_{1}

^{*}

The new parity value of
π
^{0 }was determined according to the hypothesis of conservation of particle number. The theo-retical pentaquark proton’s parity value was also determined, and it was found that the conservation of parity is account nicely for the
τ-θ puzzle.

In 1951, Panofsky et al. [

In the general two-body system, the parity formula is

where P_{a} and P_{b} 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

The final state’s parity is

It was considered that the two parities are same by the conservation of parity.

In 1954, Chinowsky and Steinberger [

By the way, the two different decays were found for the positively charged strange mesons [

The charged kaon (K^{+}) [

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 [

The traditional formula and quark contents by experiment [1,3] are

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 [

where the {(), (n)} is a pentaquark proton (), the quark content is {u, d-bar} {u, d, d} [

The initial state’s parity is

By the conservation of parity,

The new parity value of is +1, not –1 in common use.

The numbers of down and anti-down quarks are not add up between the left-hand member and the right-hand member by experiment [

It is necessary for the adjustment of particle numbers. To adjust their member, the pentaquark proton () is adopted [

where the {(),(n)} is the deuteron(D′) [

The deuteron’s parity (P_{D′}) is –1, since the parity formula is

The initial state’s parity is

The final state’s parity is

By the conservation of parity,

The new parity value of in this reaction is also +1.

The reaction between the and by experiment [

This reaction was not considered by Aoki [

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

The formula of the right-hand parity is:

To adjust their member, the pentaquark proton (p′) is adopted [

The formula of the left-hand parity is

The formula of the right-hand parity is

The parity is conserved by the hypothesis of conservation of particle number.

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 [

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.

The and masses, lifetimes, and spins are no difference with each other. In the traditional expression, the parities are

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.

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.

The final state’s parity for is –1.

The final state’s parity for is –1.

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.