1. Study of the radiative decays f  f0(980)g and f  a0(980)g
with the KLOE detector
C.Bini
Universita’ “La Sapienza” and INFN Roma
for the KLOE collaboration
Outline
Scalar Mesons at a f - factory
The KLOE experiment
Results:
3.1 p+p-g
3.2 p0p0g
3.3 hp0g
4. Summary and perspectives

2. How a f-factory can contribute to the understanding of
the scalar mesons
f(1020)
Mass (MeV/c2)
500
1000
Motivations:
Extract f to scalar “coupling”
Since f  |ss>
G(f  g”scalar”)  s-quark content
 4-quark vs. 2-quark states
Radiative decays:
f  f0(980)g
f  a0(980)g
f  f0(600)g
a0(980)
I=0
I=1/2
I=1
f0(980)
f0(600)
“s”
K*0(800)
“k”
2. Comparison a0(980) – f0(980);
3. Need to introduce f0(600) ?

3. How to detect these radiative decays - I
 f0(980)g  p+p-g (charged mode)
 p0p0g (neutral mode)
 K+K-g [ 2m(K)~m(f0)~m(f) ]  BR [Achasov, Gubin] ~ 10-6
 K0K0g “ “ ~ 10-8
(charged mode): f0(980) signal vs. huge unreducible background:
Initial state radiation (ISR), Final state radiation (FSR), f r±p± with r ±  p±g
(neutral mode): same as above BUT different backgrounds
e+e-  wp0 with w  p0g, f r0p0 with r 0  p0g
General Comments:
 fit of mass spectra are needed;
 the background is not fully known (parameters from data);
 interference between signal and background;

4. How to detect these radiative decays - II
 a0(980)g  hp0g
 K+K-g BR [Achasov, Gubin] ~ 10-6
 K0K0g “ ~ 10-8
2 decay modes considered:
h  gg [39.4%]  5 photons
h  p+p-p0 [22.6%]  2 tracks and 5 photons
Combined analysis
General comments:
 the unreducible background is lower;
 the combined analysis allows systematics checks.
 f0(600)g  p+p-g (charged mode)
 p0p0g (neutral mode)
Search for “structures” in the m(p+p-) and m(p0p0) spectra.

5. How to detect these radiative decays - III
How do we extract the signal ?
Electric Dipole Transitions (E1):
 G(E1)  Eg3 × |Mif(Eg)|2
2. Distortions due to KK thresholds;
3. Mif(Eg) requires a model.
Kaon-loop model (by N.N.Achasov):
For each scalar meson S: gSpp, gSKK, MS
(2) No-Structure model (in collaboration with G.Isidori and L.Maiani):
A modified BW + a polynomial continuum;
Parameters: gfSg, gSpp, gSKK, MS + polynomial continuum
f0,a0 f
Kaon-loop
No-structure K+ K- p+ p- g

6. The KLOE experiment (see S.Miscetti talk in plenary session)
The KLOE detector:
Drift Chamber
E.M. Calorimeter
Magnetic field
= 0.52 T (solenoid)
Data taking period
Integrated Luminosity (pb-1)
2000 20
p0p0g : PLB537 (2002) 21
hp0g : PLB536 (2002) 209
450
Results presented here on p0p0g, hp0g, p+p-g
(up to date)
1500 ( 2000 end y2005)
“final results” next years
N(scalars) = N(f) × BR(fg+scalars)  8 ×109 × 10-4 = 8 ×105

7. The p+p-g analysis - I I - event selection:
2 tracks with qt>45o; missing momentum qpp>45o (Large Angle);
Each track is pion-like;
“trackmass” compatible with pion;
1 photon matching the missing momentum
(“trackmass”)
muons
pions
(Likelihood: Tof and Shower shape)
electrons
pions, muons
W(rad)
(Photon matching)
p+p-g
p+p-p0
Reducible Background rejection:

8. The p+p-g analysis - II II – The data sample
6.7 ×105 events / 350 √s = Mf
2.2 ×104 events / pb-1 “off-peak”
m(pp) spectra:
(blue) “Small angle” qpp<15o;
(red) “Large angle” qpp>45o;
This analysis
m(pp) (MeV)
photon
efficiency
f0(980) region
m(pp) (MeV)
“Large angle”:
clear f0(980) signal

9. The p+p-g analysis - III
(Kaon-loop fit)
f0(980) only
[p(c2)=5%];
III - Fit to the m(pp) spectrum
(491 bins, 1.2 MeV wide, 420 to 1009 MeV)
F=ISR (Kuhn-Santamaria, mr, Gr, a , b)
+FSR+rp
+scalar (Kaon-Loop, mf0 ,g2fKK /4p ,R)
+interference
Comments:
1. Adding f0(600)  no improvement;
2. f0(980) is narrow (FWHM = 30 MeV)
BUT large destructive interference
with FSR
3. f0(980) parameters:
mf (MeV)
980 ÷ 987
g2fKK /4p (GeV2)
2.0 ÷ 3.2
R= g2fKK /g2fp+p-
2.5 ÷ 2.8
R>1 [as in PLB537(2002) 21]

10. The p+p-g analysis - IV IV – Alternative fit: No Structure.
scalar = NS amplitude.
f0(980) + polynomial (2nd order):
f0(980)+p2
[p(c2)=4%];
Comments:
Adding f0(600) no improvement;
Parametrization is still under
development;
3. Parameters (preliminary values)
mf (MeV)
970 ÷ 981
gff0g (GeV-1)
1.2 ÷ 2.0
R= g2fKK /g2fp+p-
2.6 ÷ 4.4
R > 1 in both fits;
A value for gffg.

11. The p+p-g analysis - V V - The charge asymmetry:
A = (N(q+>90o) – N(q+<90o)) / sum
p+p- system: A(ISR) C-odd
A(FSR) & A(scalar) C-even
Cross-section: |A(tot)|2 = |A(ISR)|2 + |A(FSR)|2 + |A(scalar)|2
+ 2Re[A(ISR) A(FSR)] + 2Re[A(ISR) A(scalar)]
+ 2Re[A(FSR) A(scalar)]
(Red) = p+
(Blue) = p-
Pion polar angle distributions
Pion momentum distributions

12. The p+p-g analysis - VI
VI – Effect of the scalar amplitude on the charge asymmetry:
Plot of A in slices of m(pp);
Comparison with simulation with and without the scalar amplitude.
Circles = data points
Triangles = predictions
ISR+FSR
Squares = predictions
+f0(Kaon-Loop
fit parameters)
Qualitative description of:
f0(980) region behaviour;
Low mass behaviour.
Remarkable result: not a fit
but an absolute prediction

13. The p+p-g analysis - VII
VII – Cross section dependence on √s:
Absolute prediction based on Kaon-Loop fit parameters
Red and Blue = data points
Green = KL predictions
In 2006 we will increase our “off-peak” statistics to study better
the scalar contribution in the p+p-g data.

14. The p0p0g analysis - I I - event selection:
5 photons with qg>21o ; no tracks;
Kinematic fit  energy-momentum conservation;
Kinematic fit  p0 masses: choice of the pairing.
KLOE PLB537 (2002) 21
New analysis scheme:
Removed the cut of events
with m(p0g) ~ m(w)
wp0 with w  p0g in the sample
[ s ~ 0.5 nb ~ 2 s(“signal”) ]
2.Bi-dimensional analysis
[ Dalitz-plot m(p0p0) – m(p0g) ]
New treatment of systematics
[ pairing problem...]
Improved VDM parametrization
of wp0

15. The p0p0g analysis - II Dalitz plot components II – The data sample:
1. e+e-  wp0 with w  p0g
(√s dependence checked
agreement with SND results)
√s (MeV)
II – The data sample:
400 kevents out of 450 pb-1.
Dalitz plot [M(pp) vs. M(pg)]
2. “signal”:f  “scalar”+g  p0p0g
√s (MeV)

16. The p0p0g analysis - III
III – The fit of the Dalitz plot (still preliminary results)
Residuals vs. DP
position
Data- fit comparison (on projections)
Kaon-loop fit: 1. VDM part still not perfect (see residuals);
2. Scalar part ok BUT f0(600) is still needed
[p(c2) ~ 10-4  30% !];
3. f0(980) parameters agree with p+p-g analysis
again R > 1 (gfKK > gfp+p-).

17. The hp0g analysis - I I – The data samples: out of 400 pb-1 :
Statistics of PLB536 (2002) 209 × 20
(h  gg) Improved reducible
background subtraction:
2.2 ×104 events
[ ½ are signal]
Red = signal
Other colors= bck
M(hp) (MeV)
(h  p+p-p0) almost “background
Free”  4100 events [ bck < 3%]
Full points = “20 pb-1” data
Empty points = “400 pb-1” data
(norm. to the same luminosity)

18. The hp0g analysis - II
II – The combined fit: scalar amplitude with kaon-loop.
Red points = data
Blue hist = fit
M(hp) (MeV)
M(hp) (MeV)
Results (preliminary statistical errors only):
a good combined fit is obtained
[BR(gg)/BR(p+p-p0) fixed to PDG value]
the spectrum is entirely due to the scalar amplitude;
M(a0) = ± 0.4 MeV
g2aKK/4p = ± GeV2
R = g2aKK/g2hp = ± 0.006

19. Summarizing: The KLOE scalar analysis is not yet completed. However:
(1) The Kaon-Loop frame describes our entire data-set.
Emerging picture:
f0(980) strongly coupled to kaons
g2fKK ~ 2 ÷ 3 GeV2;
R = g2fKK/g2fp+p- ~ 2 ÷ 4.
a0(980) is less strongly coupled to kaons
g2aKK ~ 0.4 GeV2
R = g2aKK/g2ahp ~ 0.8
f0(600) required in the p0p0 channel
(2) No Structure analysis is promising:
still theoretical effort required BUT
first results “confirm” the kaon-loop picture:
f0 and a0 have large |ss> contents.

20. KLOE perspectives on scalar mesons
Conclude analysis on data sample (~ 400 pb-1)
for f0(980) (neutral and charge final states) and a0(980)
(KL and NS fits).
 With 2000 pb-1: improvement expected for f0 → p+p-
Better precision on the couplings and on the asymmetry.
Combined fit p+p- AND p0p0 ?
 Study of the √s-dependence of the cross-section.
 Search for f0, a0  KK ?

21. Spare Slides
Hadron 2005

23. Slightly lower BR obtained (preliminary):
(hgg) BR(fhp0g)=(7.49±0.10)×10-5
[it was: (8.5  0.5stat  0.6syst)x10-5]
(hp+p-p0) BR(fhp0g)=(7.45±0.19)×10-5
[it was: (8.0  0.6stat  0.5syst)x10-5]

24. Theory: KL (KL) by N.N.Achasov; where: g(m) = kaon-loop function
d(m) = phase shift (based on pp scattering data)
Df(m) = f0 propagator (finite width corrections)
If only one meson (no s included):
3 free parameters: mf, gfKK, gfpp

25. Theory: NS (NS) after several discussions with G.Isidori, L.Maiani and
(recently) S.Pacetti;
where the propagator (Flatte’ revised) is:
Nota che 3 dei 7 sono anche in KL quindi questo e’ piu’ generale e molto piu’ libero.
with couplings
7 free parameters: mf, gffg, gfKK, gfpp,a0, a1, b1