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Meeting on e + e - physics perspectives (non-K-decays) at LNF

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. with Bianconi (Brescia) B. Pasquini (Pavia). Outline. Review master formulae

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Meeting on e + e - physics perspectives (non-K-decays) at LNF

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  1. 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 • with • Bianconi (Brescia) • B. Pasquini (Pavia) M. Radici - Simulation of time-like form factors

  2. Outline • Review master formulae • [ Gakh & Tomasi-Gustafsson hep-ph/0511240 ] • 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 M. Radici - Simulation of time-like form factors

  3. 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 ~ 270 000 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 M. Radici - Simulation of time-like form factors

  4. 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) 054022 M. Radici - Simulation of time-like form factors

  5. 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) 055204 (dipole core)x(,, poles) VMD Lomon Lomon P.R. C66 (02) 045501 (double dipole)x(,’,,’,) VMD M. Radici - Simulation of time-like form factors

  6. 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 M. Radici - Simulation of time-like form factors

  7. 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 M. Radici - Simulation of time-like form factors

  8. 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 M. Radici - Simulation of time-like form factors

  9. 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 M. Radici - Simulation of time-like form factors

  10. 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 M. Radici - Simulation of time-like form factors

  11. 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 M. Radici - Simulation of time-like form factors

  12. 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 M. Radici - Simulation of time-like form factors

  13. 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 M. Radici - Simulation of time-like form factors

  14. 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 M. Radici - Simulation of time-like form factors

  15. 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 M. Radici - Simulation of time-like form factors

  16. 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  M. Radici - Simulation of time-like form factors

  17. 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 M. Radici - Simulation of time-like form factors

  18. 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 try C = 0.02 ! see nothing ; try C = 0.2 ! see something M. Radici - Simulation of time-like form factors

  19. 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 M. Radici - Simulation of time-like form factors

  20. 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 C = 0.2 Re(A)=Im(A) M. Radici - Simulation of time-like form factors

  21. 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) M. Radici - Simulation of time-like form factors

  22. 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 M. Radici - Simulation of time-like form factors

  23. 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 M. Radici - Simulation of time-like form factors

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