Radiative transitions of χcJ→ ψγ and χbj→ Υγ
A bstract In the framework of instantaneous Bethe-Salpeter equation, according to the J PC of quarkonia, we find that their wave functions all contain multiple partial waves, rather than pure waves. In the radiative electromagnetic transitions χ cJ → γψ and χ bJ → γ Υ ( J = 0, 1, 2), the main wave o...
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Published in | The journal of high energy physics Vol. 2024; no. 8; pp. 191 - 27 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
22.08.2024
Springer Nature B.V SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | A
bstract
In the framework of instantaneous Bethe-Salpeter equation, according to the
J
PC
of quarkonia, we find that their wave functions all contain multiple partial waves, rather than pure waves. In the radiative electromagnetic transitions
χ
cJ
→
γψ
and
χ
bJ
→
γ
Υ (
J
= 0, 1, 2), the main wave of quarkonium gives the non-relativistic contribution, while other waves provide the relativistic corrections. Our results indicate that the relativistic effect of charmonium, especially highly excited states, is significant. Such as the relativistic effects of
χ
cJ
(2
P
) →
γψ
(1
S
) (
J
= 0, 1, 2) are {49.7%, 30.9%, 37.5%}, much larger than the corresponding {17.8%, 7.08%, 12.9%} of
χ
bJ
(2
P
) →
γ
Υ(1
S
). The decay of
χ
cJ
(2
P
) →
γψ
can be used to distinguish between
χ
c
0
(3860) and
χ
c
0
(3915), which particle is the charmonium
χ
c
0
(2
P
). Although our result of
χ
c
1
(3872)→
γψ
(2
S
) is consistent with data, but the one of
χ
c
1
(3872)→
γψ
(1
S
) is much larger than data, so whether
χ
c
1
(3872) is the conventional
χ
c
1
(2
P
) remains an open question. The undiscovered Υ(1
D
) and Υ(2
D
) have large production rates in decays of
χ
b
0
(2
P
) →
γ
Υ(1
D
) and
χ
bJ
(3
P
) →
γ
Υ(2
D
) (
J
= 0, 1), respectively. To search for χ
bJ
(3
P
) (
J
= 0, 1, 2), the most competitive channels are the decays
χ
bJ
(3
P
) →
γ
Υ(3
S
). And the best way to find
χ
b
2
(1
F
) is to search for the decay of
χ
b
2
(1
F
) →
γ
Υ(1
D
). |
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ISSN: | 1029-8479 |
DOI: | 10.1007/JHEP08(2024)191 |