1. Simulation of time-like form factor measurements at DAFNE-2
Meeting on e+e- physics perspectives
(non-K-decays) at LNF
Frascati Jan. 2006
Simulation of time-like form factor
measurements at DAFNE-2
Marco Radici
INFN - Pavia
with
Bianconi (Brescia)
B. Pasquini (Pavia)
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

2. M. Radici - Simulation of time-like form factors
Outline
Review master formulae
[ Gakh & Tomasi-Gustafsson hep-ph/ ]
describe setup of Monte Carlo simulation
q2 -, – distributions of unpolarized cross section
extraction of |GM|, |GE|
q2 -,  – distributions of Ay
extraction of phases
4. explore sensitivity to 2 mechanisms
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

3. M. Radici - Simulation of time-like form factors
Born and 2 amplitudes
Unpolarized cross section
Normal polarization
Details of simulation
Input parametrizations of FF
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Sort events distributed as 1/q10 in 4m2 < q2 < 50 GeV2
[ |GM| » 1/q4 ) do » 1/q10 ]
Accept / reject event according to do
each event is a n-tuple of 6 elements: q2,,,Px,Py,Pz
Sample of ~ events
DAFNE-2 L=1032 cm-2s-1 ;  (e+e- ! ppbar) ~ 1nB
) rate 0.1 Hz ; collect sample in ~ 1 month
DAFNE-2 range: (m)2 < q2 < (2.4)2 GeV2
simulation for 4m2=3.52 < q2 < 5.76 GeV2
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

4. M. Radici - Simulation of time-like form factors
Born and 2 amplitudes
Unpolarized cross section
Normal polarization
Details of simulation
Input parametrizations of FF
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Which form factors provide to Monte Carlo ?
DAFNE-2
Brodsky et al.
P.R. D69 (04)
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

5. M. Radici - Simulation of time-like form factors
Born and 2 amplitudes
Unpolarized cross section
Normal polarization
Details of simulation
Input parametrizations of FF
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Iachello Iachello et al.
P.L. B43 (73) 191
P.R.C69 (04)
(dipole core)x(,, poles)
VMD
Lomon Lomon
P.R. C66 (02)
(double dipole)x(,’,,’,)
VMD
Lomon simulates behaviour of CQM 1/Q and improved pQCD fits (see Brodsky). Moreover both give Re/Im of GE/GM separately (needed for cross section)
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

6. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects P1 P2
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

7. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects P1 P2
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

8. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

9. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

10. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

11. M. Radici - Simulation of time-like form factors
Lomon fit to Born cross section
Iachello fit to Born cross section
Statistical comparison of two fits
Fits to total Born cross section
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Need good coverage over whole range in 
q2 close to threshold ! more events, better statistics
q2 close to upper bound ! low statistics, no selective power
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

12. M. Radici - Simulation of time-like form factors
Lomon angular fit to Born Ay
Iachello angular fit to Born Ay
Statistical relevance of Lomon fit
Statistical comparison of fits for Ay(45o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects P3
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

13. M. Radici - Simulation of time-like form factors
Lomon angular fit to Born Ay
Iachello angular fit to Born Ay
Statistical relevance of Lomon fit
Statistical comparison of fits for Ay(45o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

14. M. Radici - Simulation of time-like form factors
Lomon angular fit to Born Ay
Iachello angular fit to Born Ay
Statistical relevance of Lomon fit
Statistical comparison of fits for Ay(45o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

15. M. Radici - Simulation of time-like form factors
Lomon angular fit to Born Ay
Iachello angular fit to Born Ay
Statistical relevance of Lomon fit
Statistical comparison of fits for Ay(45o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

16. M. Radici - Simulation of time-like form factors
Lomon angular fit to Born Ay
Iachello angular fit to Born Ay
Statistical relevance of Lomon fit
Statistical comparison of fits for Ay(45o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
in 4m2<q2<5.76 GeV2 Ay is small
) extraction of phases via Im [GMGE* ] is difficult
2. study Ay(q2) at specific  enhances statistical noise
) look at angular distribution
3. angular fit is problematic, but the sin2 Born trend is
visible ) extracting Im [GMGE* ]: is it possible ?
) again need full coverage of 
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

17. M. Radici - Simulation of time-like form factors
Born and 2 amplitudes
Unpolarized cross section
Normal polarization
Details of simulation
Input parametrizations of FF
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
k1+k2 -> p1+p2 => 4 independent vectors: k1,k2,p=(p1+p2)/2,gamma => 8 independent structures in amplitude: (g^\mu, k1^mu,k2^\mu,p^\mu) x (1 , g.q) current conserv. => 6 indep. el. => 3 complex FF
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

18. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Neglect t dep. of A. For q^2 -> oo 2gamma ~ Born because counting rules give the 1/q^n trend => ReA ~ C ReGE . C can be small or large: C< 25% => dsig_2gamma ~ 6% of dsig_Born from CEBAF SL GE/GM
try C = ! see nothing ; try C = 0.2 ! see something
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

19. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
From now on use only Lomon, because Iachello gives too small observables.
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

20. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects P1 P2 P3
For some q^2 it is impossible to fit histograms with Born formula => deduce info on Re[GM A*]
C = 0.2
Re(A)=Im(A)
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

21. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
C = 0.2
Re(A)= -Im(A)
Re(A)= Im(A)
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

22. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors

23. M. Radici - Simulation of time-like form factors
Test functions for A(q2,t)
Angular fits for unpol. cross section
Statistical comparisons of fits
Statistical comparisons of fits for Ay(90o)
Summary
Monte Carlo
Extraction of moduli
Extraction of phases
2 effects
Modelling 2 diagram is very difficult ! approximations:
GE = GM = 0 ; A(q2,) ¼ A(q2)
if non-Born dependence = cos ) boundary  are important
2. Counting rules ) asymptotically Re[A(q2)] / Re[GE(q2)]
Im[A] = § Re[A] ) test interference Re[GE/M]§ Im[GE/M]
angular separation possible
3. Ay(q2) at =/2 only from 2 ; but too few events
) statistical noise, no selectivity
) again full  coverage important
Frascati 20/01/06 LNF
M. Radici - Simulation of time-like form factors