Meeting on ee physics perspectives nonKdecays at LNF

Outline 1. Review master formulae 2. [ Gakh & Tomasi-Gustafsson hep-ph/0511240 ] 3. describe

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects

1. 2. 3. 4. 5. Monte Carlo Extraction of moduli Extraction of phases 2

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Meeting on e+e- physics perspectives (non-K-decays) at LNF Frascati 19 -20 Jan. 2006 Simulation of time-like form factor measurements at DAFNE-2 Marco Radici INFN - Pavia Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors with A. Bianconi (Brescia) B. Pasquini (Pavia) 1

Outline 1. Review master formulae 2. [ Gakh & Tomasi-Gustafsson hep-ph/0511240 ] 3. describe setup of Monte Carlo simulation 2. q 2 -, – distributions of unpolarized cross section 3. extraction of |GM|, |GE| 3. q 2 -, – distributions of Ay 4. extraction of phases 4. explore sensitivity to 2 mechanisms Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 2

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Born and 2 amplitudes Unpolarized cross section Normal polarization Details of simulation Input parametrizations of FF 1. Sort events distributed as 1/q 10 in 4 m 2 < q 2 < 50 Ge. V 2 2. [ |GM| » 1/q 4 ) d o » 1/q 10 ] 2. Accept / reject event according to d o 3. each event is a n-tuple of 6 elements: q 2, , , Px, Py, Pz 3. Sample of ~ 270 000 events 4. DAFNE-2 L=1032 cm-2 s-1 ; (e+e- ! ppbar) ~ 1 n. B 5. ) rate 0. 1 Hz ; collect sample in ~ 1 month 4. DAFNE-2 range: (m )2 < q 2 < (2. 4)2 Ge. V 2 5. simulation for 4 m 2=3. 52 < q 2 < 5. 76 Ge. V 2 Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 5

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Born and 2 amplitudes Unpolarized cross section Normal polarization Details of simulation Input parametrizations of FF Which form factors provide to Monte Carlo ? DAFNE-2 Brodsky et al. P. R. D 69 (04) 054022 Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 6

1. 2. 3. 4. 5. Monte Carlo Extraction of moduli Extraction of phases 2 effects Iachello Born and 2 amplitudes Unpolarized cross section Normal polarization Details of simulation Input parametrizations of FF Iachello et al. P. L. B 43 (73) 191 P. R. C 69 (04) 055204 (dipole core)x( , , poles) VMD Lomon P. R. C 66 (02) 045501 (double dipole)x( , ’, ) VMD Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 7

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects Frascati 20/01/06 e+e- @ LNF 1. 2. 3. 4. 5. Lomon fit to Born cross section Iachello fit to Born cross section Statistical comparison of two fits Fits to total Born cross section Summary M. Radici - Simulation of time-like form factors 10

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Lomon fit to Born cross section Iachello fit to Born cross section Statistical comparison of two fits Fits to total Born cross section Summary Need good coverage over whole range in q 2 close to threshold ! more events, better statistics q 2 close to upper bound ! low statistics, no selective power Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 13

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects Frascati 20/01/06 e+e- @ LNF 1. 2. 3. 4. 5. Lomon angular fit to Born Ay Iachello angular fit to Born Ay Statistical relevance of Lomon fit Statistical comparison of fits for Ay(45 o) Summary M. Radici - Simulation of time-like form factors 16

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Lomon angular fit to Born Ay Iachello angular fit to Born Ay Statistical relevance of Lomon fit Statistical comparison of fits for Ay(45 o) Summary 1. in 4 m 2<q 2<5. 76 Ge. V 2 Ay is small 2. ) extraction of phases via Im [GMGE* ] is difficult 2. study Ay(q 2) at specific enhances statistical noise ) look at angular distribution 3. angular fit is problematic, but the sin 2 Born trend is visible ) extracting Im [GMGE* ]: is it possible ? ) again need full coverage of Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 19

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects Frascati 20/01/06 e+e- @ LNF 1. 2. 3. 4. 5. Born and 2 amplitudes Unpolarized cross section Normal polarization Details of simulation Input parametrizations of FF M. Radici - Simulation of time-like form factors 20

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Test functions for A(q 2, t) Angular fits for unpol. cross section Statistical comparisons of fits for Ay(90 o) Summary try C = 0. 02 ! see nothing ; try C = 0. 2 ! see something Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 21

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects Frascati 20/01/06 e+e- @ LNF 1. 2. 3. 4. 5. Test functions for A(q 2, t) Angular fits for unpol. cross section Statistical comparisons of fits for Ay(90 o) Summary M. Radici - Simulation of time-like form factors 22

1. 2. 3. 4. Monte Carlo Extraction of moduli Extraction of phases 2 effects 1. 2. 3. 4. 5. Test functions for A(q 2, t) Angular fits for unpol. cross section Statistical comparisons of fits for Ay(90 o) Summary 1. Modelling 2 diagram is very difficult ! approximations: 2. GE = GM = 0 ; A(q 2, ) ¼ A(q 2) 3. if non-Born dependence = cos ) boundary are importa 2. Counting rules ) asymptotically Re[A(q 2)] / Re[GE(q 2)] Im[A] = § Re[A] ) test interference Re[GE/M]§ Im[GE/M] angular separation possible 3. Ay(q 2) at = /2 only from 2 ; but too few events ) statistical noise, no selectivity ) again full coverage important Frascati 20/01/06 e+e- @ LNF M. Radici - Simulation of time-like form factors 28