Extraction of np andN scattering lengths from anddierential photoproduction cross sections on the deuterium target Chengdong Han1 2Wei Kou1 2yRong Wang1 2zand Xurong Chen1 2 3x

2025-05-06 0 0 442.38KB 7 页 10玖币
侵权投诉
Extraction of ωn, ωp and φN scattering lengths from ωand φdifferential
photoproduction cross sections on the deuterium target
Chengdong Han,1, 2, ∗Wei Kou,1, 2, †Rong Wang,1, 2, ‡and Xurong Chen1, 2, 3, §
1Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter,
South China Normal University, Guangzhou 510006, China
(Dated: November 1, 2022)
In this study, we try to extract ωn,ωp and φN scattering lengths from the differential cross-section
data of near-threshold ωand φphotoproductions not only to the energy at threshold tthr , but also in
t to t = 0. The incoherent data of ωand φphotoproductions on deuterium target for scattering length
extractions are provided by CBELSA/TAPS Collaboration and LEPS Collaboration respectively,
where the deuteron is usually approximated as a weakly bound state of a quasi-free neutron plus
a quasi-free proton. Under the Vector Meson Doninance model and the assumption of energy
independence of the differential cross-section, we obtained the |αωn∗|and |αωp∗|of loosely bound
neutron and proton in the deuteron to be 0.709 ±0.078 fm and 0.621 ±0.022 fm respectively at
threshold tthr (1.258 ±0.130 fm and 1.056 ±0.032 fm respectively in t to t = 0) for the first
time by fitting the near-threshold data of γd→ωn(p) and γd→ωp(n). For a comparison study,
we also extracted the scattering length |αωp|of the free proton from the ωphotoproduction on
the hydrogen target by CBELSA/TAPS Collaboration. With the near-threshold and incoherent φ
photoproduction data of γd→φpn by LEPS Collaboration, we obtained scattering length |αφN |of
the bound nucleon inside the deuteron to be 0.109 ±0.008 fm at threshold tthr and 0.276 ±0.010
fm in t to t = 0, respectively. The obtained |αωp |and |αφN |are basically in agreement with the
experimental indications and the theoretical predictions within the current uncertainties.
I. INTRODUCTION
Vector meson-nucleon interactions are the extremely
important research topics in the non-perturbation do-
main of quantum chromodynamics (QCD). Since the dis-
covery of the vector mesons, they have become attractive
probes for the study of hadronic interaction. Due to the
behavior of the near threshold cross section is related
to the vector meson-nucleon scattering length [1], exper-
imentally, the vector meson-nucleon interaction can be
investigated using vector meson photoproduction within
the Vector Meson Dominance (VMD) model. The ωp,
φp,J/ψ −p,ψ(2S)pand ρ0pscattering lengths have
been fully analysed in Refs. [2–7]. Based on the VMD
model, the absolute value of the scattering length may be
determined from the total near-threshold vector-meson
photoproduction cross-section [1] or the differential cross-
section of vector-meson photoproduction at threshold [8].
We try to extract the scattering length of the vec-
tor meson-neutron and vector meson-proton with current
available experimental data. In Ref. [3], they estimate
the J/ψ −pscattering length using the VMD model with
the new GlueX data to the threshold. Within the VMD
model, the total γN →XN cross-section is related to
both the total XN →XN cross-section at threshold en-
∗chdhan@impcas.ac.cn
†kouwei@impcas.ac.cn
‡rwang@impcas.ac.cn
§xchen@impcas.ac.cn (Corresponding author)
ergy and the scattering length |αXN |by [8]:
σγN (sthr) = απ
γ2
X
qXN
kγN
·σXN (sthr ) = απ
γ2
X
qXN
kγN
·4πα2
XN ,
(1)
where α= 1/137 denotes the fine structure constant, and
Xis a index which represents the vector mesons (e.g. ω,
φ,J/ψ, etc.) The kγN and qXN in the above equation are
the momenta in the center-of-mass of the initial and final
state particles, respectively, and γXis the photon-vector
meson coupling constant obtained from the X→e+e−
decay width. The photon–ωand photon–φcoupling con-
stants used in this work are 8.53 and 6.71 [9], respectively.
Eq. (1) is taken at the threshold energy, where sthr =
(M+m)2with M and m being the masses of the vector
meson and nucleon, respectively.
To estimate the scattering length with the experi-
mental measurements of the differential photoproduction
cross-section, in this study, we adopted the relation be-
tween the total cross-section and the differential cross-
section at the threshold [5]. The relationship between
the scattering length and the differential cross-section is
expressed as:
dσγX
dt (sthr, t =tthr) = απ
γ2
X
π
k2
γN
·α2
XN .
dσγX
dt (sthr, t = 0) = απ
γ2
X
π
k2
γN
·α2
XN .
(2)
A key problem in determining the scattering length
at threshold tthr is to extrapolate the cross section
to the point of t→tthr or s→sthr. In addition, the
arXiv:2210.11276v3 [hep-ph] 29 Oct 2022
2
dσγX /dt(sthr, t = 0) at left-hand side of Eq. (2) is not a
directly measurable quantity, as it requires extrapolation
of the energy to the threshold and extrapolation of t from
the physical region (tmin < t < tmax) to the non-physical
point t = 0. Therefore, when the vector meson nucleon
scattering length is extracted from the differential cross-
section data, we can not only extrapolate the energy at
the threshold tthr, but also extrapolate t to t = 0.
In this work, the following exponential function was
used to fit the differential cross-section data of near-
threshold ωand φphotoproductions on deuterium target
or hydrogen target.
dσ
dt =Ae−bt,(3)
where A=dσ/dt|t=0 denotes the forward differential
cross-section and bdescribes the slope parameter. Com-
bining Eq. (2) and Eq. (3), we can obtain the forward
differential cross-section value dσ/dt|t=tthr and dσ/dt|t=0
and extract the vector meson-nucleon scattering length
|αXN |.
Great progress has been made in meson-proton scatter-
ing length measurements, but little is known about the
vector meson-neutron scattering length. As the vector
meson-proton scattering length has already been fixed
by the data of ω,φ J/ψ,ψ(2S) and ρ0vector meson
photoproductions near threshold in the previous analy-
ses [3, 5–8, 10], We want to try whether we can extract
the vector meson-neutron scattering length using the
deuterium target data that the neutron and the proton
are loosely bound. The differential cross-section data of
near-threshold ωand φphotoproductions on deuterium
target were used for this analysis, including the inco-
herent photoproduction of vector meson (ωand φvec-
tor mesons) [11, 12] where the neutron or the proton is
knocked out. The incoherent data of ωand φphoto-
productions for scattering length extraction are provided
by CBELSA/TAPS Collaboration and LEPS Collabora-
tion, respectively. In this work, we extract ωn,ωp and
φN scattering length from the differential cross-section
data of near-threshold ωand φphotoproductions on deu-
terium target, where the deuteron is usually approxi-
mated as a weakly bound state of a quasi-free neutron
plus a quasi-free proton. For comparison study, we also
extracted the scattering length |αωp|of the free proton
from the ωphotoproduction on the hydrogen target by
CBELSA/TAPS Collaboration.
II. ωn,ωp AND φN SCATTERING LENGTHS
FROM ωAND φDIFFERENTIAL
PHOTOPRODUCTION CROSS SECTIONS
A. ωn∗scattering length from ωdifferential
photoproduction cross sections on the deuterium
target
Figure 1 shows the differential cross sections of the ω
meson photoproductions produced off the bound neutron
0.2 0.4 0.6 0.8
)
2
-t (GeV
1
10
2
10
)
2
b/GeVµ/dt (σd
n(p)ω →d γCBELSA data: = 1.175 GeV]
γ
[Eω
= 1.215 GeV]
γ
/4 [Eω
= 1.240 GeV]
γ
/16 [Eω
FIG. 1. Differential cross sections of the near threshold pho-
toproduction of ωmeson produced off the quasi-free neutron
versus the momentum transfer -t in the deuterium target [11].
The three incident photon energies Eγ(1.175, 1.215 and 1.240
GeV) near the threshold of ωmesons produced off the quasi-
free neutron are marked in the figure. Some cross sections are
scaled using the coefficients shown in the figure.
as a function of momentum transfer −t, with three inci-
dent photon energies Eγ. This reaction with exactly four
neutral hits (ω→γγγ and neutron) of the experiment at
ELSA [11] is detected where the ωmeson was produced
off the bound neutron in the liquid deuterium target giv-
ing the quasi-free reaction γd→ωn(p). The differential
cross sections of the |t|-dependence are fitted with an ex-
ponential function. We determined the parameters A and
the b at three incident photon energies Eγ(1.175, 1.215
and 1.240 GeV) through fitting to the ωmesons pro-
duced off the bound neutron with deuterium target data
[11] with Eq. (3). Then the values of dσγn∗/dt(sthr , tthr )
and dσγn∗/dt(sthr,0) are calculated by fitting parame-
ters A and b obtained by fitting the |t|-dependent differ-
ential photoproduction cross-section data. The scatter-
ing length |αωn∗|at the threshold tthr and in t to t =
0 are then calculated by Eq. (2). The extracted scat-
tering length |αωn∗|are listed in Table I. The averaged
scattering length |αωn∗|for the three extracted values
at different Eγenergies at threshold is calculated to be
0.709 ±0.078 fm. The averaged scattering length |αωn∗|
for the three extracted values at different Eγenergies in t
to t = 0 is calculated to be 1.258 ±0.130 fm. Here we use
the following formula to calculate the weighted average:
x±δ x = Σiωixi/Σiωi±(Σiωi)−1/2with ωi= 1/(δxi)2
[13]. It is worth noting that the weighted average values
of scattering length at different energies obtained here
are consistent with the simultaneous fitting results of all
data sets.
摘要：

Extractionof!n,!pandNscatteringlengthsfrom!anddi erentialphotoproductioncrosssectionsonthedeuteriumtargetChengdongHan,1,2,WeiKou,1,2,yRongWang,1,2,zandXurongChen1,2,3,x1InstituteofModernPhysics,ChineseAcademyofSciences,Lanzhou730000,China2UniversityofChineseAcademyofSciences,Beijing100049,China3G...

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