Electromagnetic hadron form factors: status and perspectives

Electromagnetic hadron form factors: status and perspectives Egle Tomasi-Gustafsson CEA, IRFU,SPhN, Saclay, France Egle Tomasi-Gustafsson 1

Hadron Electromagnetic Form factors Characterize the internal structure of a particle ( point-like) Elastic form factors contain information on the hadron ground state. In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors. Neutron and proton form factors are different. Deuteron: 2 structure functions, but 3 form factors. Playground for theory and experiment at low q 2 probe the size of the nucleus, at high q 2 test QCD scaling Egle Tomasi-Gustafsson 2

Recent experimental achievements: LNS-Saclay polarization Hadron polarimetry in the GeV range JINR-Dubna and also: polarized sources and targets, high intensity e - beams, high luminosity colliders, large acceptance spectrometers, high resolution 4π detectors VEPP-Novosibirsk Egle Tomasi-Gustafsson 3

Proton Charge and Magnetic Distributions e - q 2 <0 p p e - Space-like FFs are real G E (0)=1 G M (0)=µ p Unphysical region p+p e + e - +π 0 Asymptotics - QCD - analyticity e + e - q 2 >0 _ p p _ Time-Like FFs are complex e+p e+p 0 q 2 =4m p 2 GE=GM p+p e + +e - q 2 Egle Tomasi-Gustafsson 4

Hadron Electromagnetic Form Factors e - q 2 <0 GM p e - GE Polarized GE unpolarized p Space-like FFs are real GE(0)=1 GM(0)=µ p e+p e+p Unphysical region p+p e + +e - +π 0 q 2 =4m p 2 Asymptotics - QCD - analyticity e + GE=GM q 2 >0 e - GE=GM p+p e + +e - _ p p Time-Like _ FFs are complex q 2 Egle Tomasi-Gustafsson 5

Hadron Electromagnetic Form Factors GE Polarized GE unpolarized GE=GM GM e+p e+p GE=GM Egle Tomasi-Gustafsson 6

The Space-Like region: low Q 2 e+p e+p Egle Tomasi-Gustafsson 7

Root mean square radius Fourier Transform Egle Tomasi-Gustafsson 8

The Proton Radius Rp=0.84184(67) fm (muonic atom) Rp=0.879(8) fm (e-p Mainz) Rp=0.8768(69) fm Rp=0.82-0.85 fm (DR PRC75 035202(2007)) Rp=0.897(18) fm Rp=0.78-0.86 fm (lattice QCD PRD 79 094001(2009)) Egle Tomasi-Gustafsson 9

The Proton Radius Rp=0.84184(67) fm (muonic atom) Rp=0.879(8) fm (e-p Mainz) Rp=0.8768(69) fm Rp=0.82-0.85 fm (DR PRC75 035202(2007)) Rp=0.897(18) fm Rp=0.78-0.86 fm (lattice QCD PRD 79 094001(2009)) Egle Tomasi-Gustafsson 10

Mainz, A1 collaboration (1400 points) Q 2 >0.004 GeV 2 Radiative corrections Two photon exchange Coulomb corrections..comments MUSE Experiment Jlab CLAS What about extrapolation to Q 2 0? G.I. Gakh, A. Dbeyssi, E.T-G, D. Marchand,V.V. Bytev, Phys.Part.Nucl.Lett. 10 (2013) 393, Phys.Rev. C84 (2011) 015212 Egle Tomasi-Gustafsson 11

Why I do not trust the fits Slide from Savely Karshenboim G E (q 2 ) Egle Tomasi-Gustafsson 12

Why I do not trust the fits Slide from Savely Karshenboim Egle Tomasi-Gustafsson 13

The Space-Like region e+p e+p Wolfgang Pauli Niels Bohr ( 30ies) Egle Tomasi-Gustafsson 14

2 4M 2 Q, 1 2 e 2 )tan 2(1 1 = + + = τ θ τ ε 2 M G 2 E G R τ ε σ + = Egle Tomasi-Gustafsson 15 Holds for 1γ exchange only Linearity of the reduced cross section PRL 94, 142301 (2005) tan 2 θ e dependence ε Q 2 fixed ep-elastic scattering : Rosenbluth separation 1950 + + Ω = Ω 2 ) ( 2 2 ) 2 ( ) (1 1 Q M G Q E G Mott d d d d ε τ τ σ σ

ep-elastic scattering : Akhiezer-Rekalo method 1967 The polarization induces a term in the cross section proportional to G E G M Polarized beam and target or polarized beam and recoil proton polarization Egle Tomasi-Gustafsson 16

The polarization method (exp: 2000) C. Perdrisat, V. Punjabi, et al., JLab-GEp collaboration The simultaneous measurement of P t and P l reduces the systematic errors Egle Tomasi-Gustafsson 17

Polarization Experiments A.I. Akhiezer and M.P. Rekalo, 1967 Jlab-GEp collaboration 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) QCD scaling not reached 3) Zero crossing of Gep? 4) contradiction between polarized and unpolarized measurements A.J.R. Puckett et al, PRL (2010), PRC (2012) Egle Tomasi-Gustafsson 18

Some models (IJL 73, Diquark, soliton..) predicted such behavior before the data appeared BUT Issues Simultaneous description of the four nucleon form factors......in the space-like and in the time-like regions Consequences for the light ions description When pqcd starts to apply? Source of the discrepancy Egle Tomasi-Gustafsson 19

The Time-Like region p + p e + + e - (γ) GE=GM 4M 2 Egle Tomasi-Gustafsson 20

Time-like observables: G E 2 and G M 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. A761,120 (2005). As in SL region: - Dependence on q 2 contained in FFs - Even dependence on cos 2 θ (1γ exchange) - No dependence on sign of FFs - Enhancement of magnetic term but TL form factors are complex! Egle Tomasi-Gustafsson 21

VMD: Iachello, Jakson and Landé (1973) Isoscalar and isovector FFs γ* ω,ρ,ϕ Egle Tomasi-Gustafsson 22

The Experimental Status The Time-like Region F p GE=GM No individual determination of GE and GM 1 10 1 10 TL proton FFs twice larger than in SL at the same Q 2 Steep behaviour at threshold Babar:Structures? Resonances? 2 10 3 10 4 6 8 10 10 20 30 40 2 q 2 [GeV ] S. Pacetti, R. Baldini-Ferroli, E.T-G, Physics Reports, 514 (2014) 1 Panda contribution: M.P. Rekalo, E.T-G, DAPNIA-04-01, ArXiv:0810.4245. Egle Tomasi-Gustafsson 23

The Time-like Region F p Expected QCD scaling (q 2 ) 2 1 10 GE=GM 1 10 2 10 4 6 8 10 3 10 10 20 30 40 2 q 2 [GeV ] Egle Tomasi-Gustafsson 24

Oscillations : regular pattern in P Lab The relevant variable is p Lab associated to the relative motion of the final hadrons. F p 0.3 (a) 0.2 0.1 0.04 (b) 0.02 D 0-0.02 A: Small perturbation B: damping C: r < 1fm D=0: maximum at p=0-0.04 0 1 2 3 p [GeV] Simple oscillatory behaviour Small number of coherent sources A. Bianconi, E. T-G. Phys. Rev. Lett. 114,232301 (2015) Egle Tomasi-Gustafsson 25

Oscillations : regular pattern in P Lab The relevant variable is (a) p Lab associated (b) to the relative 0.3 0.3 motion of the final hadrons. F p 0.2 F p 0.2 F p 0.3 0.1 D (a) 0.04 (b) 0.1 D 0.04 0.2 0.02 0 0.02 0 0.1 0.02 0.02 0.04 0.04 0 1 2 3 p [GeV] 0 1 2 3 p [GeV] 0.04 (b) 0.02 D 0-0.02-0.04 F p 0.3 0.2 0.1 D 0.04 0.02 0 1 2 3 0 0.02 0 p [GeV] 0.04 A. Bianconi, E. T-G. Phys. Rev. 0.05 Lett. 114,232301 (2015) 0 1 2 3 (c) p [GeV] F p 0.3 0.2 0.1 D 0.05 A: Small perturbation B: damping C: r < 1fm D=0: maximum at p=0 Simple oscillatory behaviour Small number of coherent sources 0 1 2 3 (d) p [GeV] Egle Tomasi-Gustafsson 26

Fourier Transform 2 10 3 M 0 (r) (1/fm ) 0.15 3 M(r) (1/fm ) F 0 = = 10 1-1 10 0.1 0.05-2 10-3 10-4 10 0-0.05 0 0.5 1 1.5 2 r (fm) 0.6 0.8 1 1.2 1.4 1.6 r (fm) Rescattering processes Large imaginary part Related to the time evolution of the charge density? (E.A. Kuraev, E. T.-G., A. Dbeyssi, PLB712 (2012) 240) Consequences for the SL region? Data expected at BESIII, PANDA Varenna, 15-VI-2015 Egle Tomasi-Gustafsson 27

The nucleon 3 valence quarks and a neutral sea of qq pairs antisymmetric state of colored quarks Main assumption Does not hold in the spatial center of the nucleon: the center of the nucleon is electrically neutral, due to strong gluonic field E.A. Kuraev, E. T-G, A. Dbeyssi, Phys.Lett. B712 (2012) 240 Egle Tomasi-Gustafsson 28

The annihilation channel: The neutral plasma acts on the distribution of the electric charge (not magnetic). Prediction: additional suppression due to the neutral plasma similar behavior in SL and TL regions Implicit normalization at q 2 =4M p2 : GE = GM =1 No poles in unphysical region Egle Tomasi-Gustafsson 29

The asymptotic region Egle Tomasi-Gustafsson 30

Large q 2 : : where the extremes meat Phragmèn-Lindelöf theorem PANDA E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001) Applies to NN and NN Interaction (Pomeranchuk theorem) t=0 : not a QCD regime! Analyticity Connection with QCD asymptotics? Egle Tomasi-Gustafsson 31

Conclusions Large activity at all world facilities both in Space and Time-like regions Theory: unified models in SL and TL regions: - describe proton and neutron, electric and magnetic - pointlike behavior at threshold? - understand GE, GM(SL) < GE,GM(TL); Experiment: to measure - zero crossing of GE/GM in SL? 2γ? Proton radius? - GE and GM separately in TL - complex FFs in TL region: polarization! - new structures in TL: access to hadron formation? Egle Tomasi-Gustafsson 32

Egle Tomasi-Gustafsson 33

Point-like form factors? S. Pacetti Egle Tomasi-Gustafsson 34

Radiative return (ISR) e + +e - p + p + γ dσ( e + e ppγ dm d cosθ ) = 2m W ( s s, x, θ ) σ( e + e pp )(m ), x = 2E s γ = 1 m s 2, W ( s, x, θ ) = α πx 2 2x + sin 2 θ x 2 x 2 2, θ >> m e s. B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006) Egle Tomasi-Gustafsson 35