1. M. Radici - Time-like form factors
Working group Frascati
Milano 4 Nov. 2005
Time - like form factors
Marco Radici
INFN - Pavia
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

2. M. Radici - Time-like form factors
Outline
Why should we measure time-like (TL)
form factors (FF) ?
What should we learn from TL FF
with respect to SL FF ?
3. Which measurements are needed ?
4. Available data and calculations ?
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

3. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
elastic scattering
cross section
Rosenbluth separation
fixed Q2, vary
GE slope , GM intercept
large errors in GE
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

4. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
polarization
transfer
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

5. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
JLab – Hall A Qattan et al.
P.R.L. 94 (05)
Blunden et al. nucl-th/
2 ?
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

6. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
pQCD
JLab polar. transfer data
where is onset of
pQCD scaling ?
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

7. M. Radici - Time-like form factors
GEp
GEn
GMp
GMn
Miller, P.R. C66 (02) (R) : LFCBM
Ma, Qing, Schmidt, P.R. C65 (02) : LF diquark
Lomon, P.R. C66 (02) : VMD
from H. Gao
Int. J. Mod. Phys. E12 (03) 1
erratum E12 (03) 567
Holzwarth, hep-ph/
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

8. But SpaceLike TimeLike analytic continuation by
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
SpaceLike
TimeLike
analytic continuation by
Dispersion Relations (DR)
But
fit to pQCD TimeLike
fit to pQCD SpaceLike
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

9. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
pQCD + analyticity
But
fit to |GMp|
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

10. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
poor statistic
integrate d
over wide
angular range
all data assume
it’s true only at
where steep rise is observed
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

11. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
only 1 measurement for neutron (ADONE-1998) again with
scarce angular distributions and with low statistics
no polarization of protons and/or electrons
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

12. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Questions in SL region
Surprise in SL $ TL
Few and poor TL data
Better constrain models
IJL
CQM
pQCD
“improved”
Brodsky et al.
P.R. D69 (04)
Dispersive approach on BaBar and Lear
Pacetti talk at Nucleon ’05 - Frascati
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

13. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
F(t) analytic function in t 2 C with
cut [t0 = 4m2, 1)
Dispersion Relation (DR) R
Im F(t’)  0 only in [t0=4m2, 1 ) C
vector-meson poles and multi-hadron continuum
dipole fit to F2 (q2e-i ) / F1 (q2 e-i ) ! R !
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

14. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
unpolarized cross section for
R angular
asymmetry
q2<0 Rosenbluth plot
change E, e at fixed q2
) linear plot in 
q2>0
measure 2  at fixed q2
) get R
cos2 typical of Born diagram
measure 3 
) explore 2
mechanisms
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

15. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
polarized cross section for
Ax, Az require polarization of the electron beam: Pe  0
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

16. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
phases of FF from Final-State Interactions (FSI) of final baryon system :
interference of channels with different phases ( Im (GE*GM) )
pQCD : FSI ! 0 for Q2 ! 1
) test transition to scaling and Color Transparency (CT)
FSI ! T-odd mechanisms are allowed : generates
GE = F1 +  F2 = |GE| ei E
GM = F1 + F2 = |GM| ei M
not possible in elastic scattering
Im (GE*GM) = ( -1) Im F2*F1
threshold t1=4M2 ! Im( )=0
consistent with |GE|=|GM|
from GT=1(t1)=0
ambiguity  $  -  solved by
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

17. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
discriminate among models that are close in SL region
IJL
CQM
pQCD
“improved”
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

18. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
Form factors are complex
|FF| from unpol. cross section
Phases from polarization
Unphysical region
steep rise at threshold
tail of narrow resonance at
t ≤ 4M2 (baryonium) ?
should show up as a dip in some
hadronic cross section
E687 diffractive photoproduction of 6
Upcoming results from BaBar also
W » 1.9 GeV
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

19. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
measure angular dependence of unpol. cross section
) angular asymmetry R and test 2 mechanisms
measure Ay / sin (E - M)
measure Ay / Ax / tan (E - M)
utopia : measure Ai j
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

20. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
data : proton
models
ADONE Q2 = 4.4 GeV (1973)
CERN Q2 ~ (1977)
Orsay-DM1 Q2 ~ (1979)
Orsay-DM2 Q2 = (1983)
LEAR Q2 ~ (1994)
E Q2 ~ (1993)
FENICE Q2 ~ (1994)
E Q2 ~ (1999)
(2003)
CLEO Q2 ~ (2005)
BES Q2 ~ (2005)
BaBar Q2 ~ (2005)
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

21. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
data : proton
models
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

22. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
data : neutron
models
FENICE Q2 ~3.7-6
(1994)
but always assumed
|GEN| = |GMN| N=p,n
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

23. M. Radici - Time-like form factors
Why TL FF ?
What do we learn ?
Which measurements ?
Available data and models ?
data
models
Dispersion Relations (DR):
analyticity+unitarity+Vector Mesons (VM) (Drechsel, Meissner,
Hammer, Hoehler,..)
“ “ input exp. data (Baldini, Pacetti, …)
VM Dominance (VMD) based models (Iachello, Bijker, Lomon, …)
Soliton (Holzwarth)
CQM : Light Front Form (Pace, Salmè, Simula, …)
“ “ “ + \pi cloud (Miller, Jennings, .. )
Point Form (Pavia + Graz collaboration)
Diquark (Ma, …)
pQCD “inspired” (Brodsky, Ji, Belitski, Yuan, ..)
reviews: Brodsky et al. P.R. D69 (04)
Tomasi-Gustafsson et al. E.P.J. A24 (05) 419
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors

24. M. Radici - Time-like form factors
Possible logo ?
(from Pacetti talk at Nucleon’05)
Milan 4/11/05 Work group e+e-
M. Radici - Time-like form factors