Author:
Hu Dan-Dan,Fu Hai-Bing,Zhong Tao,Wu Zai-Hui,Wu Xing-Gang
Abstract
AbstractIn the paper, we investigate the moments $$\langle \xi _{2;a_1}^{\Vert ;n}\rangle $$
⟨
ξ
2
;
a
1
‖
;
n
⟩
of the axial-vector $$a_1(1260)$$
a
1
(
1260
)
-meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale $$\mu _0=1~{\mathrm{GeV}}$$
μ
0
=
1
GeV
are $$\langle \xi _{2;a_1}^{\Vert ;2}\rangle |_{\mu _0} = 0.223 \pm 0.029$$
⟨
ξ
2
;
a
1
‖
;
2
⟩
|
μ
0
=
0.223
±
0.029
, $$\langle \xi _{2;a_1}^{\Vert ;4}\rangle |_{\mu _0} = 0.098 \pm 0.008$$
⟨
ξ
2
;
a
1
‖
;
4
⟩
|
μ
0
=
0.098
±
0.008
, $$\langle \xi _{2;a_1}^{\Vert ;6}\rangle |_{\mu _0} = 0.056 \pm 0.006$$
⟨
ξ
2
;
a
1
‖
;
6
⟩
|
μ
0
=
0.056
±
0.006
, $$\langle \xi _{2;a_1}^{\Vert ;8}\rangle |_{\mu _0} = 0.039 \pm 0.004$$
⟨
ξ
2
;
a
1
‖
;
8
⟩
|
μ
0
=
0.039
±
0.004
and $$\langle \xi _{2;a_1}^{\Vert ;10}\rangle |_{\mu _0} = 0.028 \pm 0.003$$
⟨
ξ
2
;
a
1
‖
;
10
⟩
|
μ
0
=
0.028
±
0.003
, respectively. We then construct a light-cone harmonic oscillator model for $$a_1(1260)$$
a
1
(
1260
)
-meson longitudinal twist-2 distribution amplitude $$\phi _{2;a_1}^{\Vert }(x,\mu )$$
ϕ
2
;
a
1
‖
(
x
,
μ
)
, whose model parameters are fitted by using the least squares method. As an application of $$\phi _{2;a_1}^{\Vert }(x,\mu )$$
ϕ
2
;
a
1
‖
(
x
,
μ
)
, we calculate the transition form factors (TFFs) of $$D\rightarrow a_1(1260)$$
D
→
a
1
(
1260
)
in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point ($$q^2=0$$
q
2
=
0
), we obtain $$ A(0) = 0.130_{ - 0.013}^{ + 0.015}$$
A
(
0
)
=
0
.
130
-
0.013
+
0.015
, $$V_1(0) = 1.898_{-0.121}^{+0.128}$$
V
1
(
0
)
=
1
.
898
-
0.121
+
0.128
, $$V_2(0) = 0.228_{-0.021}^{ + 0.020}$$
V
2
(
0
)
=
0
.
228
-
0.021
+
0.020
, and $$V_0(0) = 0.217_{ - 0.025}^{ + 0.023}$$
V
0
(
0
)
=
0
.
217
-
0.025
+
0.023
. By applying the extrapolated TFFs to the semi-leptonic decay $$D^{0(+)} \rightarrow a_1^{-(0)}(1260)\ell ^+\nu _\ell $$
D
0
(
+
)
→
a
1
-
(
0
)
(
1260
)
ℓ
+
ν
ℓ
, we obtain $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) e^+\nu _e) = (5.261_{-0.639}^{+0.745}) \times 10^{-5}$$
B
(
D
0
→
a
1
-
(
1260
)
e
+
ν
e
)
=
(
5
.
261
-
0.639
+
0.745
)
×
10
-
5
, $${\mathcal {B}}(D^+\rightarrow a_1^0(1260) e^+\nu _e) = (6.673_{-0.811}^{+0.947}) \times 10^{-5}$$
B
(
D
+
→
a
1
0
(
1260
)
e
+
ν
e
)
=
(
6
.
673
-
0.811
+
0.947
)
×
10
-
5
, $${\mathcal {B}}(D^0\rightarrow a_1^-(1260) \mu ^+ \nu _\mu )=(4.732_{-0.590}^{+0.685}) \times 10^{-5}$$
B
(
D
0
→
a
1
-
(
1260
)
μ
+
ν
μ
)
=
(
4
.
732
-
0.590
+
0.685
)
×
10
-
5
, $${\mathcal {B}}(D^+ \rightarrow a_1^0(1260) \mu ^+ \nu _\mu )=(6.002_{-0.748}^{+0.796}) \times 10^{-5}$$
B
(
D
+
→
a
1
0
(
1260
)
μ
+
ν
μ
)
=
(
6
.
002
-
0.748
+
0.796
)
×
10
-
5
.
Funder
the Project of Guizhou Provincial Department of Education
National Natural Science Foundation of China
the Fundamental Research Funds for the Central Universities
the Project of Guizhou Provincial Department of Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
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