1. Study of the decay   f 0 (980)    +  -  C.Bini, S.Ventura, KLOE Memo 294 03/2004 (upd. 06/2005) C.Bini, KLOE Memo 304 03/2005 (upd. 06/2005)

2. Outline Motivations of this analysis. The data sample: what we measure and how the data look like. Theory, KL, NS, SA,.... The fits. Discussion of the results. Conclusion: what we learn from this analysis.

3. Motivations of this analysis Assess clearly the   f 0 (980)        signal; determine the f 0 (980) parameters (coupling to the  to KK and  ); assess the quark content of the f 0 ; any further meson is needed to describe the data ? Compare models.

4. The data sample: the event selection drc stream “vertex”: R v <8 cm; Z v <15 cm; “2 tracks”: +,-; 45 o <  +,  - <135 o ; “pion identification”L 1 vs. L 2 cut (AND); “large angle”: 45 o <   <135 o ; “track mass”:129<M T <149 MeV; “photon matching”:E cl >10 MeV;  cl >22 o   <0.03+3/E cl N  > 0 See Memo 294

5. The data sample: dN/dm  6.7 ×10 5 events / 350 pb -1 “on-peak” data  1.2 ×10 4 events /6.58 pb -1 “off-peak” data 1017 MeV  1.0 ×10 4 events /4.93 pb -1 “off-peak” data 1022 MeV “off-peak” data “on-peak” data spectrum f 0 (980) signal

6. The data sample: large angle vs. small angle Red = LA Blue = SA In the f 0 (980) region: ISR(LA)/ISR(SA)~5  [S/B] LA ~ 60 [S/B] SA f 0 signal in LA vs. SA events

7. The data sample: A c Charge asymmetry A c in bins of m “on-peak” data “off-peak” data

8. The data sample: √s dependence  (900-1000 MeV) = N(events 900<m<1000 MeV) / L int  (m)) Blue = “on-peak” sliced data Red = “off-peak” data

9. The data sample: detection efficiency Acceptance loss Vetocos loss Photon request loss MC stream ppphvlag (ISR+FSR) Sample size ~ data All selection chain apart from: Filfo Vetocos TCA+Likelihood (taken from data) Corrections from: tracking efficiency photon efficiency (1-exp(-E/a)) a~8-10 MeV

10. The data sample: estimated background Dedicated MC generations of      ,      and     (no  ): Check done “before photon request”: good agreement above 450 MeV Black = data Blue =       Red =      Pink =     (no  ) Red = data (40 pb -1 sample) Green = background Pink = estimated signal

11. Zoom (signal region) At the end of the selectionBefore the photon request data Surviving     Red = data (40 pb -1 sample) Blue = MC(     ) + data/  

12. The data sample: systematics due to low energy photons The larger systematic effect is due to the data-MC linearity difference Efficiency change after application of the data-MC correction The difference is assumed as an uncertainty (quad. add to stat.). (*) also tried ½ correct.+ ½ error

13. Theory: KL,NS,SA,.... e+e+ e-e-  f0f0 ++ -- {M} has to rely on “some” model with “some” parameters

14. Theory: KL (KL) by N.N.Achasov; where: g(m) = kaon-loop function  (m) = phase shift (based on  scattering data) D f (m) = f 0 propagator (finite width corrections) If only one meson (no  included): 3 free parameters: m f, g fKK, g f 

15. Theory: NS (NS) after several discussions with G.Isidori, L.Maiani and (recently) S.Pacetti; where the propagator (Flatte’ revised) is: with couplings 7 free parameters: m f, g  f , g fKK, g f ,a 0, a 1, b 1

16. Theory: SA (NS) by M.E.Boglione and M.R.Pennington; where T 11 = T(    ) and T 12 = T(   KK): (1-m 2 /s) satisfies gauge invariance requirement. From the polynomials  coupling g  (GeV) residual at the f 0 pole. 8 free parameters: m 0, a 1, b 1, c 1, a 2, b 2, c 2,

17. The fits. 491 bins, 1.2 MeV wide from 420 to 1009 MeV Free parameters: Background: m ,  , , , a  Signal: depending on the fit (3 for KL, 7 NS, 8 SA)

18. The fits: KL (KL) f 0 (980) only:  2 /ndf 538/481 (3.7%) g 2 f0KK /  (GeV 2 )2.76  0.13 R 2.66  0.10 m f0 (MeV) 983.0  0.6 m  (MeV) 773.1  0.2   (MeV)144.0  0.3  (x10 -3 )1.65  0.05  (x10 -3 )-123  1 a  0.0  0.6 Fit uncertainties. Covariance matrix of the 3 signal parameters: 1.00.560.0 1.0-0.36 1.0

19. The fits: KL m f0 (MeV) 983.0  0.6 980 ÷ 987 g 2 fKK /4  (GeV 2 )2.76  0.13 2.0 ÷ 3.2 R= g 2 fKK /g 2 f  2.66  0.10 2.5 ÷ 2.8 Study of the systematics on the 3 f 0 (980) parameters: The fits are repeated with fixed “non-scalar” part Summarizing: g 2 fKK has large systematic uncertainty Fitm f0 (MeV) g 2 f0KK /  (GeV 2 ) R √s +0.5 MeV982.52.882.77 √s -0.5 MeV983.72.622.54 Abs.scale + 2%985.22.522.64 Abs.scale - 2%980.42.922.65  free   = 2.3±0.2 983.02.762.66 bin = 2.4 MeV983.53.122.76 start = 492 MeV983.22.852.69 start = 564 MeV983.63.162.77 end= 1002 MeV983.02.752.66  =0.47/2 983.53.062.74  =0.47*2 981.92.232.50 Full correction to low E  982.82.782.70 (1-exp(-E/b)) b=11.6982.93.152.95 (1-exp(-E/b)) b=7.6982.92.502.47 Back NS987.22.002.22

20. The fits: NS  2 /ndf 533/477 (3.6%) m f0 (MeV) 977.3  0.9 g  f  ×g f  1.46  0.05 g  0.062  0.002 g KK 0.117  0.017 a0a0 6.00  0.02 a1a1 4.10  0.04 b 1 (rad/GeV) 3.13  0.05 m  (MeV) 773.0  0.1   (MeV)145.1  0.1  (x10 -3 )1.64  0.04  (x10 -3 )-137  1 a  1.5  1.4

21. The fits: NS fit P(  2) m f0 (MeV) g  f  ×g f  g  g KK no , b 0 constrained 4.6%977.91.290.0570.102 no , b 0 free 2.6%978.11.170.0550.093 no , b 0 = b 1 2.3%978.91.120.0530.077 no , b 0 = 0 1.2%980.71.150.0510.058 no , b 0 free b 1 = 0 2.3%978.71.130.0530.081  BES b 0 constrained ~10 -7 983.20.760.034<0.01  E791 b 0 constrained ~10 -6 983.40.800.034<0.01  BES b 0 free 0.1%983.60.880.040<0.02  E791 b 0 free ~10 -5 983.40.810.035<0.01 (NS) systematics 1: dependence on the shape of the background baseline fit Polynomial background Second pole background

22. The fits: NS (NS) systematics 2: correlation between mass and couplings fitm f0 (MeV)g  S  (GeV -1 )g f  (GeV)g fKK (GeV) √s +0.5 MeV979.01.561.001.73 √s -0.5 MeV976.21.390.981.67 Abs.scale + 2%981.41.230.890.97 Abs.scale - 2%973.01.741.092.29 bin = 2.4 MeV976.51.501.001.82 start = 492 MeV978.41.460.981.60 start = 564 MeV978.51.450.981.58 end= 1002 MeV977.21.481.001.74  =0.47/2 976.91.491.001.78  =0.47*2 977.71.470.991.68 Full correction to low E  977.31.480.991.72 (1-exp(-E/b)) b=11.6972.91.481.052.07 (1-exp(-E/b)) b=7.6970.01.471.082.27 Back KL977.42.051.102.14 m f0 (MeV) 977.3  0.9 970 ÷ 981 g  S  (GeV -1 ) 1.48  0.06 1.2 ÷ 2.0 g f  (GeV) 0.99  0.02 0.9 ÷ 1.1 g fKK (GeV) 1.73  0.12 1.0 ÷ 2.3 Summarizing.... In terms of couplings

23. (1) Fit KL P(  2) m f0 (MeV) g 2 f0KK /4  (GeV 2 ) R 2001 data (115 pb-1)979.31.442.17 2002 data (234 pb -1 )982.72.552.58  s=1019.51 (145 pb -1 ) 981.42.182.54  s=1019.67 (108 pb -1 ) 977.01.752.49 Test of fit stability (on sub-samples); (2) Fit NS P(  2) m f0 (MeV) g  S  (GeV -1 )g f  (GeV)g fKK (GeV) 2001 data (115 pb-1)982.81.270.910.83 2002 data (234 pb -1 )974.71.561.032.01  s=1019.51 (145 pb -1 ) 978.31.540.991.72  s=1019.67 (108 pb -1 ) 979.81.560.981.45 In red the results outside the ranges given before for the parameters

24. The fits: SA  2 /ndf 577/477 (0.11%) a1a1 11.9 b1b1 3.3 c1c1 -15.1 a2a2 -14.7 b2b2 -15.3 c2c2 35.8 m0m0 0.  (rad) 1.63 m  (MeV) 774.4  0.2   (MeV)142.8  0.3  (x10 -3 )1.74  0.05  (x10 -3 )-100  18 a  0202  g  = 6.6 ×10 -4 GeVIn collaboration with M.R.Pennington

25. The fits: try to include the  (KL) f 0 (980) +  BES (541 MeV)  coupling ~ 0 no change (KL) f 0 (980) +  E791 (478 MeV)to f 0 parameters (KL) f 0 (980) +  free mass  found a solution with m=600 MeV (NS) f 0 (980) +  BES (541 MeV) OR  E791 (478 MeV)  bad fit

26. The fits: comment on the background Use  –  interference pattern to test mass scale and resolution m  = 782.18 ± 0.58 MeVPDG value = 782.59 ± 0.11 MeV    = 8.87 ± 0.84 MeVPDG value = 8.49 ± 0.08 MeV Two curves: fit with m  and   fixed or free Fit KLFit NSFit SA m  (MeV)773.1773.0774.4   (MeV) 144.0145.1142.8  (x10 -3 ) 1.651.641.74  (x10 -3 ) -123-137-100 Background parameters: pion form factor (Kuhn-Santamaria parameters)  determines the background level in the f 0 (980) region  the signal size: Difference up to 5% in the f 0 region.

27. Discussion of the results: the line- shape Background-subtracted spectra: KL fit NS fit SA fit Peak size: KL fit  25% of bck NS fit  24% of bck SA fit  33% of bck Peak FWHM: KL fit  37 MeV NS fit  30 MeV SA fit  45 MeV Different background parameters  different signal shapes Ratio between “non-scalar part” resulting from NS and KL fits.

28. Discussion of the results: the scalar amplitude A is the scalar amplitude: Re(A), Im(A), |A|,  (A) as functions of m: KL (solid), NS (dashed)  (A) = 3/2  @ f 0 pole =  (resonance) +  /2 (kaon-loop, background) Not enough sensitivity to the intermediate region

29. Discussion of the results: the f 0 parameters. KLNS m f0 (MeV)983 [980 ÷ 987]978 [970 ÷ 981] g f0KK (GeV)5.9 [5.0 ÷ 6.5]1.7 [1.6 ÷ 2.3] g f0  (GeV)3.6 [3.3 ÷ 3.8]1.0 [0.9 ÷ 1.1] R=( g f0KK / g f0  ) 2 2.7 [2.5 ÷ 2.8] 3.0 [2.6 ÷ 4.4] g  f0g (GeV -1 )--1.5 [1.2 ÷ 2.0] 1.5 ÷10 MeV mass difference: all within PDG 980 ±10 MeV. 2.Discrepancies due to a different interpretation of the line-shape: for KL all is f 0, for NS there is background also. 3.Agreement on R 4. g  f0g >> g  Mg with M any pseudoscalar meson (naïve statement) Summarizing...

30. Discussion of the results: extrapolation to “off-peak” data Red = data points Blue = KL predictions Black = background Red and Blue = data points Green = KL predictions Not a fit but an “absolute” prediction

31. Discussion of the results: interpretation of the charge asymmetry  KL amplitude is able to describe the observed behaviour ! Again: not a fit but an “absolute” prediction Full = data points traingles = predictions ISR+FSR Squares = predictions ISR+FSR+f 0 (KL) “Diluition” due to residual       background is included. The effect is at m<600 MeV

32. Conclusion. Goto publication soon including KL and NS results (not SA). Main results of this analysis: –Observation of   f 0 (980)        ; –Determination of f 0 (980) parameters; –Positive test of the kaon-loop model; –Model-Independent approach very difficult; –We have no sensitivity in the low mass region (we don’t see any  but this is not a good place to look for it). 2 fb -1 analysis to be done