LEPTON PAIR PRODUCTION AS A PROBE OF TWO PHOTON EFFECTS IN EXCLUSIVE PHOTON-HADRON SCATTERING

1. LEPTON PAIR PRODUCTION AS A PROBE OF TWO PHOTON EFFECTS IN EXCLUSIVE PHOTON-HADRON SCATTERING Pervez Hoodbhoy Quaid-e-Azam University Islamabad

2. OUTLINE OF TALK • INTRO: 1. Nucleon Form Factors And GPDs • 2. Why Does Rosenbluth Fail? • RADIATIVE CORRECTIONS • TWO-PHOTON EFFECTS • AN ASYMMETRY OBSERVABLE • CALCULATION FOR LARGE-t • SUMMARY AND OPEN QUESTIONS

3. Nucleon Electro-Magnetic Form Factors • Fundamental ingredients in “Classical” nuclear theory • A testing ground for theories that construct nucleons • - Spatial distribution of charge, magnetization • - Wavelength of probe can be tuned by selecting Q2: • < 0.1 GeV2 integral quantities (charge radius,…) • 0.1-10 GeV2 internal structure of nucleon > 20 GeV2 pQCD scaling • Additional insights can be gained from the measurement of the form factors of nucleons embedded in the nuclear medium • Implications for binding, equation of state, EMC, precursor to QGP

4. Sachs Charge and Magnetization Form Factors GEand GM with E (E’) incoming (outgoing) energy, q scattering angle, k anomalous magnetic moment In the Breit (centre-of-mass) frame the Sachs FF can be written as the Fourier transforms of the charge and magnetization radial density distributions GEand GM are often alternatively expressed in the Dirac (non-spin-flip) F1 and Pauli (spin-flip) F2 Form Factors

5. Rosenbluth separation method One-photonexchange elastic electron-nucleon crosssection Method : at fixed Q2, vary angle q (or equivalently e) and plot reduced cross section versus e

6. One-photon theorist’s view

7. Polarization transfer method Method : measure ratio of sideways ( ) to longitudinal ( ) recoil polarization of proton (absolute normalization drops out !) in one-photon exchange approximation :

8. Rosenbluth vs polarization transfer measurements of GE/GM of proton SLAC Rosenbluth data Jlab/Hall A Polarization data Gayouetal. (2002) Twomethods, twodifferentresults !

9. Speculation : missing radiative corrections Speculation : there are radiative corrections to Rosenbluth experiments that are important and are not included missing correction : linear in e, not strongly Q2 dependent Q2 = 6 GeV2 GE term is proportionally smaller at large Q2 effect more visible at large Q2 if both FF scale in same way

10. Basics Of QED Radiative Corrections (First) Born approximation Initial-state radiation Final-state radiation Cross section ~ dω/ω => integral diverges logarithmically: IR catastrophe Vertex correction => cancels divergent terms; Schwinger (1949) Multiple soft-photon emission: solved by exponentiation, Yennie-Frautschi-Suura (YFS), 1961

11. Radiative correction diagrams bremsstrahlung vertex corrections 2 photon exchange box diagrams

12. Two-Photon Exchange • 1g-2g interference is of the order of a=e2/4p=1/137 (in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’) • Due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2g- contribution can become very large.

13. Qualitative estimationof Two-Photon exchange ( for ed) Form factors → quark counting rules: Fd ~ t-5 and FN~t-2 For t = -4 GeV2, For d, 3He, 4He, 2g effect should appear at ~1 GeV2, for protons ~ 10 GeV2

14. Calculation of soft part at nucleon level LET : sum of soft contributions from the partonic calculation has to match the soft contributions at nucleonic level To satisfy the LET, one has to include the soft-photon contributions from the cats’ ears diagrams Pictorially : soft soft soft soft

15. Proposal: use real photons to investigate 2-photon effects. To get more insight take an extreme case where the proton structure is relatively well-understood.

20. Typical suppressed diagrams

21. Assume transverse momentum of quarks is negligible • Assume lowest Fock state dominates at large -t

24. A Quick Aside: Charge Conjugation • C operation - interchange of particle with its antiparticle. • C symmetry in classical physics - invariance of Maxwell’s equations under change in sign of the charge, electric and magnetic fields. • C symmetry in particle physics - the same laws for a set of particles and their antiparticles: collisions between electrons and protons are described in the same way as collisions between positrons and antiprotons. The symmetry also applies for neutral particles.

25. A Quick Aside: Charge Conjugation – cont’d • Cy = ± y: Even or odd symmetry. • Example: particle decay into two photons, for example p o 2g, by the electromagnetic force. Photon is odd under C symmetry; two photon state gives a product (-1)2 and is even. So, if symmetry is exact, then 3 photon decay is forbidden. In fact it has not been observed. • C symmetry holds in strong and electromagnetic interactions.

29. x1P (1-x1)P

31. Assume transverse momentum of quarks is negligible • Assume lowest Fock state dominates at large -t

35. SUMMARY • Real photons are used to probe nucleon structure. • Real photons are easily available at many labs. • At large-t the proton structure is much simpler. • The expression for the asymmetry is very compact. • The size of the signal is large at modest –t. • Only F1 form-factor considered here: F2 involves spin-flip which is zero for massless, collinear quarks.

36. OPEN QUESTIONS • How big will Sudakov effects be? • Will the next order calculation (few thousand diagrams!) change the angular structure? • Will it dominate the present calculation?