11 Professor John Alexander Tjon ( 張尊儒 ) in Tarogo Gorge, Taiwan (April, 2006) John has great devotion to science, not for fame/PR, but only for science. Einstein on Madame Curie: “She was probably the only person who was not corrupted by the fame she had won”

22 Two-boson exchange physics Shin Nan Yang National Taiwan University Two-boson exchange physics Shin Nan Yang National Taiwan University The 5th Asian-Pacific Conference on Few-Body Problems in Physics, Seoul, Korea, August 21-26, 2011 In memory of Professor John Alexander Tjon Collaborators NTU: Yu-Chun Chen, Haiqing Zhou CYCU: Chung-Wen Kao, Keitaro Nagata

33 Outline 1.Two-photon exchange in ep elastic scattering nucleon e.m. form factors, discrepancy btw G E /G M ’s extracted from Rosenbluth and polarization experiments, radiative corrections to ep elastic scattering and TPE current developments and future prospect 2.Two-boson exchange correction to parity-violating ep elastic scattering strangeness content of the proton parity-violating ep scattering in one-boson exchange approximation extraction of strange form factors from parity-violating asymmetry A PV and weak radiative corrections two-boson exchange effects on strange form factors γZ corrections to the proton weak charge 3. Summary

44 Nucleon e.m. form factors How to measure form factors?

5 Elastic electron-proton scattering In one-photon exchange approximation, Note θ → 0, ε → 1 (forward); θ → π, ε → 0 (backward) Method: fix Q 2, vary angle (vary ε), adjusting incoming electron energy as needed and plot reduced cross section vs. ε ( Rosenbluth separation method ) Rosenblut h formular

66 Polarized scattering In one-photon exchange approximation, P t and P l : polarization components of the recoiling proton perpendicular and parallel to its momentum in the scattering plane The one-photon-exchange diagram for the polarized electron-nucleon scattering Longitudinally polarized electron-proton elastic scattering with one-photon exchange. Polarization of the recoiled proton is measured.

77 Up until the end of last century, experimental results, mostly from Rosenbluth separation method, give

88 big surprise!!! M.K. Jones et al., Phys. Rev. Letts. 84, 1398 (2000). exp. in Hall A, Jlab with E lab = GeV G E falls faster than G M G M /μ p G D is approximately constant

99 Ensuing efforts to verify the discrepancy - experimental  New global analysis of the world’s cross section data (Arrington 2003) → still inconsistent with the polarization measurements  High-precision Super-Rosenbluth experiment → with 4 - 8% precision,

10 proton e.m. form factor : status green : Rosenbluth data (SLAC, JLab) Pun05 Gay02 JLab/HallA recoil pol. data new JLab/HallC recoil pol. exp. (spring 2008) : extension up to Q 2 ≈ 8.5 GeV 2 new MAMI/A1 data up to Q 2 ≈ 0.7 GeV 2

11 Ensuing efforts to understand the discrepancy - theoretical Re-examination of the radiative corrections O ( α 2 ) Feynman diagrams for elastic amplitudes Feynman diagrams for inelastic amplitudes

12 Mo and Tsai, RMP 41, 205 (1969). basically in soft-photon approximation 1% accuracy in cross section measurements requires knowing radiative corrections to 3% ( 3% x ~ 1%)

13 Maximon & Tjon, PR C62, (2000). Improve Mo and Tsai’s treatment –mathematical, e.g., the soft bremstralung cross section is evaluated without approximation, and box diagrams are calculated with less drastic approximation –physical, namely, q 2 -dependence in the proton form factor is kept. –εdependence comes only from proton vertex and TPE corrections –δ(proton vertex corr.) < 0.5% How about TPE?

14 Rigorous treatment of TPE diagrams Blunden, Melnitchouk & Tjon, PRL 19, (2003) NN Difficulty in the integration on the left lies mostly with power in k. Feyncalc & Formcalc can handle power of k up to 4. LT separation: data - open squares dashed line – global fit Solid line – with TPE corr. PT data: open circles

15 N, Δ Blunden, Melnitchouk, & Tjon, 2005 from Arrington, Blunden, Melnitchouk, arXiv:1105:0951 Two-photon exchange calculation : hadronic N, Δ

16 Two-photon exchange : partonic calculation GPDs Chen, Afanasev, Brodsky, Carlson, Vdh (2004) TPE can account for at least 50% of the discrepancy in the value of μ p G E /G M extracted from LT and PT methods !!

17 Recent developments  How to quantify TPE contributions ? theoretical: inclusion of higher resonances, dispersion relation, model independent parametrization, pQCD…………. experimental: more precision measurements, high Q 2, e + p/e - p, beam and target single spin asymmetries……  How to extract G M and G E in the presence of two-photon exchange ?  TPE in other processes, electron-nuclei scattering, hydrogen hyperfine splitting, precise description of simple atoms and positronium, R EM of Δ electro- excitation……..

18 Model independent parametrization of TPE In general, charge conjugation and crossing symmetry

19 If F(Q 2, ε) is required to be smooth and finite within 0 ≦ y ≦ 1, and F → 0, y = 0 (ε=1 ), F≠0, y = 1 (ε= 0). choice A, choice B,

20 fit II: choice A fit III:choice B

21 e + p/e - p probes the real part of TPE data from Nikolenko et al., Phys. Atom. Nucl. 73, 1322 (2010). Q 2 = 1.6 GeV 2, ε= 0.4, R = ± 0.011

22 Single spin asymmetries (SSA) -probe imaginary part of TPE- Expt.E(GeV)Q 2 GeV 2 B n (ppm) SAMPLE ±5.9 A ±0.89 A ±2.31 HAPPEX ± 1.5 G ± 1.62 G ± 2.85 E-158(ep) > - 2.5

23 Beam normal spin asymmetry E e = GeV Θ e = 145 deg E e = GeV Θ e = 35 deg E e = GeV Θ e = 35 deg Pasquini & Vanderhaeghen Phys.Rev. C70 (2004) MAMI data A4 experiment

24 1. σ term in  N scattering → an admixture of 20-25% strange quarks 2.  p deep inelastic scattering with longitudinally polarized  ’s and p’s (EMC) → ΔS=-0.12 (EMC94) low energy elastic p cross section (BNL 1987) → ΔS=-0.19± parity-violating electron-proton scattering SAMPLE, HAPPEX, A4, G0 4. from K + production in DIS (HERMES) → 5.double polarizations in photo- and electroproduction of  meson – planned for 2012 at SPring8 Possible experimental indications for “ strangeness in the nucleon ”

25 Parity-violating ep scattering in one-boson exchange approximation weak form factors :

26 one-boson exchange approximation Via quark flavor decomposition for and assumption of charge symmetry → Strange form factors

27 Radiative corrections Marciano and Sirlin (1983,1984)

28 Radiative corrections are parametrized via ρ≠1 and κ≠1 PDG values: ρ= and κ= Marciano and Sirlin evaluated γZ exchange in Q 2 = 0 approximation → Strange form factors

29 Quantification of TBE effects first define δ by set the experimental parity asymmetry use to extract the strange form factors introduce

30 Two-boson exchange effects hadronic model N, Δ Zhou, Kao, Yang, Nagata, 2007, 2009, 2010; Tjon et al. 2008, 2009.

31 Two-boson exchange effects partonic calculation Afanasev and Carlson, PRL 94, (2005).

32 Zhou, Kao, Yang, Nagata, PR C81, (2010). ＊ ＊

33 NRQM cal., Kiswandhi, Lee, Yang, arXiv: ; talk by Kiswandhi on Mon. Solid and dashed lines correspond to 0.06% and 2.4% of strangeness content.

34 QWEAK expeiment at Hall C/Jlab Ee = GeV, Q 2 = GeV 2, θ = 8 0, 85% polarization In the above kinematics, A PV ～ ppm, Objective, 0.3% determination of sin 2 θ W → requires 2% precision in A PV =

35 Standard Model running of sin 2 θ W Erler, Kurylov, Ramsey-Musolf, PR D68, (2003). Deviations → a signal of new physics Agreement → place new and strict constraints on possible SM extensions

36 At low Q 2, one has, =

37 Summary  TPE effects on proton e.m. form factors TPE can account for at least 50% of discrepancy in in the value of G E /G M from LT and PT methods. e + p/e - p and beam/target normal spin asymmetry, probe the real and imaginery parts of TPE amplitudes, respectively, and would be very useful to constrain TPE models. much theoretical and experimental works remain to be done.  TBE effects in parity-violating ep scattering Nucleon contribution is larger than Δ contribution but are of opposite sign and cancel to give small effects except in a few kinematics cases. contribution of γZ box diagrams to the proton weak charge currently under intensive study.

38 Recent developments  How to quantify TPE contributions ? theoretical: inclusion of higher resonances, dispersion relation, model independent parametrization, pQCD…………. experimental: more precision measurements, high Q 2, e + p/e - p, beam and target single spin asymmetries……  How to extract G M and G E in the presence of two-photon exchange ?  TPE in other processes, electron-nuclei scattering, hydrogen hyperfine splitting, precise description of simple atoms and positronium, R EM of Δ electro- excitation……..

39 For much more details, see the following reviews:  Carlson and Vanderhaeghen Ann. Rev. Nucl. Part. Sci. 57, (2007).  Arrington, Blunden, and Melnitchouk, arXiv: , Prog. Part. Nucl. Phys., in press

40 The End Thanks you!!