1. Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011 Odysseus and the Sirens, Greek Red-Figure Stamnos Vase, c. 480-460 BCE, British Museum

2. or get me out of the box!

3. Collaboration and Reference In Collaboration with Hai-Qing Zhou (SouthEast U, China), Keitaro Nagata(CYCU, Taiwan), Yu-Chun Chen(AS, Taiwan), M. Vanderhaeghen(Mainz, Germany), Shin-Nan Yang (NTU,Taiwan) This talk is based on the following works: (1) H-Q Zhou, CWK, S-N. Yang: Phys.Rev.Lett.99:262001,2007 (2) K.Nagata, H-Q Zhou, CWK, S-NYang: Phys.Rev.C79:062501,2009. (3) H-Q Zhou, CWK,S-N Yang, K. Nagata: Phys.Rev.C81:035208,2010 (4) Y.C. Chen, CWK, M. Vanderhaeghen: arXiv: 0903.1098

4. Prologue: All about the proton

5. Proton: our playground Nucleon is the basic building block of atomic nuclei. Its internal structure, arising from the underlying quark and gluon constituents, determines its mass, spin, and interactions. These, in turn, determine the fundamental properties of the nuclei. Furthermore, proton, as the only stable hadron, provides us the unique opportunity to explore its static properties up to very high precision.

6. Using photon as probe Since the quark carries the electric charge and photon does not participate the strong interaction, the photon is a very good probe. Experiments with highly energetic electromagnetic probe acting as a micro-scope virtuality electron  Q  

7. hadronizatio n 2 PD One-Photon Physics: From Low to High Low Q 2, elastic, exclusive High Q 2, deeply inelastic, inclusive Form factors, resonance Parton distribution

8. Oedipus explains the riddle of the Sphinx, "What walks on four feet in the morning, two in the afternoon and three at night?". Oedipus answered: "Man”. "What looks like a single particle in low Q 2, a bond state of heavy constituents in the middle and a bag of sands at high Q 2 ?". Oedipus: &^%&$$%??? To completely understand the properties of the proton from QCD is our Holy Grail …..

9. Devil is near…. With the recent development of the polarization technology, many experiments can reach record-breaking precision. However when experimentalists march, a devil is approaching in silence… We think we know many things about the proton precisely, but do we? Not really, HiHiHi…..

10. ACT 1: In the beginning…. Form factors and TPE effects 10

11. Form factor in quantum mechanics Atomic form factor: is the Fourier transform of the charge density. The cross section: E.g., the hydrogen atom in the ground state: charge density with Bohr radius

12. Nucleon E.M form factors Hofstadter determined the precise size of the proton by measuring their form factor in late 1950s. "for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons.(1961)

13. Rosenbluth Separation Method Within one-photon-exchange framework:

14. Polarization Transfer Method Polarization transfer cannot determine the values of G E and G M but can determine their ratio R.

15. Inconsistency between two methods SLAC, JLab Rosenbluth data JLab/HallA Polarization data Jones et al. (2000) Gayou et al (2002)

16. J.Arrington, P.G.Blunden, W.Melnitchuk, arXiv1105.0951

17. Go beyond One-Photon exchange New Structure P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

18. Two-Photon-Exchange Effects on two techniques large small P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

19. One way or another ……. There are two ways to estimate the TPE effect: Use models to calculate Two-Photon-Exchange diagrams: Like parton model, hadronic model and so on….. Direct analyze the cross section and polarization data by including the TPE effects: One-Photon-exchangeTwo-photon-exchange

20. Why Box diagram is not trivial ? One needs evaluate the Compton tensor. In general, it owns 18 structures! Furthermore, There is no single framework to computer this quantity with arbitrary k 2 and (q-k) 2.

21. Results of hadronic model Insert the on-shell form factors P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 91 (2003) 142304

22. Inclusion of resonances Insert the on-shell form factors S.Kondratyuk, P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 95 (2005) 172503

23. Partonic Model Calculation GPDs A. V. Afanasev, S. J. Brodsky, C. E. Carlson, Y.-C. Chen, and M. Vanderhaeghen, Phys. Rev. D 72, 013008 (2005).

24. 5/6 GPDs DVCS Deeply Virtual Compton Scattering Longitudinal response only GPDs can be accessed via exclusive reactions in the Bjorken kinematic regime.  The DVCS process is identified via double (eg) or triple (egN) coincidences, allowing for small scale detectors and large luminosities. Factorisation applies only to longitudinally polarized virtual photons whose contribution to the electroproduction cross section must be isolated.. GPDs DA DVMP Deeply Virtual Meson Production Hard gluon

25. QCD factorization approach 1γ1γ 1 γ+2 γ(BLW) 1 γ+2 γ(COZ) N.Kivel and M.Vanderhaeghen, Phys. Rev. Lett.103 (2009) 092004 The leading perturbative QCD (pQCD) contribution to the 2 γ exchange correction to the elastic ep amplitude is given by a convolution integral of the proton distribution amplitudes (DAs) with the hard coefficient function

26. Comparison with data arXiv:1012.0339 JLab Hall C

27. Model-independent analysis Determined from polarization transfer data TPE effects From crossing symmetry and charge conjugation: Inputs

28. Our Choice of F(Q 2, ε ) Fit (A) Fit (B) ε→ 1, y→0, F→0ε→0, y→1, F≠0

29. Result of fits Dashed Line: Rosenbluth Solid line: Fit (A) Dotted line: Fit (B)

30. Result of fits Dashed Line: Rosenbluth Solid line: Fit (A) Dotted line: Fit (B)

31. Puzzle about nonlinearity V.Tvaskis et al, PRC 73, 2005 Purely due to TPE

32. Fit (A) : Fit (B): TPE vs OPE

33. Dashed Line : Fit (B)Solid line: Fit (A) TPE contribution to slope SLOPE(TPE)/SLOPE(OPE) =C 1 /(G E /τ)

35. Fit (A) Fit (B)

36. Empirical extraction of TPE

37. Upcoming TPE experiments J.Guttmann, N. Kivel, M. Meziane,and M. Vanderhaeghen, arXiv1012.0564 Olympus@DESY experiment are underway. Over the measured range of this experiment, the 2TPE corrections to the e + p/e − p elastic cross section ratio are predicted to vary in the 1 - 6 % range.

38. Jlab Hall B E-07-005

39. More TPE….. TPE and pion form factors: Y.-B.Dong, S.D.Wang, Phys.Lett. B684, 123-126 (2010). P.G.Blunden, W.Melnitchouk, J.A.Tjon, Phys. Rev. C81, 018202 (2010). TPE and deuteron form factors: Y.B.Dong, D.Y.Chen,'Phys. Lett. B675, 426-432 (2009). A.P.Kobushkin, Y.D.Krivenko-Emetov, S.Dubnicka, Phys. Rev. C81, 054001 (2010). A.P.Kobushkin, Y.D.Krivenko-Emetov, [arXiv:1101.1867 [nucl-th]]. Y.~B.~Dong, Phys. Rev. C82, 068202 (2010). TPE and time-like proton form factors: H.Q.Zhou, D.Y.Chen, Y.B.Dong, Phys.Lett. B675, 305-307 (2009). J.Guttmann, N.Kivel, M.Vanderhaeghen, [arXiv:1101.5967 [hep-ph]].

40. Act 2: How strange is strange? TPE effect in parity-violating ep elastic scattering 40

41. Strangeness in the nucleon Goal: Determine the contributions of the strange quark sea ( ) to the charge and current/spin distributions in the nucleon : “strange form factors” G s E and G s M « sea » s quark: cleanest candidate to study the sea quarks

42. Parity Violating ep Elastic Scattering Interference with EM amplitude makes Neutral Current (NC) amplitude accessible Tiny (~10 -6 ) cross section asymmetry isolates weak interaction Interference:  ~ |M EM | 2 + |M NC | 2 + 2Re(M EM* )M NC

43. OPE vs OZE

44. Isolating the neutral weak form factors: vary the kinematics or the targets ~ few parts per million For a proton: Forward angleBackward angle

45. NC probes same hadronic flavour structure, with different couplings: G Z E /M provide an important new benchmark for testing non-perturbative QCD structure of the nucleon Flavour decomposition

46. Apply Charge Symmetry G  p E,M G s E,M G u E,M G d E,M G  n E,M Charge symmetry G  p E,M G n E,M G p E,M G s E,M Shuffle Well Measured

48. Tree Level is not enough! The strange form factors are found to be very small, just few percents. To make sure the extracted values are accurate, it is necessary to take the radiative correction into consideration! So one has to draw many diagrams as follows…..

50. Electroweak radiative corrections Squeeze eq→eq amplitudes into 4-Fermion contact interactions

51. Extraction of strange form factors with radiative corrections ρ and κ are from electroweak radiative corrections Strange form factors

52. Be aware of the Box! Box diagram is intricate because it is related with nucleon intermediate states. Box diagram is special because of its complicated Q 2 and ε dependence So Can one squeeze the box diagrams into a point?

53. Zero Transfer Momentum Approximations for Box diagrams p q Q 2 =t=(p-q) 2 =0 Approximation made in previous analysis: p=q=k Marciano, Sirlin (1983) P e =P e ’=0 PePe P e’

54. High and Low Momentum Integration N Low Loop momentum Integration: Only include N intermediate state. Insert the on-shell form factors High Loop momentum Integration: Lepton and a single quark exchange bosons. Convoluation with PDF N = ll

55. But this is nothing but a Procrustean bed! Gee..it hurts! Get you!

56. MS approximation Initially it is for atomic parity violation. Two exchanged boson carry the same 4-momentum and lepton momenta are set to be zero. In other words MS approximation is three-fold approximation: Q 2 =0. E lab =0 Coulomb force is taken away

57. One-loop box diagrams in hadronic model ＝ ＝ + + N N Quark-level Contribution

58. Indeed MS is not good enough !

59. HQ. Zhou, CWK and SN Yang, PRL, 99, 262001 (2007)

60. Adding resonances…. Δ(1232) plays an important role in the low energy regime due to its light mass and its strong coupling to πN systeam. PRC79:062501 2009; PRC81 035208 2010 Keitaro Nagata, Hai Qing Zhou, CWK and SN Yang

61. Nagata et al, arXiv:0811.3539 PRC79:062501 2009

62. Old New Impact of our results Avoid double counting

63. Here we only subtract the soft parts of ρ and κ HQ Zhou, CWK, SN Yang, K Nagata PRC 81, 035208,2010

64. G0 data

65. Preliminary G M s = 0.28 +/- 0.20 G E s = -0.006 +/- 0.016 ~3% +/- 2.3% of proton magnetic moment ~20% +/- 15% of isoscalar magnetic moment ~0.2 +/- 0.5% of Electric distribution One needs to be more sophisticated to extract the strangeness including box diagrams…..

66. Partonic calculation of Box diagrams = Yu-Chun Chen, C-W K, M. Vanderhaeghen, arXiv 0903.1098

67. Partonic calculation of Box diagrams In MS limit c 1 =0 so that t 1 q is associated with g e V and t 2 q is associated with g e A. removed because it is Soft contribution

68. Partonic calculation of Box diagrams

69. Result of Partonic calculation

70. Comparison with Marciano and Sirlin’s approximation

71. Act 3. Heading for the New world, but isn’t it India? TBE and QWEAK

72. Q weak experiment δQw / Qw = 4% δsin 2 θ W / sin 2 θ W = 0.3%

73. Cut the Box into two pieces Zee axial coupling g A e Zee vector coupling g V e δ γz A δ γz V In dispersion calculation the N intermediate state is excluded. δ γzA (ν=0)=0 δ γzV (ν=0) ≠0

74. Dispersion relation approach

75. M.Gorchtein and C.J.Horowitz, Phys.Rev.Lett. 102 (2009) 091806

76. Dispersion calculation

77. The result of hadronic model is quite different δ N =0.6% δ Δ =-0.1% H.Q. Zhou, CWK and S. N.Yang, in progress.

78. Recent progress on dispersion relation calculation A. Sibirtsev, P. G. Blunden, W. Melnitchouk, A. W. Thomas, Phys. Rev. D82 (2010), 013011. B. C. Rislow, C. E. Carlson, [arXiv:1011.2397]. P. G. Blunden, W. Melnitchouk and A. W. Thomas, arXiv:1102.5334 Mikhail Gorchtein, C. J. Horowitz, and Michael J. Ramsey-Musolf, arXiv.1102.3910

80. Result of Gorchtein, Horowitz, and Ramsey-Musolf

81. Act 4: The puzzle on the size of the proton

82. Lamb shift of hydrogen (1947) According to the hydrogen Dirac equation solution, the energy levels of 2p 1/2 state is same with the energy level of 2s 1/2. However, in 1947, Willis Lamb discovered that this was not so - that the 2p 1/2 state is slightly lower than the 2s 1/2 state resulting in a slight shift of the corresponding spectral line. 82

83. The size of proton and Lamb shift The Lamb shift is the splitting of an energy level caused by vacuum polarization and other higher order radiative corrections. The excellent agreement between experimental data and the QED calculation has been seen as the greatest triumph of QED. However as the experimental technique develops the effect of finite size of the proton becomes non-negligible such that the measurement of Lamb shift provides information of the charge radius of the proton. 83

84. The size of the proton? From measurement of hydrogen Lamb shift: From low Q 2 ep elastic scattering data Charge Radius

85. Muonic hydrogen The muon is about 200 times heavier than the electron Therefore, the atomic Bohr radius of muonic hydrogen is smaller than in ordinary hydrogen. The μp Lamb shift, ΔE(2P-2S) ≈ 0.2 eV, is dominated by vacuum polarization which shifts the 2S binding energy towards more negative values. The relative contribution of the proton size to ΔE(2P-2S) is as much as 1.8%, two orders of magnitude more than for normal hydrogen atoms. Thus, the measurement of the Lamb shift of muonic hydrogen is expected to provide the more accurate value. 85

86. Muonic hydrogen Spectrum

87. How to calculate it? To calculate the theoretical shift corresponding to the measured transition, some have used perturbation theory with non-relativistic wave-functions to predict the size of the contributing effects, including relativistic effects. Alternatively one can use the Dirac equation for the muon with the appropriate potential as an effective approximation to the two-particle Bethe-Saltpeter equation to calculate the perturbed wave-functions

88. Hard work for 40 years This kind of measurement has been considered for over 40 years, but only recent developements in laser technology and muon beams made it feasible to carry it out The experiment is located at a new beam ‐ line for low ‐ energy (5keV) muons of the proton accelerator at the Paul Scherrer Institute (PSI) in Switzerlan 88

89. Surprisingly new result The transition frequency between 2P 3/2 and 1S 1/2 is obtained to be Δ ν = 49881.88(77) GHz, corresponding to an energy difference of ΔE = 206.2949(32) meV Theory predicts a value of ΔE = 209.9779(49) ‐ 5.2262 r p ² + 0.0347 r p ³ meV [r p in fm] This results in a proton radius of r p = 0.84184(36) fm 4% smaller than the previous best estimate, which has been the average of many different measurements made over the years. 89

90. 90 To match the 2010 value with the CODATA value, an additional term of 0.31meV would be required in the QED equation. This corresponds to 64 times its claimed uncertainty! Surprisingly new result R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben, et al., Nature 466, 213–216 (2010).

91. Third Zeemach moment If G E is dipole form

92. Four possibilities The experimental results are not right. The relevant QED calculations are incorrect. There is, at extremely low energies and at the level of accuracy of the `p-atom experiments, physics beyond the standard model“. A single-dipole form factor is not adequate to the analysis of precise low-energy data.

93. Controversy about Third Zeemach moment De Rújula pointed out that if the proton’s third Zemach moment is very large the discrepancy between the two results can be removed. He used some “toy model” and obtained the result: His number is 13 times larger than the experimental extraction of Friar and Sick, who use electron-proton scattering data to determine:

94. Controversy about Third Zeemach moment Clöt and Miller show that published parametrizations, which take into account a wide variety of electron scattering data, cannot account for the value of the third Zemach moment found. They concluded that enhancing the Zemach moment significantly above the dipole result is extremely unlikely.

95. Controversy about Third Zeemach moment However De Rújula still argued that there is possible to make third Zeemach large and not ruled out by the ep data. His argument based on the fact that There is no data corresponds to the A result based on those data has to be an extrapolation of data with a large spread and a poor χ 2 per degree of freedom.

96. Higher order QED calculation one-loop electron self-energy and vacuum polarization two-loops three-loops pure recoil correction radiative recoil correction finite nuclear size corrections By Pachucki

97. TPE and Lamb shift

98. Dispersion calculation The imaginary part of TPE is related to the structure functions measured in DIS Dispersion relations :

99. Three kinds of contributions

100. Reevaluation of TPE C. Carlson and M. Vanderhaeghen, arXiv:1101.5965

101. New Physics? V. Barger Cheng-Wei Chiang, Wai-Yee Keung, and Danny Marfatia5 explore the possibility that new scalar, pseudoscalar, vector, axial-vector, and tensor flavor-conserving nonuniversal interactions may be responsible for the discrepancy. They consider exotic particles that among leptons, couple preferentially to muons and find that the many constraints from low energy data disfavor new spin-0, spin-1 and spin-2 particles as an explanation. Phys.Rev.Lett.106:153001,2011

102. Conclusion and Outlook TBE are crucial for the extraction of the EM form factors and strangeness inside the nucleon! More delicate estimate of the TBE effect is needed badly! (including more resonances, consider quark- level contributions…….) Upcoming positron-proton scattering will provide us the precious information of TPE effects. Uncertainty of TBE may jeopardize the interpretation of QWEAK data and requests an answer.

103. Epilogue: Current status of TBE physics Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning. Winston Churchill After the second battle of El Alamein, Nov 10,1942 we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, June 4, 1940

104. Two bosons are too many, But two cups of ice cream are just perfect! Thank you for listening….