Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO 16-VI-2009 1 Space-Like and Time-Like Form Factors Compared analysis Egle Tomasi-Gustafsson SPhN-Saclay and IPN-Orsay Varenna, June 16, 2009 2009
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 1
Space-Like and Time-LikeForm Factors
Compared analysisEgle Tomasi-Gustafsson
SPhN-Saclay and IPN-Orsay
Varenna, June 16, 2009 2009
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 2
PLAN•Introduction:Form factors in one photon exchange approximation
….Model Independent Statements
q2>0
e-
e+ p
p
•Experimental Situation– Space-Like– Time-like
•Future Panda/FAIR and JLab 12 GeV:– Determination of proton form factors– Transition to QCD: Asymptotics– Reaction mechanism (1 or 2 exchange)
•Conclusions
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 3
Hadron Electromagnetic Form factorsHadron 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 2S+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 q2 probe the size of the nucleus,
– at high q2 test QCD scaling
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 4
The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2
Electromagnetic InteractionElectromagnetic Interaction
q2<0
e-e-
p p)2q(2F
M2qi
)2q(1F
or in terms of Sachs FFs:GE=F1-F2, GM=F1+F2, =-q2/4M2
The electron vertex is known,
The interaction is carried by a virtual photon of mass q2
What about high order
radiative corrections?
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 5
AnalyticityAnalyticity
__
q2<0
e-e-
p p
q2>0
e-
e+ p
p
q2q2=4mp2
FFs are complexFFs are real Unp
hysi
cal r
egio
n
GE=GM
Space-like
Time-likeGE(0)=1
GM(0)=p
Asymptotics- QCD- analyticity
p+p ↔ e++e-e+p e+p
p+p
↔ e
++
e- +
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 6
The Rosenbluth separation
)2(2)2(2
)1(1 QMGQEG
Mottd
ddd
2M4
2Q,1
2e2)tan1(21
2MG2
EGR
Holds for 1exchange only
Linearity of the reduced cross section
PRL 94, 142301 (2005)
tan2e dependence
Q2 f
ixed
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 7
Crossing SymmetryCrossing Symmetry
Scattering and annihilation channels:
- Described by the same amplitude :
- function of two kinematical variables, s and t
p2 → – p2
k2 → – k2
- which scan different kinematical regions
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 8
Time-like observables: | GE| 2 and | GM| 2 .
As in SL region:- Dependence on q2 contained in FFs- Even dependence on cos2(1 exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex!
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).
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 9
Experimental Status (space-like)
q2<0
e-e-
p p
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 10
The nucleon form factors
VDM : IJLF. Iachello..PLB 43, 191 (1973)
Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002)
HohlerNPB 114, 505 (1976)
BostedPRC 51, 409 (1995)
Electric Magneticne
utro
npr
oton
E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (2005)
To update…new
data!
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 11
The simultaneous measurement of Pt and Pl reduces the systematic errors !
Polarization Method (exp)
A.I. Akhiezer, M.P. Rekalo
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 12
Statistics and Preliminary Results from GEp(III)
New equipment workedbeautifully: BigCal and FPP
8.54 GeV2 point: 1.63 billion triggers collected
Analyzing power at 5.4 GeV/c close to Dubna value
6.8 GeV2 point: 160 million triggers
5.2 GeV2 point: a test of the spin transport at 180o
μpGEp/GMp=1.056-0.1427Q2
C. Perdrisat, V. Punjabi
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 13
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.
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 14
Two-photon exchange
Different results with different experimental methods !!
- Both methods based on the same formalism
- Experiments repeated
New mechanism?
•1-2 ~ =e2/4=1/137
•1970’s: Gunion, Lev…
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 15
Experimental Status (time-like)
q2>0
e-
e+ p
p
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 16
Time-Like Region
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419 (2005)
VDM : IJLF. Iachello..PLB43 191 (1973)
Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002)
‘QCD inspired’
proton
neutron
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 17
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
QCD =0.3 GeV
A(p) = 56.3 GeV4 A(n) = 77.15 GeV4
)]/(ln[ 2222
ss
AGM
VMD or pQCD inspired parametrizations (for p and n):
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 18
Models in T.L. Region (polarization)
VDM : IJL
Ext. VDM
‘QCD inspired’
R
Ay Axx Ayy
Axz
Azz
E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419(2005)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 19
Space-like and Time-like E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
=0.5=0.2
=0.8
FE=G2Ered
FE=tot
FM=tot
GeV2----- 8 GeV2
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 20
Space-like and Time-like
=0.2=0.5
=0.8
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
10%
10%
FE=G2Ered
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 21
Radiative Return (ISR)
.s
m,
x
sin
xx
x),x,s(W
,s
m
s
Ex),m)(ppee(),x,s(W
s
m
cosddm
)ppee(d
e
2
22
122
2
2
2
2
e+ +e- p + p +
B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 22
Results (ISR)
GE = GM ?
B. Aubert [Babar Collaboration, PRD 73, 012005 (2006)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 23
Form Factors with
p+p e++ e-
1) Knowledge of proton form factors up to large q2
2) Transition to QCD: Asymptotics3) Reaction mechanism (1 or 2 photon exchange)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 24
D. Marchand, IPN Orsay24
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- : 610~
ee
Are we able to discriminate e+e- from π+ π- ?
YES !YES !High statistics GEANT4 simulations Worse case : few Worse case : few 00//0000 pollution / cos pollution / cosCMCM bin (0.1) bin (0.1) < 1% on the total cross section up to 16 GeV2
Physical Background
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 25
Individual determination of GE and GM up to large Q2
Expected Results(I)
R=GE/GM
BaBAR
PS170 PANDA sim
L = 2x1032 cm-2.s-1, 107 s (~100 days)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 26
Proton: F2 /F1 and pQCD
Brodsky and Farrar (75):Q2F2/F1 constant
Belitsky, Ji and Yuan (03):
Q2F2/F1 → ln2(Q2/2)→
C. Perdrisat
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 27
-Asymptotic region
-Test of analytical properties
Expected Results (II)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 28
Phragmèn-Lindelöf theorem
Asymptotic properties for analytical functions
E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)
=0.05, 0.1
If f(z) a as z along a straight line, and f(z) b as zalong 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.
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 29
Phragmèn-Lindelöf theorem
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Applies to NN and NNInteraction (Pomeranchuk theorem)t=0 : not a QCD regime!
Connection with QCD asymptotics?
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 30
Conclusions•Hadron form factors: a bridge between perturbativeand non perturbative QCD•Progress in experiment and theory
•Next future (> 2014)– 12 GeV beams at JLab: increase Q2 to 15 GeV2. Two experiment in preparation
- Fair@GSI, antiprotons up to 15 GeV/cPrecise determination of |GE| and |GM|
Cross section measurement up to q2 to ~20 GeV2.
Towards a unified description of form factors, for a better comprehension of the hadron structure
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 31
GEp/GMp with 12 GeV at JLab
31
Two new experiments approved to run after the 12 GeV upgrade (to be completed end of 2013).
Whether they should run depends again on Dubna calibration to 7.5 GeV/c (12.5 GeV2).
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 32
Two-Photon exchange•1-2 interference is of the order of =e2/4p=1/137
(in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’)
•The 2 amplitude is expected to be mostly imaginary.•The 1-2 interference is more important in time-like region, as the Born amplitude is complex
•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…]
that, at large momentum transfer, due to the sharp decrease
of the FFs, if the momentum is shared between the two
photons, the 2- contribution can become very large.
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 33
Two Photon exchange
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 34
Fitting the angular distributions..
E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section:
is equivalent to:
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 35
Mpp=1.877-1.9Mpp=1.877-1.9
A=0.01A=0.01±±0.020.02
Mpp=2.4-3Mpp=2.4-3
E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 36
Simulations
Approximations:•Neglect contributions to GE,GM•Consider only real part
Main effect: odd cos- distribution
20.0/3 MGF
02.0/3 MGF
0/3 MGF
05.0/3 MGF
q2=5.4,8.2,13.8 GeV2
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 37
2 0.02
2 0.05 2 0.2
1
q2=5.4 GeV2
N=a0+a2cossin2+a1 cos2, a2~2
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 38
Two photon exchange•The calculation of the box amplitude requires
thedescription of intermediate nucleon excitation
and of their FFs at any Q2
•Different calculations give quantitatively different results
Theory not enough constrained!
Model independent statements
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 39
1{g
1-2 interference
{ 21 {
M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 40
Unpolarized cross section
•Induces four new terms•Odd function of •Does not contribute at =90°
Two Photon Exchange:
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 41
•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
Symmetry relationsSymmetry relations
E. T.-G., G. Gakh, NPA (2007)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 42
•Differential cross section at complementary angles:
Symmetry relations
The DIFFERENCE enhances the 2contribution:
The SUM cancels the 2contribution:
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 43
Is there any experimental evidence of
two photon exchange?
(real
part)
NO
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 44
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 45
From the data:
deviation from linearity
<< 1%!
Parametrization of 2-contribution for e+p
E. T.-G., G. Gakh, Phys. Rev. C 72, 015209 (2005)
)(1
1),( 2)(2 QfQF a
2222
22
]1[ a
Dγ(a)
/m[GeV]Q
GC)(Qf
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 46
Linear fit to e+4He scattering
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 47
2γ-Gamma Models and Data
47
The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model
04/22/23
Expt. Jlab 04-019 measuredRatio PL/PT for Q2=2.49 GeV2
at 3 values of ε
PRELIMINARY
C. Perdrisat,L. Pentchev
NO ε-dependence at 0.01 level
NO evidence of 2 contribution
Bystriskyi et al., LSFPR C75, 015207 (2007)
Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 48
Asymptotics