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  1.  Radiative Decays • Scalars: f0, a0 •  f000 •  a0g0 • Pseudoscalars:  ,  • f   g p+ p- p0 g p+ p- 3 g • f   g p+ p-  g p+ p- 3 g A. Antonelli (Laboratori Nazionali di Frascati dell’INFN) XXII Physics in Collision June 20-22 2002 Stanford

  2. f0(980) Narrow meson with vacuum quantum numbers • First seen in p-p np+p- • I=0 S-wave pp ppelastic scattering • cross section shows a dip close to KK threshold. • Similarly from p-p nK+K-,K0K0 the sharp onset of inelasticity shows a large coupling to KK • J/Y decays (MarkIII, DM2, Bes) BR(J/Y Ff0) =(3.2  0.9)10-4 BR(J/Y wf0) =(1.4  0.5)10-4 Evidence for strange quarks content in the f0 • Clear peak in D sp+p-p (FNAL-E791) not seen in Dp+p-p • Produced in central pp collisions (WA102 (CERN) • G (f0gg) ~ 0.3 KeV measured from gg interaction • G ~ 60 MeV

  3. a0(980) • First seen in Kp hpS • Precise data from Crystal Barrel and OBELIX: pp00, 0,KKp • Recent data from E853:-p+-n and -p0n • And from WA102: a0 production in central pp collisions • G (a0gg) ~ 0.25 KeV measured by Crystal Ball/Jade • G ~ 70 MeV 2 scalar mesons close in mass with small visible width and small gg coupling

  4. Br(f0) 5  10-5 10-4 10-5 Br(a0) 10-5 10-4 10-5 Interpretations • S = f0(980) (I=0) , a0(980) (I=1) not easily interpreted as qq states: • M , Gtotal , Ggg too small • Their KK coupling suggest a large ss content • f0 ss interpretation: difficult to understand f0/a0 mass degeneration • (quark-gluon transition do not help: f0 weakly coupled to gluon • BR(J/Y gf0) <1.4x10-5 • Possible interpretations: qqqq states (Jaffe ’77) KK molecules (Weinstein, Isgur ’90) • Br(f0(980)) and Br(a0(980)) and mass spectra are sensitive to the nature of these scalar particles • Gribov suggested the existence of peculiar mesons with vacuum quantum numbers near the proton mass to explain quark confinement

  5. S(0++) • Pub. data from: KLOE@DAFNE, SND CMD-2 @ VEPP-2M • 5.3x107 2x107 2x107 F decays • Results on • f0 ; f000  5  final state • (f0+-  large background from Initial State • Radiation and Final State Radiation (interference)) • a0 ; a00  (39%)  5  final state • “ “ +-0 (23%)  2 tracks +5  • (KLOE: first observation)

  6. 00 • Signal cross section (nb) • different amplitudes contribute to00 final state • (f0+00)00 ~0.35 • (+ possible contribution from  ,00) • (s meson seen by: Fermilab E791,BES) • Background: • e+e-0 00 dominant ~ 0.5 • 0 ~ 0.13 (2 accidentals/g splittings) (17.0) •  000 (2 g lost) (14.0)

  7. 1+cos2   0 0 KLOE: 00 • exactly 5 prompt g with Eg> 700 MeV (reject KLKS neutrals) • Cut on|M - M| < 5(M) • Veto on events with: • |M - M| < 3(M) • Constrained Kinematic fit •  3102 events • <> = 40% • Estimated background (~ 20%): • e+e-0 00 33924 • 0 16616 •  000 15912

  8. SND&CMD-2: 00 SND: 712 evts after cut <> ~ 20% 419  31 signal events CMD-2: 268  27 signal events SND CMD-2 CMD-2 Mpp>800 MeV 0 + 0 cos

  9. Fit to M spectrum • Contributions: • 1) f0 ; f000 • 2)  ; 00 • 3) 00 ; 00 • (expected Br=1.2  10-5 Bramon-Grau-Pancheri, • Phys.Lett.B283(1992),416 • = 1.8  10-5 Achasov-Gubin, (fit to SND data) • Phys.Rev.D63(2001)094007)

  10. gKK gf0KK gf0 0 K+ f0 K- 0 Model • Scalar term: (S=f0,) radiative g • f0 term from kaon loop : • (Achasov-Ivanchenko, • Nucl.Phys.B315(1989)465) f g(m) satisfy gauge invariance ~ Eg at low g energy, act as f.f. at higher Eg

  11. radiative g f  0 g 0 Model •  term point-like coupling • (Gokalp,Yilmaz,Phys.Rev.D64(2001)053017) • Decay width: • Inverse propagators: Df0 with finite width corrections, • from Achasov-Ivanchenko, Nucl.Phys.B315(1989)465 • D = Breit-Wigner with M=478 MeV and =324 MeV • (Fermilab E791-Phys.Rev.Lett.86(2001)770) •  + interference term parameterizations from Achasov-Gubin, • Phys.Rev.D63(2001)094007

  12. (bckg subtracted) KLOE:Fit results Fit A : only f0 + 00 + interf. term Fit B : (f0 + ) + 00 + interf. term  contribution negligible  fixed to 0 M=478 MeV and =324 MeVfixed theoretical function folded with: resolution, efficiency and normalized by L and sF f0 +  f0 A B 2/ndf 109.5/33 43.2/32 Mf0 (MeV) 9624 973 1 g2f0KK/(4) 1.290.14 2.79 0.12 (GeV2) g2f0KK/g2f0 3.220.29 4.000.14 g — 0.060 0.008 Br(00) (1.09  0.03  0.05)  10-4 From fit B

  13. KLOE:Fit results • Large f0- destructive • interference at M < 700 MeV • By integrating over the f0 and  • curves: • Br(f000) = (1.49  0.07)  10-4 • Br(00) = (0.28 0.04)  10-4

  14. SND: Fit results 2x107 F decays • 2 Fit: f0 + 00 • f0 • Fit including the s • (fixing ms=600 MeV and Gs=400 MeV) • neglegible sg contibution • f0 by kaon loop model • f0 ,00interf. termapprox. • formula • Br (00 ; 00 )=1.2  10-5 f0 + 00 2/ndf 3/14 Mf0 (MeV) 969.84.5 g2f0KK/(4)(GeV2) 2.470.73 g2f0KK/g2f0 4.60.8 (degrees)18036 • Neglecting00 contribution 2 is good but the fit shows a systematic deviation from mass spectrum • Fitting with point-like model 2/ndf = 28/14

  15. SND: Fit results Point-like model does not fit data kaon loops model reproduces well the mass spectra data well fitted by f0 + 0 s contribution not necessary even if not completely excluded • Gokalp-Yilmaz(Phys.Rev.D64(2001)053017) reproduce the SND spectrum with f0 +  + , with M=478 MeV , =324 MeV and a large f0 ,destructive interference Br(00) (1.220.10 0.06)  10-4 SND has not much sensitivity in the s region

  16. CMD-2: Fit results 2x107 F decays • Fit: assuming mass spectrum dominated byf0 • f0 by kaon loop model • possible sg and00contribution estimated to be ~15% and included in systematic error .... kaon loop --- narrow pole f0 2/ndf 1.5 Mf0 (MeV) 9754 6 g2f0KK/(4)(GeV2) 1.480.32 g2f0KK/g2f0 3.610.62 Br(00) (1.080.170.09)  10-4 Integral over the spectrum

  17. Comparison between experiments F decays other KLOE SND(1) CMD-2(1) WA102(2) E791(3) Mf0 (MeV)9731 9695 9757 9878 9774 g2f0KK/(4) 2.790.12 2.470.73 1.480.32 0.400.06 0.020.05 (GeV2) g2f0KK/g2f04.000.14 4.60.8 3.610.62 1.630.46 g0.060 0.008 Br(00)104 0.960.05 1.030.09 0.920.09 Mpp>700 MeV • f0 and  only , without  • WA102 (CERN) : f0 production in central pp collisions(g2f0KK directly measured) • E791 (Fermilab) : f0 production in D+S-++

  18. Data • — MC Events Events M (MeV) KLOE: 05 • Data • — 00 • —000  • —000 • — • same5 gsample as for00 • 00rejected by proper g pairing • Constrained kinematic fit •  916 events • <> = 33%  60736 events after bckg subtraction • estimated background (30%): • 00 15216 • e+e-0 00 546 •  000 9810 •   52 1+cos2 cos

  19. KLOE:0 +-5 M (MeV/c2) |cos| • No backgrounds from same final state: 2 Tracks + 3/4 g, 2 Tracks + 6 g (0, , KSKL) • Minv(p+p-) < 425 MeV to reject KSp+p- • 1 vertex in IR with 2 tracks, 5 prompt  • constrainedkinematic fit •  197 selected events • <>=19% • 44 background events fit 1 1+cos2 fit 2 fit 2 Clear po and h peaks MC signal reproduces data

  20. KLOE: Fit results • Contributions: • a0 ; a00 (kaon loops) • 00 ; 0 • (expected Br = 0.54  10-5 (Bramon, Grau, Pancheri,Phys.Lett.B283(1992),416) • Combined fit, relative normalization fixed to • Br()/Br(+-0) Free parameters: g2a0KK, ga0/ga0KK, Br(000) Ma0 = 984.8 MeV (PDG value) - fixed 2/ndf 27.2/25 g2a0KK/(4) (GeV2) 0.40  0.04 ga0/ga0KK1.35  0.09 Br(000) (0.5  0.5)  10-5 By integrating over the whole spectrum: Br(a00)= (7.4  0.7)  10-5

  21. SND&CMD-2: 0 • 2x107 F decays • 39 evts after cut • <> ~ 2.3% • 35 6 signal events • Fit: assuming mass spectrum dominated bya0 • Ma0 (MeV) 995 +52-10 • g2a0KK/(4) (GeV2) 1.4+9.4-0.9 • ga0/ga0KK 0.750.52 • 2x107 F decays • 80 22 signal events • <> ~ 4% • No fit to mass spectrum SND Br(h0) (0.88  0.14  0.09)  10-4 CMD-2 Br(h0) (0.9  0.24  0.10)  10-4

  22. Comparison between experiments other F decays KLOE SND CMD-2 E852(1) Crystal (2) Barrel Ma0 (MeV)984.8 (fixed) 995+52-10 -- 9913 1000 2 g2a0KK/(4) 0.400.04 1.4+9.4-0.9 -- (GeV2) ga0/ga0KK 1.350.09 0.750.52 -- 1.050.06 0.93—1.07 Br(h0)1057.4  0.7 8.8 1.7 9.0 2.6 ---- ---- (1) E852 (BNL) : a0 production in -p+-nand -p0n at 18.3 GeV/c (2) pp00

  23. Summary of couplings • Comparison with predictions based on the kaon loop model with point-like coupling • of the scalars to kaons (Achasov-Ivanchenko) KLOE f0model qqqq g2f0KK/(4) 2.790.12 “super-allowed” “OZI-allowed” “OZI-forbidden” (GeV2) (~2 GeV2) (~0.3 GeV2) gf0 /gf0KK 0.500.01 0.3—0.5 0.5 2 a0model qqqq g2a0KK/(4) 0.400.04 “super-allowed” “OZI-forbidden” (GeV2) (~2 GeV2) ga0/ga0KK 1.350.09 0.91 1.53 • f0 parameters are compatible with qqqq model • a0 parameters seem not compatible with qqqq model

  24. Pseudoscalars:f   g ,  g • Br(  ’) can probe the gluonic content of the ’: • theoretical predictions range from 2x10-4 down to ~10-6 in case of significant gluonic content. • [N.Deshapande and G. Eilam., Phys. Rev. D25 (1980) 270, J. L. Rosner, Phys. Rev. D27 (1983) 1101, • F.E.Close, The DAFNE Physics Handbook Vol. II, Frascati 1992] • The mass eigenstates , ’ can be related to the SU(3) octet-singlet • states 8, 0 through the mixing angle p, whose value has • been discussed many times in thelast 30 years: both from theoretical • predictions and from phenomenologicalanalyses it varies from -23° to -10°. • [A. Bramon et al., Eur. J. C7 (1999) , A. Bramon et al., Phys. Lett. B503 (2001 ) 571 ] • [ F.J. Gilman, R. Kauffman, Phys. Rev. D 36 (1987) 2761] • Recent developments in ChPTand phenomenologicalanalyses suggest the need to • use two mixing parameters 8and0in the octet-singlet basis. • [H. Leutwyler, Nucl. Phys. Proc. Suppl. 64 (1998) 223, R. Kaiser and H. Leutwyler, hep-ph/9806336, • P. Ball, J. M. Frere and M. Tytgat, Phys. Lett. B365 (1996) 367] • In the flavour basis the mixing can be descibed by one angleFP(Fq  Fs  Fp) and can be extracted from the ratio of the amplitudes of   ’ and    • [T. Feldmann,P. Kroll and B. Stech, Phys.Lett.B449 (1999) 339, T. Feldmann Int. J. Mod. Phys. A15(2000)]

  25. h invariant mass (MeV) KLOE:f   g ,  g f   g p+ p- p0 g p+ p- 3 g BR 3 ·10 - 3 f   g p+ p-  g p+ p- 3 gBR 2 ·10 - 5 The main background comes from:f  KS KL , f  p + p- p0 R = BR(f hg) / BR(f hg) R=( Nh eh / Nheh )•RBR=(4.7 ± 0.5± 0.3)•10-3 Using PDG’00 for BR(f hg) : BR(f hg) =(6.1 ± 0.6 ± 0.4)•10-5 •  128  events • <> = 23% • 120 ±12 after bck subtraction

  26. |h> = Xh|uu+dd>/2 + Yh|ss> + Zh|glue> |h> = Xh|uu+dd>/2 + Yh|ss> + Zh|glue> 3 G(h rg)mh2-mr2mw G(w  p0g)mw2-mp2mh _ ~ 3 X2h · · 4) 3 2 G(h gg)1mh G(p0 gg)9mp0 5) · = 5 Xh + 2Yh fp f8 Z2h= 0.06 + 0.09 - 0.06 |Yh|= cos P KLOE:f   g ,  g Using the Bramon or the Feldman parametrization we can relateR to the mixing angle in the flavour basis: FP= (42.2 ±1.7 )° gluonium content <15%

  27. Conclusions • The data from the f radiative decays are fundamental in clarifying • the nature of scalar mesons. • The branching ratios00,0 and the f0,a0coupling • constants have been measured with a better accuracy by KLOE • and are in agreement with VEPP-2M results. • Best measurement of BR(f   g) and / mixing angle • There is still work to do in this field and more data are expected • from KLOE and from other experiment (D decays etc) • KLOE analysis on 2001 data (190 pb-1) is in progress, • (results on f0+- are also expected), other 300 pb-1 expected • by the end of 2002