Study of the decay f 0 (980) + - C.Bini, S.Ventura, KLOE Memo /2004 (upd. 06/2005) C.Bini, KLOE Memo /2005 (upd. 06/2005)
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.
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.
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
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
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
The data sample: A c Charge asymmetry A c in bins of m “on-peak” data “off-peak” data
The data sample: √s dependence ( MeV) = N(events 900<m<1000 MeV) / L int (m)) Blue = “on-peak” sliced data Red = “off-peak” data
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
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
Zoom (signal region) At the end of the selectionBefore the photon request data Surviving Red = data (40 pb -1 sample) Blue = MC( ) + data/
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
Theory: KL,NS,SA,.... e+e+ e-e- f0f0 ++ -- {M} has to rely on “some” model with “some” parameters
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
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
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,
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)
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) 0.6 m (MeV) 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:
The fits: KL m f0 (MeV) ÷ 987 g 2 fKK /4 (GeV 2 )2.76 ÷ 3.2 R= g 2 fKK /g 2 f 2.66 ÷ 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 MeV √s -0.5 MeV Abs.scale + 2% Abs.scale - 2% free = 2.3± bin = 2.4 MeV start = 492 MeV start = 564 MeV end= 1002 MeV =0.47/ =0.47* Full correction to low E (1-exp(-E/b)) b= (1-exp(-E/b)) b= Back NS
The fits: NS 2 /ndf 533/477 (3.6%) m f0 (MeV) 0.9 g f ×g f 1.46 0.05 g g KK a0a 0.02 a1a 0.04 b 1 (rad/GeV) 3.13 0.05 m (MeV) 0.1 (MeV)145.1 0.1 (x10 -3 )1.64 0.04 (x10 -3 )-137 1 a 1.5 1.4
The fits: NS fit P( 2) m f0 (MeV) g f ×g f g g KK no , b 0 constrained 4.6% no , b 0 free 2.6% no , b 0 = b 1 2.3% no , b 0 = 0 1.2% no , b 0 free b 1 = 0 2.3% BES b 0 constrained ~ <0.01 E791 b 0 constrained ~ <0.01 BES b 0 free 0.1% <0.02 E791 b 0 free ~ <0.01 (NS) systematics 1: dependence on the shape of the background baseline fit Polynomial background Second pole background
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 MeV √s -0.5 MeV Abs.scale + 2% Abs.scale - 2% bin = 2.4 MeV start = 492 MeV start = 564 MeV end= 1002 MeV =0.47/ =0.47* Full correction to low E (1-exp(-E/b)) b= (1-exp(-E/b)) b= Back KL m f0 (MeV) ÷ 981 g S (GeV -1 ) 1.48 ÷ 2.0 g f (GeV) 0.99 ÷ 1.1 g fKK (GeV) 1.73 ÷ 2.3 Summarizing.... In terms of couplings
(1) Fit KL P( 2) m f0 (MeV) g 2 f0KK /4 (GeV 2 ) R 2001 data (115 pb-1) data (234 pb -1 ) s= (145 pb -1 ) s= (108 pb -1 ) 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) data (234 pb -1 ) s= (145 pb -1 ) s= (108 pb -1 ) In red the results outside the ranges given before for the parameters
The fits: SA 2 /ndf 577/477 (0.11%) a1a b1b1 3.3 c1c a2a b2b c2c m0m0 0. (rad) 1.63 m (MeV) 0.2 (MeV)142.8 0.3 (x10 -3 )1.74 0.05 (x10 -3 )-100 18 a 0202 g = 6.6 ×10 -4 GeVIn collaboration with M.R.Pennington
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
The fits: comment on the background Use – interference pattern to test mass scale and resolution m = ± 0.58 MeVPDG value = ± 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) (MeV) (x10 -3 ) (x10 -3 ) 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.
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.
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
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 ) [2.5 ÷ 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...
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
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
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