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 Radiative Decays Scalars: f 0 , a 0  f 0   0  0   a 0 g   0  Pseudoscalars:  ,  f   g  p + p - p 0 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

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radiative decays
 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

f 0 980
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
a 0 980
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

interpretations

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
slide5
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)
slide6
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)
kloe 0 0

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
snd cmd 2 0 0
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

fit to m spectrum
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)
model

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

model11

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
kloe fit results

(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

kloe fit results13
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
snd fit results
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
snd fit results15
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

cmd 2 fit results
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

comparison between experiments
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-++
kloe 0 5

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

kloe 0 519
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

kloe fit results20
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

snd cmd 2 0
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

comparison between experiments22
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

summary of couplings
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
pseudoscalars f g g
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)]
kloe f g g

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
kloe f g g26

|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%

conclusions
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