References - Bogoliubov Laboratory of Theoretical Physics - JINR

TOWARDS STUDY OF LIGHT SCALAR MESONS IN POLARIZATION
PHENOMENA
N.N. Achasov 1 † and G.N. Shestakov 1
(1) Laboratory of Theoretical Physics, Sobolev Institute for Mathematics, Academician Koptiug
Prospekt, 4, Novosibirsk, 630090, Russia; † E-mail: achasov@math.nsc.ru
Abstract
After a short review of the production mechanisms of the light scalars which
reveal their nature and indicate their quark structure, we suggest to study the
mixing of the isovector a 0 0 (980) with the isoscalar f0(980) in spin effects.
1 Introduction.
The scalar channels in the region up to 1 GeV became a stumbling block of QCD.
The point is that both perturbation theory and sum rules do not work in these channels
because there are not solitary resonances in this region.
As experiment suggests, in chiral limit confinement forms colourless observable hadronic
fields and spontaneous breaking of chiral symmetry with massless pseudoscalar fields.
There are two possible scenarios for QCD realization at low energy: 1. UL(3) × UR(3)
non-linear σ model, 2. UL(3) × UR(3) linear σ model. The experimental nonet of the light
scalar mesons suggests UL(3) × UR(3) linear σ model.
2 SUL(2) × SUR(2) Linear σ Model, Chiral Shielding in ππ → ππ [1]
Hunting the light σ and κ mesons had begun in the sixties. But the fact that both
ππ and πK scattering phase shifts do not pass over 900 at putative resonance masses
prevented to prove their existence in a conclusive way.
Situation changes when we showed that in the linear σ model there is a negative
background phase which hides the σ meson [1]. It has been made clear that shielding
wide lightest scalar mesons in chiral dynamics is very natural. This idea was picked up
and triggered new wave of theoretical and experimental searches for the σ and κ mesons.
Our approximation is as follows (see Fig. 1): T 0(tree)
0 = m2π −m2σ 32πf2 �
5 − 3
π
m2σ −m2π m2 σ−s − 2 m2σ −m2π s−4m2 π
�
× ln 1+ s−4m2 ��
π , T 0 0 = e2iδ0 0 −1
2iρππ = Tbg + e2iδbgTres, Tres =
m2 σ
√
sΓres(s)/ρππ
M 2 res −s+ReΠres(M 2 res
× m2 σ −m2 π
s−4m 2 π
�
ln
gres(s)= gσππ
1+ s−4m2 π
m 2 σ
0(tree)
T0 =
1−iρππT 0(tree) =
0
e(2iδbg +δres) −1
2iρππ
e2iδres−1 = , Tbg =
)−Πres(s) 2iρππ
e2iδbg −1
2iρππ =
λ(s)
1−iρππλ(s) , λ(s) = m2π−m 2 σ
32πf2 [5 − 2
π
��
, ReΠres(s)=− g2 res (s)
16π λ(s)ρ2ππ, ImΠres(s)= √ sΓres(s)= g2 res (s)ρππ
, 16π
�
1 − 4m2 �
π
3 , gσππ=
s 2gσπ + π− �
|1−iρππλ(s)| , M 2 res=m2 σ − ReΠres(M 2 res), ρππ=
�
3 m
= 2
2 π−m2 σ ; T fπ
2(tree)
0 = m2 π−m2 σ
16πf2 �
1 −
π
m2σ−m 2 π
s−4m2 ln 1+
π
s−4m2 π
m2 ��
, T
σ
2 2(tree)
T0 0 =
1−iρππT 2(tree) =
0
e2iδ2 0 −1
2iρππ .
The results in our approximation are: Mres =0.43 GeV, Γres(M 2 res
=0.93 GeV, Γrenorm res (M 2 res )=
Γres(M 2 res)
=0.53GeV, gres(M
1+dReΠres(s)/ds| s=M2 res
2 res )/gσππ=0.33, a0 0 =
)=0.67 GeV, mσ
0.18 m −1
π , a 2 0=−0.04 m −1
π , the Adler zeros (sA) 0 0=0.45 m 2 π and (sA) 2 0=2.02 m 2 π.Thechiral
shielding of the σ(600) meson in ππ → ππ is illustrated in Fig. 2 with the help of the ππ
phase shifts δres, δbg, δ0 0 (a), and with the help of the corresponding cross sections (b).
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