Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge I.} Bottomonia
V.V. Anisovich, L.G. Dakhno, M.A. Matveev, V.A. Nikonov, A.V. Sarantsev
Abstract
In the framework of the spectral integral equation, we consider the
b
b
¯
states and their radiative transitions. We reconstruct the
b
b
¯
interaction on the basis of data for the levels of the bottomonium states with
J
PC
=
0
−+
,
1
−−
,
0
++
,
1
++
,
2
++
as well as the data for the radiative transitions
Υ(3S)→γ
χ
bJ
(2P)
and
Υ(2S)→γ
χ
bJ
(1P)
with
J=0,1,2
. We calculate bottomonium levels with the radial quantum numbers
n≤6
, their wave functions and corresponding radiative transitions. The ratios
Br[
χ
bJ
(2P)→γΥ(2S)]/Br[
χ
bJ
(2P)→γΥ(1S)]
for
J=0,1,2
are found in the agreement with data. We determine the
b
b
¯
component of the photon wave function using the data for the
e
+
e
−
annihilation,
e
+
e
−
→Υ(9460)
,
Υ(10023)
,
Υ(10036)
,
Υ(10580)
,
Υ(10865)
,
Υ(11019)
, and predict partial widths of the two-photon decays $\eta_{b0}\to\ggam$, $\chi_{b0}\to\ggam$, $\chi_{b2}\to\ggam$ for the radial excitation states below
B
B
¯
threshold (
n≤3
).