Egle TOMASI-GUSTAFSSON Conclusions Discussion Homework Egle Tomasi-Gustafsson IRFU, SPhN-Saclay, and IN2P3- IPN Orsay France Orsay, October 8, 2013 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Questions Which are my OBSERVABLES? What am I measuring? What do I extract from the data? Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON The Rosenbluth separation (1950) Elastic ep cross section (1-γ exchange) point-like particle:  Mott Linearity of the reduced cross section! Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

The polarization method (1967) The Rosenbluth separation (1950) The polarization induces a term in the cross section proportional to GE GM Polarized beam and target or polarized beam and recoil proton polarization Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

The proton magnetic form factor The polarization results induce 1.5-3% global effect The difference is not at the level of the measured observables, but on the slope (derivative)! E. Brash et al. Phys. Rev. C65, 051001 (2002) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Rosenbluth separation Contribution of the electric term =0.8 …to be compared to the absolute value of  and to the size and dependence of RC =0.2 =0.5 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle Tomasi-Gustafsson Gatchina, July 10, 2012 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’) “Invent a mechanism” to enhance this contribution In the 70’s it was shown [J. Gunion and L. Stodolsky, V. Franco, F.M. Lev, V.N. Boitsov, L. Kondratyuk and V.B. Kopeliovich, R. Blankenbecker and J. Gunion] that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2g- contribution can become very large. The 2g amplitude is expected to be mostly imaginary. Egle Tomasi-Gustafsson Gatchina, July 10, 2012

Egle TOMASI-GUSTAFSSON 1-2 interference M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C (1999) 1 2 1{g { { Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

The 1-2 interference destroys the linearity of the Rosenbluth plot! Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON 1-2 interference (ed) C/A D/A M. P. Rekalo, E. T-G and D. Prout, Phys. Rev. C60, 042202 (1999) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Parametrization of 2-contribution for e+p From the data: deviation from linearity << 1%! E. T.-G., G. Gakh, Phys. Rev. C (2005) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Linear fit to e+4He elastic scattering G.I Gakh, and E. T.-G., Nucl.Phys. A838 (2010) 50-60 Egle Tomasi-Gustafsson Gatchina, July 10, 2012

Egle Tomasi-Gustafsson Gatchina, July 10, 2012 WHY these points are aligned? Egle Tomasi-Gustafsson Gatchina, July 10, 2012

Egle TOMASI-GUSTAFSSON Two-Photon exchange The 2 amplitude is expected to be mostly imaginary. In this case, the 1-2 interference is more important in time-like region, as the Born amplitude is complex. Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Unpolarized cross section 2contribution: Induces four new terms Odd function of  Does not contribute at =90° Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Symmetry relations Properties of the TPE amplitudes with respect to the transformation: cos  = - cos  i.e.,    -  (equivalent to non-linearity in Rosenbluth fit) Based on these properties one can remove or single out TPE contribution Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Symmetry relations Differential cross section at complementary angles: The SUM cancels the 2 contribution: The DIFFERENCE enhances the 2 contribution: Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Angular distribution Mpp=1.877-1.9 Mpp=2.4-3 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Mpp=1.877-1.9 A=0.01±0.02 Mpp=2.4-3 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Radiative Corrections to the data - RC can reach 40% on  - Declared error ~1% Same correction for GE and GM - Have a large -dependence - Affect the slope el=meas · RC slope Slope negative if : The slope is negative starting from 2-3 GeV2 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Reduced cross section and RC Data from L. Andivahis et al., Phys. Rev. D50, 5491 (1994) Q2=1.75 GeV2 Q2=2.5 GeV2 Q2=3.25 GeV2 Q2=4 GeV2 Q2=5 GeV2 Q2=6 GeV2 Slope from P. M. Radiative Corrected data Q2=7 GeV2 Raw data without RC E. T.-G., G. Gakh Phys. Rev. C (2005) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Radiative Corrections (ep) Andivahis et al., PRD50, 5491 (1994) Q2=1.75 GeV2 Q2=3.75 GeV2 May change the slope of sR (and even the sign !!!) Q2=5 GeV2 RC to the cross section: - large (may reach 40%) e and Q2 dependent - calculated at first order C.F. Perdrisat,, Progr. Part. Nucl. Phys. 59,694 (2007) Egle Tomasi-Gustafsson Gatchina, July 10, 2012

Experimental correlation el=meas · RC RC() only published values!! Correlation (<RC•) Q2 > 2 GeV2 Q2 < 2 GeV2 Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Results Q2=1 GeV2 Q2=3 GeV2 SF Born RC Born ……… Polarization Q2=5 GeV2 Both calculations assume dipole FFs The slope changes (due to different RC) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Correction (SF method) SLAC data JLab data Polarization data Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, 015207 (2007) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Polarization ratio  =80° Born SF …..  =60°  =20° 2 exchange very small! Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Homework Exercise -Table with SLAC kinematics, data etc… -Extract published radiative corrections -Plug-in ‘your’ radiative corrections (in MC: ratio of histos..) - Plot RC(epsilon) -Autopsia of RC (epsilon) -Outcome: report GDR-PH-QCD and more ECT*, 17-VII-2007 Egle TOMASI-GUSTAFSSON

Egle TOMASI-GUSTAFSSON Homework Exercise Even electron Even proton interference Total ECT*, 17-VII-2007 Egle TOMASI-GUSTAFSSON

Interference of 1 2 exchange Explicit calculation for structureless proton The contribution is small, for unpolarized and polarized ep scattering Does not contain the enhancement factor L The relevant contribution to K is ~ 1 E.A.Kuraev, V. Bytev, Yu. Bystricky, E.T-G Phys. Rev. D74 013003 (1076) Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON

Perspectives and Conclusions Fundamental measurement: the electric and the magnetic distributions of the proton are different in SL region. What about TL ? Separation of GE and GM via angular dependence of differential cross section Clarify reaction mechanism: 2exchange by model independent symmetry requirements Unified description in TL and SL region : zero of GEp? Asymptotic properties : QCD and analyticity Model independent properties Lessons from QED Orsay, 8-X-2013 Egle TOMASI-GUSTAFSSON