SpaceLike and TimeLike Form Factors Compared analysis Egle

Space-Like and Time-Like Form Factors Compared analysis Egle Tomasi-Gustafsson SPh. N-Saclay and IPN-Orsay Varenna, June 16, 2009 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 1

PLAN • Introduction: Form factors in one photon exchange approximation e+ q 2>0 p • Experimental Situation – Space-Like p – Time-like e • Future Panda/FAIR and JLab 12 Ge. V: – Determination of proton form factors – Transition to QCD: Asymptotics – Reaction mechanism (1 or 2 exchange) • Conclusions …. Model Independent Statements 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 2

Hadron Electromagnetic Form factors – Characterize the internal structure of a particle ( point-like) – In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2 S+1 form factors. – Elastic form factors bring information on the nucleon ground state – Neutron and proton form factors are different – Playground for theory and experiment – at low q 2 probe the size of the nucleus, – at high q 2 test QCD scaling 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 3

Electromagnetic Interaction e- e- The electron vertex is known, gm The interaction is carried by a virtual photon of mass q 2<0 The proton vertex is parametrized in terms of FFs: Pauli and Dirac F 1, F 2 p p What about high order radiative corrections? 16 -VI-2009 or in terms of Sachs FFs: GE=F 1 -t F 2, GM=F 1+F 2, t=-q 2/4 M 2 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 4

Analyticity Space-like ee- GE(0)=1 GM(0)=mp p p FFs are real e+p 16 -VI-2009 Time-like Unphysical region p+p ↔ e++e- +p q 2<0 Asymptotics - QCD - analyticity q 2=4 mp 2 GE=GM Egle TOMASI-GUSTAFSSON e+ p q 2>0 p e_ _ FFs are complex p+p ↔ e++e- q 2 CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 5

Q 2 fixed The Rosenbluth separation Linearity of the reduced cross section tan 2 qe dependence Holds for 1 exchange only 16 -VI-2009 Egle TOMASI-GUSTAFSSON e PRL 94, 142301 (2005) CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 6

Crossing Symmetry Scattering and annihilation channels: - Described - - by the same amplitude : function of two kinematical variables, s and t which scan different kinematical regions k 2 → – k 2 p 2 → – p 2 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 7

Time-like observables: | GE| 2 and | GM| 2. A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento XXIV, 170 (1962) B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993). G. Gakh, E. T-G. , Nucl. Phys. A 761, 120 (2005). As in SL region: - Dependence on q 2 contained in FFs - Even dependence on cos 2 (1 g exchange) - No dependence on sign of FFs - Enhancement of magnetic term but TL form factors are complex! 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 8

e- e- q 2<0 p p Experimental Status (space-like) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 9

The nucleon form factors E. T. -G. , F. Lacroix, Ch. Duterte, G. I. Gakh, EPJA 24, 419 (2005) Electric Magnetic proton VDM : IJL F. Iachello. . PLB 43, 191 (1973) w e n … e t Extended VDM (G. -K. 92): a d p neutron E. L. Lomon PRC 66, 045501 2002) 16 -VI-2009 T u o ! a t a d Hohler NPB 114, 505 (1976) Bosted PRC 51, 409 (1995) Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 10

Polarization Method (exp) A. I. Akhiezer, M. P. Rekalo The simultaneous measurement of Pt and Pl reduces the systematic errors ! 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 11

Statistics and Preliminary Results from GEp(III) New equipment worked beautifully: Big. Cal and FPP C. Perdrisat, V. Punjabi 8. 54 Ge. V 2 point: 1. 63 billion triggers collected Analyzing power at 5. 4 Ge. V/c close to Dubna value 6. 8 Ge. V 2 point: 160 million triggers 5. 2 Ge. V 2 point: a test of the spin transport at 180 o μp. GEp/GMp=1. 056 -0. 1427 Q 2 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 12

STATUS on EM Form factors Space-like region 1) "standard" dipole function for the nucleon magnetic FFs GMp and GMn 2) linear deviation from the dipole function for the electric proton FF GEp 3) contradiction between polarized and unpolarized measurements 4) non vanishing electric neutron FF, GEn. 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 13

Two-photon exchange Different results with different experimental methods !! - Both methods based on the same formalism - Experiments repeated New mechanism? • 1 g-2 g ~ a=e 2/4 =1/137 • 1970’s: Gunion, Lev… 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 14

e+ e- q 2>0 p p Experimental Status (time-like) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 15

Time-Like Region proton VDM : IJL F. Iachello. . PLB 43 191 (1973) Extended VDM (G. -K. 92): E. L. Lomon PRC 66 045501(2002) neutron ‘QCD inspired’ E. T-G. , F. Lacroix, C. Duterte, G. I. Gakh, EPJA 24, 419 (2005) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 16

STATUS on EM Form factors Time-like region 1) No individual determination of |GE| and |GM| 2) Assume GE=GM (valid only at threshold) 3) TL nucleon FFs are twice larger than SL FF VMD or p. QCD inspired parametrizations (for p and n): A(p) = 56. 3 Ge. V 4 A(n) = 77. 15 Ge. V 4 L QCD =0. 3 Ge. V 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 17

Models in T. L. Region (polarization) Ay Axx Ayy VDM : IJL Ext. VDM ‘QCD inspired’ Axz R Azz E. T-G. , F. Lacroix, C. Duterte, G. I. Gakh, EPJA 24, 419(2005) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 18

Space-like and Time-like E. T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) F E= e G 2 E FM=s. M/stot /sred e=0. 8 e=0. 2 16 -VI-2009 5 Ge. V 2 ----- 8 Ge. V 2 e=0. 5 FE=s. E/stot Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 19

Space-like and Time-like E. T-G, Phys. Part. Nucl. Lett. 4, 281 (2007) FE=e. G 2 E/sred 10% e=0. 8 e=0. 2 16 -VI-2009 10% e=0. 5 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 20

Radiative Return (ISR) e+ +e- p + B. Aubert ( BABAR Collaboration) Phys Rev. D 73, 012005 (2006) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 21

Results (ISR) GE = G M ? B. Aubert [Babar Collaboration, PRD 73, 012005 (2006) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 22

Form Factors with p+p e ++ e - 1) Knowledge of proton form factors up to large q 2 2) Transition to QCD: Asymptotics 3) Reaction mechanism (1 or 2 photon exchange) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 23

Physical Background 3 body reactions: “easy” to eliminate kinematical constraints PID 2 charged body reactions (π+π-, μ+μ-, K+K-) Most important background is π+ π- : Are we able to discriminate e+e- from π+ π- ? High statistics GEANT 4 simulations YES ! Worse case : few 0/00 pollution / cos CM bin (0. 1) < 1% on the total cross section up to 16 Ge. V 2 16 -VI-2009 Egle TOMASI-GUSTAFSSON D. Marchand, IPN Orsay CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 24 24

Expected Results(I) L = 2 x 1032 cm-2. s-1, 107 s (~100 days) R=GE/GM Ba. BAR Individual determination of GE and GM up to large Q 2 16 -VI-2009 PS 170 Egle TOMASI-GUSTAFSSON PANDA sim CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 25

Proton: F 2 /F 1 and p. QCD C. Perdrisat Brodsky and Farrar (75): Q 2 F 2/F 1 → constant 16 -VI-2009 Belitsky, Ji and Yuan (03): Egle TOMASI-GUSTAFSSON Q 2 F 2/F 1 → ln 2(Q 2/ 2) CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 26

Expected Results (II) -Asymptotic region -Test of analytical properties 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 27

Phragmèn-Lindelöf theorem Asymptotic properties for analytical functions If f(z) a as z along a straight line, and f(z) b as z along another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) a uniformly in the angle. D=0. 05, 0. 1 E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 28

Phragmèn-Lindelöf theorem Connection with QCD asymptotics? Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 29

Conclusions • Hadron form factors: a bridge between perturbative and non perturbative QCD • Progress in experiment and theory • Next future (> 2014) – 12 Ge. V beams at JLab: increase Q 2 to 15 Ge. V 2. Two experiment in preparation - Fair@GSI, antiprotons up to 15 Ge. V/c Precise determination of |GE| and |GM| Cross section measurement up to q 2 to ~20 Ge. V 2. Towards a unified description of form factors, for a better comprehension of the hadron structure 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 30

GEp/GMp with 12 Ge. V at JLab Two new experiments approved to run after the 12 Ge. V upgrade (to be completed end of 2013). Whether they should run depends again on Dubna calibration to 7. 5 Ge. V/c (12. 5 Ge. V 2). 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 31 31

Two-Photon exchange • 1 g-2 g interference is of the order of a=e 2/4 p=1/137 (in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’) • 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, that, at large momentum transfer, due to the sharp decrease of the FFs, if the momentum is shared between the two photons, the 2 gcontribution can become very large. R. Blankenbecker…] • The 2 g amplitude is expected to be mostly imaginary. • The 1 g-2 g interference is more important in timelike region, as the Born amplitude is complex 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 32

Two Photon exchange 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 33

Fitting the angular distributions. . The form of the differential cross section: is equivalent to: Cross section at 900 Angular asymmetry E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 34

Mpp=1. 877 -1. 9 A=0. 01± 0. 02 Mpp=2. 4 -3 E. T. -G. , E. A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 35

Simulations q 2=5. 4, 8. 2, 13. 8 Ge. V 2 Main effect: odd cosq - distribution Approximations: • Neglect contributions to GE, GM • Consider only real part 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 36

N=a 0+a 2 cosq sin 2 q +a 1 cos 2 q, a 2~2 1 2 0. 02 2 0. 2 q 2=5. 4 Ge. V 2 2 16 -VI-2009 0. 05 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 37

Two photon exchange • The calculation of the box amplitude requires the description of intermediate nucleon excitation and of their FFs at any Q 2 • Different calculations give quantitatively different results Theory not enough constrained! Model independent statements 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 38

1 g-2 g interference M. P. Rekalo, E. T. -G. and D. Prout, Phys. Rev. C 60, 042202 (1999) 2 g { { 1 g 1{g 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 39

Unpolarized cross section Two Photon Exchange: • Induces four new terms • Odd function of q: • Does not contribute at q =90° 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 40

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 E. T. -G. , G. Gakh, NPA (2007) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 41

Symmetry relations • Differential cross section at complementary angles: The SUM cancels the 2 g contribution: The DIFFERENCE enhances the 2 g contribution: 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 42

Is there any experimental evidence of two photon exchange? NO (real part) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 43

16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 44

Parametrization of 2 g-contribution for e+p From the data: deviation from linearity << 1%! E. T. -G. , G. Gakh, Phys. Rev. C 72, 015209 (2005) 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 45

Linear fit to e+4 He scattering 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 46

2γ-Gamma Models and Data PR EL C. Perdrisat, L. Pentchev IM IN A RY Expt. Jlab 04 -019 measured Ratio PL/PT for Q 2=2. 49 Ge. V 2 at 3 values of ε NO ε-dependence at 0. 01 level NO evidence of 2 g contribution The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model 16 -VI-2009 12/27/2021 Egle TOMASI-GUSTAFSSON Bystriskyi et al. , LSF PR C 75, 015207 (2007) CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 47 47

Asymptotics 16 -VI-2009 Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPh. N and CNRS/IN 2 P 3/ IPNO 48