1. Introduction
In 1951, Panofsky et al. [1] reported on the parities of pions from the reaction of
and
. The reaction between proton (p) and charged pion (
) is
![](https://www.scirp.org/html/3-1220025\33cfdb99-2f3d-4b0a-ada8-46dddb0e506b.jpg)
In the general two-body system, the parity formula is
![](https://www.scirp.org/html/3-1220025\59e4f58c-3104-47d0-935b-3e153f29d3e9.jpg)
where Pa and Pb are the intrinsic parities, l is the angular momentum. The traditional proton, neutron, and meson’s parity values in common use are +1, +1, and –1, respectively. The parity is a multiplicative quantum number. Since the initial state (
) is S state (l = 0) and the angular momentum is 0, the initial state’s parity is
![](https://www.scirp.org/html/3-1220025\92bb70c4-416a-4e73-8e0f-653744f983b7.jpg)
The final state’s parity is
![](https://www.scirp.org/html/3-1220025\af915c40-bd0d-4048-a56e-8d3416161ad8.jpg)
It was considered that the two parities are same by the conservation of parity.
![](https://www.scirp.org/html/3-1220025\e1c26e00-b1b9-4164-aef0-42601beab294.jpg)
In 1954, Chinowsky and Steinberger [2] obtained the parity value (–1) of
from the absorption of negative pions in deuterium. In 1959, Plano et al. [3] determined the parity value (–1) of neutral pion (
). However the quark numbers by the traditional formula are not add up between the initial state and the final state. It is thought of as a serious problem.
By the way, the two different decays were found for the positively charged strange mesons [3]:
![](https://www.scirp.org/html/3-1220025\f189c2c8-6c84-4117-b83d-77c1e95f5e7d.jpg)
The charged kaon (K+) [4] used to be called
and
. Both the
and
particles were supposed to be two different particles, but they are the same particles. The two final states have different parities, and it is known as the
puzzle [5-8].
In this paper, the parities of the pentaquark proton, deuteron, and neutral pion are re-searched based on the hypothesis of conservation of particle number [9]. It is attested to the conservation of parity for the
puzzle.
2. Results and Discussion
2.1. The Parity of
for the
Reaction
The traditional formula and quark contents by experiment [1,3] are
![](https://www.scirp.org/html/3-1220025\68eaff1d-4df4-4ec8-b634-25b62e44616b.jpg)
The numbers of down and anti-down quarks, d and d-bar, are not add up between the left-hand member and the right-hand member. It is necessary for the adjustment of particle numbers. To adjust their member, the pentaquark proton (
) is adopted [9]. According to the hypothesis of conservation of particle number, the above formulae for
are as indicated below.
![](https://www.scirp.org/html/3-1220025\a2f2c290-152e-4ce6-9b38-2dd55284e820.jpg)
![](https://www.scirp.org/html/3-1220025\62a54ff4-b056-46d2-aec1-87c2a1cabc57.jpg)
where the {(
), (n)} is a pentaquark proton (
), the quark content is {u, d-bar} {u, d, d} [9]. The pentaquark proton’s parity (
) is –1, since the parity formula is
![](https://www.scirp.org/html/3-1220025\24eb3c8a-d2b5-4117-86e1-7d4adc41b2fd.jpg)
The initial state’s parity is
![](https://www.scirp.org/html/3-1220025\39a44814-aad6-4196-af12-06b3747b9d1c.jpg)
By the conservation of parity,
![](https://www.scirp.org/html/3-1220025\9644df2e-2fe4-497d-aa8d-c4ee62b898bd.jpg)
The new parity value of
is +1, not –1 in common use.
2.2. The Parity of
for the
Reaction
The numbers of down and anti-down quarks are not add up between the left-hand member and the right-hand member by experiment [1].
![](https://www.scirp.org/html/3-1220025\4b39adcd-f4f7-4410-a2d3-797c1349a448.jpg)
It is necessary for the adjustment of particle numbers. To adjust their member, the pentaquark proton (
) is adopted [9]. According to the hypothesis of conservation of particle number, the above formulae for
are as indicated below. The reaction between the deuteron (
) and charged pion (
) is
![](https://www.scirp.org/html/3-1220025\823dc4f3-142b-4a55-a123-c500e80a1037.jpg)
where the {(
),(n)} is the deuteron(D′) [9].
The deuteron’s parity (PD′) is –1, since the parity formula is
![](https://www.scirp.org/html/3-1220025\70f7ecdf-2f5f-4c45-a873-8f9c2399879a.jpg)
The initial state’s parity is
![](https://www.scirp.org/html/3-1220025\a95007a8-6e4b-4a92-93be-3f18398326f3.jpg)
The final state’s parity is
![](https://www.scirp.org/html/3-1220025\12fc8586-49a9-49e7-ad32-96a218760cc8.jpg)
By the conservation of parity,
![](https://www.scirp.org/html/3-1220025\0d840645-7143-4f38-a231-28a975fd5344.jpg)
The new parity value of
in this reaction is also +1.
2.3. The Parity of
Reaction
The reaction between the
and
by experiment [10] is
![](https://www.scirp.org/html/3-1220025\8d9e3e5f-53a1-49ec-9c86-ab8ff2fb50e3.jpg)
This reaction was not considered by Aoki [9]. The formula for the quark content
of the traditional proton is
![](https://www.scirp.org/html/3-1220025\eb9780dd-908e-488f-8c01-a2f2c8f5334b.jpg)
However the numbers of down and anti-down quarks are not add up between the left-hand member and the right-hand member. The parity is not conserved. The formula of the left-hand parity is
![](https://www.scirp.org/html/3-1220025\5ac8f73d-483e-4c84-846b-803f84a62dcd.jpg)
The formula of the right-hand parity is:
![](https://www.scirp.org/html/3-1220025\843a7604-cb1f-44f3-8fa0-8002b7c0a779.jpg)
To adjust their member, the pentaquark proton (p′) is adopted [9].
![](https://www.scirp.org/html/3-1220025\a6ef8388-ab2a-4053-b517-75277f9917b8.jpg)
The formula of the left-hand parity is
![](https://www.scirp.org/html/3-1220025\77990d3e-b0f0-4938-ba8a-4c8e92b8f616.jpg)
The formula of the right-hand parity is
![](https://www.scirp.org/html/3-1220025\b1b4f567-22e2-49f4-9a74-553d0e1b732a.jpg)
The parity is conserved by the hypothesis of conservation of particle number.
2.4. The Validation of Conservation of Parity for the
Puzzle
In the
puzzle [5-8], the two parities of
and
have same value (–1), since the positively charged Kaon (K+) is a meson. The K+ was shown as follows by Aoki [9].
![](https://www.scirp.org/html/3-1220025\43c6066f-8211-4b93-9ca9-9c1671880412.jpg)
where the anti-strange quark (s-bar) is the composite particle consisting of the anti-down quark(d-bar) and
, the
is the
and
pair, the
is the neutrino-antineutrino pair, and the
is the muonneutrino-antimuonneutrino pair. The parity of
is +1. The
may be the two photons.
![](https://www.scirp.org/html/3-1220025\eb58833b-84c3-4c55-968b-ccfe749f1cc1.jpg)
![](https://www.scirp.org/html/3-1220025\27bd6c98-c41a-43e9-80b2-aa10e4d19b77.jpg)
![](https://www.scirp.org/html/3-1220025\c0f19be3-cf3a-4135-8d06-34a2d84c60d0.jpg)
The
and
masses, lifetimes, and spins are no difference with each other. In the traditional expression, the parities are
![](https://www.scirp.org/html/3-1220025\06c334c4-b439-4dbf-9bcc-3c4c813dfa66.jpg)
![](https://www.scirp.org/html/3-1220025\c9fc1d20-bcb5-471a-a88e-dc43f6adf3fd.jpg)
where l is the angular momentum between
and
, L is the angular momentum between
and the center of
,
.
The two final states have the different parities, +1 and –1. The parity for
is not conserved. It is considered as the parity violation in weak interactions. However the parity is conserved as follows by the new parity value (+1) of
.
![](https://www.scirp.org/html/3-1220025\f6ec51b1-6dbe-4442-8b47-89a48d36e72d.jpg)
![](https://www.scirp.org/html/3-1220025\cc990617-83a4-45c3-ac1e-472b1fcaf9d9.jpg)
![](https://www.scirp.org/html/3-1220025\d719e3de-7d99-4c1f-9cb8-eafba9c39558.jpg)
The neutral pions of both initial states were added by the hypothesis of conservation of particle number. The
for
is corresponding to the
. The initial state’s parities for
and
are –1.
![](https://www.scirp.org/html/3-1220025\6bd71575-e446-4b7b-a217-6d9e446c0602.jpg)
The final state’s parity for
is –1.
![](https://www.scirp.org/html/3-1220025\bb64f856-18f7-4927-a206-540595e4291e.jpg)
The final state’s parity for
is –1.
![](https://www.scirp.org/html/3-1220025\0b52b048-85d1-4024-9147-57f511a3a6dd.jpg)
3. Conclusions
The new parity values of the the pentaquark proton (p′)deuteron (D′), and neutral pion (
), are –1, –1, and +1, respectively.
It was attested to the conservation of parity for the
puzzle.