PPT Presentation

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Beyond the Born Approximation Measuring the Two-Photon Exchange Effect at CLAS Robert Paul Bennett Old Dominion University for The CLAS Collaboration E07-005 PANIC 2011: Cambridge, MA June 24-29, 2011 Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 1 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary 1 Motivation 2 Form Factors 3 TPE 4 Experiment 5 Analysis overview 6 Projections 7 Summary Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 2 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Elastic Scattering: Born Approximation l ( k ′ ) l ( k ) e-p Kinematics γ µ ✁ k (k’): incoming (outgoing) lepton 4-vector P (P’): incoming (outgoing) proton 4-vector q Single virtual photon: q 2 = ( k − k ′ ) 2 = − Q 2 , Q 2 > 0 Proton remains intact Γ µ P ′ P Nucleon Current Operator Γ µ ( q ) Γ µ ( q ) = γ µ F 1 ( q 2 ) + 2 M N σ µν q ν F 2 ( q 2 ) 1 F 1 ( q 2 ) Non-spin flip Dirac Form Factor F 2 ( q 2 ) Spin flip Pauli Form Factor Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 3 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Elastic Scattering: Born Approximation l ( k ′ ) l ( k ) ep Kinematics γ µ ✁ k (k’): incoming (outgoing) lepton 4-vector P (P’): incoming (outgoing) proton 4-vector q Single virtual photon: q 2 = ( k − k ′ ) 2 = − Q 2 , Q 2 > 0 Proton remains intact Γ µ P P ′ F 1 and F 2 are NOT unique � � � � dσ d Ω = dσ Mott E p ( Q 2 ) + τ 1 G 2 ǫ G 2 M p ( Q 2 ) Electric form factor: d Ω 1+ τ G EP ( Q 2 ) = F P 1 ( Q 2 ) − τF p 2 ( Q 2 ) � − 1 � 1 + 2(1 + τ ) tan 2 θ e ǫ = 2 Magnetic form factor: 1 ( Q 2 ) + F p G MP ( Q 2 ) = F P 2 ( Q 2 ) Q 2 τ = ; G EP µ P ≈ G MP ≈ G D 4 M 2 P Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 4 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary How to extract G 2 E p ( Q 2 ): Rosenbluth Separation Method Step 1: Fix Q 2 Step 3: Measure at small E e and Step 2: Measure dσ d Ω at large E e large θ e ( ǫ → 0) and small θ e ( ǫ → 1) dσ d Ω ∝ G 2 M p ( Q 2 ) d Ω ∝ G 2 dσ E p ( Q 2 ) + τG 2 M p ( Q 2 ) Step 4: Subtract Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 5 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary A Better Way: Polarization Transfer Formalism Method Scatter polarized electrons off of an un polarized proton target τ (1 + τ ) G E p G M p tan θ e � I 0 P t = − 2 Electron transfers spin to the 2 proton Detect the polarization of the outgoing proton I 0 P l = 1 M p tan 2 θ e � τ (1 + τ ) G 2 M 2 E p + τ I 0 = G 2 ǫ G 2 M p � E e + E ′ G E p = − P t � tan θ e e G M p P l 2 M 2 A. I. Akhiezer and M. P. Relanko, Sov. J. Part. Nucl. 3, (1974) 277 and Arnold, Carlson and Gross, Phys. Rev. C23 (1981) 363 Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 6 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Why this is hard: Need polarized electrons (easy at JLab) Need to detect the proton, and then let it rescatter and remeasure it to determine the polarization (easy at JLab) Need to understand spin precession in the spectrometer Need lots of events (easy at JLab) Hall A & C Why this is easy: M.K. Jones et al., Phys. Rev. Lett. 84, 1398 (2000) O. Gayou et al., Phys. Rev. C64, 038202 (2001) Almost all errors cancel in the O. Gayou et al., Phys. Rev. Lett. 88, 092301 (2002) V. Punjabi et al., Phys. Rev. C71, 055202 (2005) ratio of polarizations M.K. Jones et al., Phys. Rev. C74, 035201 (2006) G. MacLachian et. al., Nucl. Phys. A764, 261 (2006) Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 7 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary The Proton Formfactor Puzzle Rosenbluth Separation: (SLAC, MIT BATES, JLab et al.) � dσ � � ε (1 + τ ) � = τG 2 M + ǫG 2 σ r = E d Ω σ mott Q 2 � − 1 τ = � 1 + 2(1 + τ ) tan 2 θ e / 2 ε = 4 M 2 Separate G E and G M contributions at a particular Q 2 using different beam energies and scattered electron angles G M measurement dominates at high Q 2 , G E is suppressed Polarization Transfer: (Hall A & C) G E P t ( E e + E e ′ ) θ e = − tan G M P l 2 M 2 Longitudinal polarized electrons incident on proton target Measure transverse and longitudinal polarization of recoiled proton Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 8 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary The Proton Formfactor Puzzle Rosenbluth Separation: (SLAC, MIT BATES, JLab et al.) � dσ � � ε (1 + τ ) � = τG 2 M + ǫG 2 σ r = E d Ω σ mott Q 2 � − 1 τ = � 1 + 2(1 + τ ) tan 2 θ e / 2 ε = 4 M 2 Separate G E and G M contributions at a particular Q 2 using different beam energies and scattered electron angles G M measurement dominates at high Q 2 , G E is suppressed Polarization Transfer: (Hall A & C) G E P t ( E e + E e ′ ) θ e = − tan G M P l 2 M 2 Longitudinal polarized electrons incident on proton target Measure transverse and longitudinal polarization of recoiled proton Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 9 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Beyond the Born Approximation Use G M from Rosenbluth Separation and G E from Polarization Transfer To account for the difference we need a ε dependent correction to the cross section on the order of a few percent: The TPE contribution expected to be ∼ 5 − 8% We’ve known about this for a long time – Just ask Sydney Drell Phys. Rev. 113, 741744 (1959) or Leon Lederman and Mike Tannenbaum Advances in Particle Physics Vol 1 1967 pp 1–70 Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 10 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Limited Previous Data TPE was a known issue Mixed Q 2 All of the data indicated that it was small so it was ignored. Reanalysis of the existing world data (2004) shows a slight ε dependence but not well constrained. Effect increases at low ε Negligible Q 2 dependence of the ratio is seen for these data. Mixed ε Large error bars limit our knowledge of the correction, especially at low ε and high Q 2 . A high precision measurement is required as TPE is only a few percent of the cross section J. Arrington, PRC69, 032201 (2004) Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 11 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Predictions There are several model dependent predictions of the TPE effect on the market Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 12 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Positrons to the rescue! At leading order, the TPE term of the elastic scattering cross section changes sign as the charge of the incident beam The elastic e ± p → e ± p scattering contribution: σ ( e ± ) | A born + · · · ± A 2 γ | 2 ∝ | A born | 2 ± 2 A born Re( A 2 γ ) σ ( e ± ) ∝ e − ↔ e + ⇒ α ↔ − α The ratio of the cross sections isolates the TPE correction term σ ( e + ) R = σ ( e − ) = 1 − 2 δ 2 γ 2Re( A 2 γ ) δ 2 γ = A born We can calculate this very well (QED) Theoretical calculation of the diagram is hard : Need to integrate over all baryon states The e − P/e + P ratio provides a model independent measurement of the TPE contribution Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 13 / 40

Outline Motivation Form Factors TPE Experiment Analysis overview Projections Summary Jefferson Laboratory Robert Paul Bennett (Old Dominion Universityfor The CLAS Collaboration E07-005 PANIC 2011: Cambridge, June 24-29, 2011 Beyond the Born Approximation 14 / 40