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Bayesian Analysis Application in Nuclear Physics
Parada. T. P. Hutauruk
Asia Pacific Center for Theoretical Physics, Gyeongbuk, 36765, South Korea
Keywords:
Bayesian Analysis, Kaon Photo-production, Nested Sampling Integration, Excited Baryon Resonances,
Associated Legendre Polynomial.
Abstract:
Bayesian analysis is applied to analyze the CLAS experimental data of the angular distributions of the differ-
ential cross sections, and C
x
0
and C
z
0
double polarizations for γ + p → K
+
+ Λ reaction. These observables can
be classified into four Legendre classes and represented by associated Legendre polynomial function itself.
In this analysis, we intend to determine the best data model for both observables. We use the Bayesian tech-
nique to select the best model by calculating the posterior probabilities and comparing the posterior among
the models for each observable. The posteriors probabilities for each data model are computed using a Nested
sampling integration. From this analysis, we found that the CLAS data set needs no more than four associated
Legendre polynomials to describe the differential cross section data. For C
x
0
and C
z
0
double polarizations
require two and three order of associated Legendre polynomials respectively to describe the data well. The
extracted coefficients of each observable of the best model are presented. It shows the structure of baryon
resonances qualitatively.
1 INTRODUCTION
Significant information on the structure of the nu-
cleon can be obtained by studying its excitation spec-
trum [1, 2]. Over the last few decades, a large amount
information about the spectrum of the nucleon has
been collected. Most of this information has been ex-
tracted from pion-induced and pion photo-production
reactions [3, 4]. However, pionic reactions may have
biased the information on the existence of certain res-
onances. Constituent quark model calculations pre-
dict a much richer resonance spectrum than that has
been observed in pion production experiments [8].
Predicted resonances which have not been observed
are called ”missing” resonances. Instead, the con-
stituent quark model (CQM) also predicts that these
”missing” resonances may couple strongly to KΛ and
KΣ channels or other final states involving vector
mesons [8, 9, 10]. Since performing kaon-hyperon,
kaon-nucleon or hyperon-nucleon scattering experi-
ments is a daunting task, kaon photo-production on
the nucleon appears to be a good alternative solu-
tion [9, 10].
Experiments on kaon photo-production and
electro-production started in the 1960s[11]. However,
the old experimental data are often inconsistent and
have large error bars. In recent years, a large amount
of data for kaon photo-production has been collected.
High statistics data from the CLAS, for differential
cross sections, recoil polarization, C
x
and C
z
double
polarizations for the reaction γ + p → K
+
+ Λ have
been published since several years ago [12, 13]. The
world database for the reaction γ + p → K
+
+ Λ is
more available now. This gives a possibility to ana-
lyze the data more accurately. Recently the newest ex-
perimental data for the K
+
Λ channel of photon asym-
metry (Σ), target polarization (T), recoil polarization
(P), and O
x
0
and O
z
0
double polarizations has been
collected [14]. Unfortunately, the experimental data
do not published yet. Furthermore the experimental
data for other observables such as G asymmetry will
available soon from Jefferson Lab. Newport News,
USA.
Additional experimental data have also been mea-
sured by SAPHIR [15, 16, 17], LEPS [18, 19] and
GRAAL [20]. Several previous analyses have been
applied to the results of these experiments, such as
Isobar models [9, 10, 21, 22, 23] and Coupled chan-
nel models [24, 25, 26]. However different theoret-
ical model calculations often produce very different
predictions.
Based on paper of Ref.[5], all sixteen observ-
ables in kaon photo-production were shown to
be classified into the classes L
0
ˆ
I;
ˆ
E;
ˆ
C
z
0
;
ˆ
L
z
0
,
310
Hutauruk, P.
Bayesian Analysis Application in Nuclear Physics.
DOI: 10.5220/0008908700002481
In Proceedings of the Built Environment, Science and Technology International Conference (BEST ICON 2018), pages 310-315
ISBN: 978-989-758-414-5
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c
2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved