References - Bogoliubov Laboratory of Theoretical Physics - JINR

104xdBR(φ--> π η 0
-1
γ )/dm, GeV
6
5
4
3
2
1
0
0.7 0.75 0.8 0.85 0.9 0.95 1
m, GeV
10 8 x dBr (φ-->π 0 π 0 γ )/dm, MeV -1
70
60
50
40
30
20
10
0
300 400 500 600 700 800 900 1000
m, MeV
Figure 4: The left (right) plot shows the fit to the KLOE data
for the π 0 η (π 0 π 0 ) mass spectrum in the φ → γπ 0 η (φ → γπ 0 π 0 )
decay caused by the a0(980) (σ(600)+f0(980)) production through
the K + K − loop mechanism.
7 Scalar Nature and Production
Mechanisms in γγ collisions [4]
Twenty seven years ago we predicted the suppression
of a0(980) → γγ and f0(980) → γγ in the q 2 ¯q 2
MIT model, Γa0→γγ ∼ Γf0→γγ ∼ 0.27 keV. Experiment
supported this prediction.
Recently the experimental investigations have
made great qualitative advance. The Belle Collaboration
published data on γγ → π + π − , γγ → π 0 π 0 ,
and γγ → π 0 η, whose statistics are huge [5], see
Fig. 5. They not only proved the theoretical expectations
based on the four-quark nature of the light
scalar mesons, but also have allowed to elucidate the
principal mechanisms of these processes. Specifically,
Σ�ΓΓ�Π � Π � Σ�ΓΓ�Π ;�cosΘ��0.6� �nb�
� � ;�cos��0.6� �nb�
Σ�ΓΓ�Π 0 Π 0 Σ�ΓΓ�Π ;�cosΘ��0.8� �nb�
0 Р0 ;�cos��0.8� �nb�
Σ�ΓΓ�Π 0 Σ�ΓΓ�Π Η;�cosΘ��0.8� �nb�
0 Η;�cosΘ��0.8� �nb�
350
Data: � Belle,� MarkII,� CELLO
300
�������� Σ�Σ0�Σ2 �������� Σ0 Born
250
������ Σ2 ����� Σ
200
� 350
300
250
Born
2
200
150
100
50
Σ
Σ 0
�a�
0
0.2 0.4 0.6 0.8 1 1.2 1.4
����� �����
s �GeV �GeV ��
175
150
125
100
75
50
25
50
40
30
20
10
Data: � Belle, CrystalBall
��������� ΣS �Σ
�
f2
��� Σ S
�� Σ � f 2
�b�
0
0.2 0.4 0.6 0.8 1 1.2 1.4
����� �����
s �GeV �GeV ��
� Belledata, Systematicerror�c�
0
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
����� �����
s �GeV �GeV ��
Figure 5: Descriptions of the Belle
data on γγ → π + π − (a), γγ → π 0 π 0 (b),
and γγ → π 0 η (c).
the direct coupling constants of the σ(600), f0(980), and a0(980) resonances with the
system are small with the result that their decays into γγ are the four-quark transitions
caused by the rescatterings σ(600) → π + π − → γγ, f0(980) → K + K − → γγ and
a0(980) → K + K − → γγ in contrast to the γγ decays of the classic P wave tensor q¯q
mesons a2(1320), f2(1270) and f ′ 2(1525), which are caused by the direct two-quark tran-
sitions q¯q → γγ in the main. As a result the practically model-independent prediction
= 25 : 9 agrees with experiment rather well. The two-
of the q¯q model g2 f2γγ : g2 a2γγ
photon light scalar widths averaged over resonance mass distributions 〈Γf0→γγ〉ππ ≈ 0.19
keV, 〈Γa0→γγ〉πη ≈ 0.3 keV and 〈Γσ→γγ〉ππ ≈ 0.45 keV. As to the ideal q¯q model prediction
g2 f0γγ : g2 a0γγ = 25 : 9, it is excluded by experiment.
8 SummaryoftheAbove [1,3,4]
(i) The mass spectrum of the light scalars, σ(600), κ(800), f0(980), a0(980), gives an
idea of their q2 ¯q 2 structure. (ii) Both intensity and mechanism of the a0(980)/f0(980)
production in the φ(1020) radiative decays, the q2 ¯q 2 transitions φ → K + K− → γ[a0(980)
/f0(980)], indicate their q2 ¯q 2 nature. (iii) Both intensity and mechanism of the scalar
meson decays into γγ, theq2¯q 2 transitions σ(600) → π + π− → γγ and [f0(980)/a0(980)] →
K + K− → γγ, indicate their q2 ¯q 2 nature also.
9 The a 0
0 (980) − f0(980) Mixing in Polarization Phenomena [6]
The a 0 0 (980) − f0(980) mixing as a threshold phenomenon was discovered theoretically
in 1979 in our work [6]. Now it is timely to study this phenomenon experimentally. 1
1 In Ref. [7] the search program of the a 0 0 (980) − f0(980) mixing at the C/τ factory has been proposed.
Recently the VES Collaboration published the data on the first effect of the a 0 0(980) − f0(980) mixing,
f1(1420) → π 0 a 0 0 (980) → π0 f0(980) → 3π [8], in agreement with our calculation 1981 [6].
31