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

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

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 Q 2 : < 0.1 GeV 2 integral quantities (charge radius,…) GeV 2 internal structure of nucleon > 20 GeV 2 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

Sachs Charge and Magnetization Form Factors G E and G M with E (E’) incoming (outgoing) energy,  scattering angle,  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 G E and G M are often alternatively expressed in the Dirac (non-spin-flip) F 1 and Pauli (spin-flip) F 2 Form Factors

Rosenbluth separation method One-photon exchange elastic electron-nucleon cross section Method : at fixed Q 2, vary angle  (or equivalently  ) and plot reduced cross section versus 

One-photon theorist’s view

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

Rosenbluth vs polarization transfer measurements of G E /G M of proton Jlab/Hall A Polarization data Gayou et al. ( 2002 ) SLAC Rosenbluth data Two methods, two different results !

Speculation : missing radiative corrections Speculation : there are radiative corrections to Rosenbluth experiments that are important and are not included missing correction : linear in  not strongly Q 2 dependent G E term is proportionally smaller at large Q 2 if both FF scale in same way effect more visible at large Q 2 Q 2 = 6 GeV 2

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

Radiative correction diagrams bremsstrahlung vertex corrections 2 photon exchange box diagrams

Two-Photon Exchange 1  -2  interference is of the order of  =e 2 /4  =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 2  contribution can become very large 

Qualitative estimation of Two-Photon exchange ( for ed) Form factors → quark counting rules: F d ~ t -5 and F N ~t -2 For t = -4 GeV 2, For d, 3 He, 4 He, 2  effect should appear at ~1 GeV 2, for protons ~ 10 GeV 2

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 Pictorially : To satisfy the LET, one has to include the soft-photon contributions from the cats’ ears diagrams soft

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.

Typical suppressed diagrams

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

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.

C  : Even or odd symmetry. Example: particle decay into two photons, for example  o  2  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. A Quick Aside: Charge Conjugation – cont’d

x1Px1P (1-x 1 )P

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

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 F 1 form-factor considered here: F 2 involves spin- flip which is zero for massless, collinear quarks.

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?