References - Bogoliubov Laboratory of Theoretical Physics - JINR

2. We remind, that the celebrated Gell-Mann–Okubo (GMO) [2] formula, written for the
vector meson octet
3m 2 (8; I = Y =0)=4m 2 (8; I =(1/2),Y = ±1) − m 2 (8; I =1,Y =0)
follows as the mass sum rule after exclusion of parameters M 2 and μ 2 introduced into the
general mass term of the phenomenological meson Lagrangian
M 2 · Tr(V8V8) − μ 2 · Tr(V8V8λ8).
Okubo [3] proposed replacing V8 → V9 in the GMO mass operator and dropping the term
proportional to Tr(V9). The well-known ”ideal mixing ” mass relations
,
m 2 (8; I =1,Y =0)=m 2 (8 ∪ 1|mix; I = Y =0)
2m 2 (8; I =(1/2),Y = ±1) − m 2 (8; I =1,Y =0)=m 2 (8 ∪ 1| mix ′ ; I = Y =0)
are fulfilled for the vector and reasonably well for the tensor nonet, but poorly for the
pseudoscalar one. We indicate also the hierarchy of meson masses following from the
effective Lagrangian GMO
m 2 (S) >m 2 (q¯s) >m 2 (N).
The idea to relate the apparently specific situation for the pseudoscalar meson sector with
an additional strong annihilation mechanism transforming the quark field combinations
into each other was put forward phenomenologically by Isgur [1] and interpreted now as
mediated by short-range fluctuations in the quark-gluon vacuum [4]. We follow this idea in
a further generalized form via introducing the ”bare” scalar glueball mass and nondiagonal
glueball-quarkonium transition-mass into the spin-zero meson mass-matrices. Hence, in
the N = 1
√ 2 (uū + d ¯ d),S = s¯s basis our symmetric mass-matrix acquires the following
form:
⎛
ˆM 2 = ⎝
√ 2AG
√ 2rAQ
M 2 N + AQ √
2AG M 2 G rAG
√
2rAQ rAG M 2 S + r2AQ ⎞
⎠ (3)
The mass-matrix (3) with additional factors r introduced in different models of the SU(3)symmetry
violations can be taken as the ingredient of the generalized Schwinger-type [5]
mass formulas for the hadron multiplets. After reducing it to the diagonal form we should
get the matrix of the eigenvalues ˆ M 2 ph:
ˆ
M 2 ph =
⎛
M
⎝
2 (1) 0 0
f0
0 M 2 (2) 0
f0
0 0 M 2 f0 (3)
⎞
⎠
and the matrix ˆ V (i) of the eigenvectors in a chosen basis.
3. We start treating the mass relations with the higher-mass scalar 0 ++ -sector:
Ma0 =1474±19, MK ∗ 0 =1425±50, Mf0(1)=1370±50,Mf0(2)=1505!pm6, Mf0(3)=1724±7
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