Describing a Baryon as a Meson Pair

We propose a new description of a baryon as a pair of mesons. This description is an extension of the previously proposed description of a nucleon as a pair of pions. The purpose of this article is to show the following two possi-bilities. The first one is that it shows the qualitative explanation to support our description of a nucleon as a pair of pions and the second one is that it gives the systematic way of estimation of baryon mass not only for light baryons but also for heavy baryons (charm baryons and bottom baryons). Each isospin group is constructed of both baryons and antibaryons. This way of construction is consistent with that of mesons. The results obtained are listed in tables (Tables 1-9). This shows that the generalized Gell-Mann-Nishijima relation equation holds under the condition that the baryon number is 0 and that the obtained masses are fairly good, even for heavy baryons. Our description also yields several examples of baryon decay modes.

quarks. In other word, it is not evident that a proton is composed of three quarks. From this fact, a different possibility for the composition of a proton can be considered. In this report, we propose a description of a nucleon as a pair of pions and obtain a plausible result for nucleon electromagnetic form factors (e.m. FFs) [7]. Because all baryons decay to a proton as a final state, it is a fair consideration that any baryon spin is not determined by the intrinsic spin of composing quarks. Thus, it is not obvious that any baryons are composed of three quarks. From this view point, we extend our consideration of proton composition to all baryons by describing a baryon as a pair of mesons. In this case, we have to reconsider the way that isospin groups are constructed. In the case of mesons, all isospin groups are constructed from both a particle and an antiparticle. Thus, it is consistent that any isospin group of baryons is also constructed from both a particle and an antiparticle. Our proposition is based on There is no useful formula to estimate baryon mass. Therefore, we need another way of estimating baryon mass. In this paper, we estimate baryon mass even though one generalized including C and B values. The previous description of a nucleon as a pair of pions shows good results for e.m. FF, especially, G E /G D for proton), but it is not obvious the reason why a nucleon can be described as a pair of pions. In this paper, we show the qualitative aspect of baryon description as a pair of mesons. This gives a support to our proposition of a nucleon description as a pair of pions.

Description of Properties
The basic meson operator is defined by the Bethe-Salpeter-like amplitude of the hadronic operator as where 0 and P denote a vacuum and physical state, respectively.
The gauge-invariant bi-local operator ( )  [12]. We then proposed that a nucleon can be described as a pair of pions and obtained the e.m. FFs and distribution functions of nucleon [7]. The results of Ref. [7] encouraged us to extend this kind description to the consideration that a baryon can be described as a pair of mesons. In Ref. [7], a nucleon operator is defined as Extending this consideration to all baryons, any baryon operator is defined as having the same form as Equation (3) and Equation (4) χ .
We show baryons described as a pair of mesons composed of u,d, and s quarks in Table 4 (spin 1/2) and Table 5 (spin 3/2). Baryons described as a pair of mesons composed of c and b quarks are shown in Tables 6-9 (Table 6 and   Table 7 for spin 1/2, Table 8 and Table 9 for spin 3/2). The terms listed in columns are paired mesons, isospin, the third component of isospin, strangeness, c value, b value, binding quarks, binding energy, excited energy, estimated mass and mass measured by experiment.
It is obvious to see that each baryon satisfies the generalized Gell-Mann-Nishijima relation equation [13] [14]. The generalized Gell-Mann-Nishijima relation equation is given as ( ) Because a baryon is composed of a pair of mesons, we need these values to determine the isospin, the third component of isospin, and the strangeness and to estimate the mass of each baryon. Table 1 shows the properties of mesons composed of u, d, and s quarks only for the spin 0 case. Table 2 shows the properties of mesons with spin 0 composed by c and b quarks baryons. Table 3 shows the properties of mesons with spin 1 composed by c and b quarks baryons.
Using the values of Tables 1-3, we construct the isospin of a baryon and describe a baryon as a pair of mesons. To construct the isospin, we regroup the T. Kurai  Notes: The listed mass of f 0 is from ref [12]. All other mass are from Oliver et al. [15]. We use 0 0 s L , κ κ Notes: The listed values are taken from Ref. [15] including mass values. All baryon numbers are 0.
baryons including antiparticles. For example, in the nucleon case, we consider p − (an antiparticle of proton p + ) and constitute p + , p 0 (n 0 : neutron), p − as one group so that the isospin is 1 instead of the normally considered value of  Table 4. We use a baryon number of 0 for all baryons as proposed in Ref. [7].
The binding energies for uu, dd, ud are determined by the mass difference between a proton and the sum of the masses of π + and π 0 . We call this binding energy the strong binding energy, and calculate it to be 664.02 MeV. A similar consideration gives the binding energy for us and ds, using the mass difference between Λ 0 and the sum of the masses of π + and κ − or π − and κ + . We call this the weak binding energy and calculate it to be 482.43 MeV. The estimated mass of each baryon is obtained by the following equation.

Mass of baryon Sum of mass of composing mesons
Binding energy Excited energy In Table 4, there is no excitation energy term, although this term appears in later tables.  The measured mass in Table 4 and in later tables is taken from Beringer et al. [16]. Table 5 shows the properties of light baryons with spin 3 2 .
The excited energy for Δ baryons is determined using the fact that Δ + and Δ 0 are normally considered as the excitation states of p + , and p 0 (n 0 ) (proton and neutron), respectively. Thus, by setting the mass of Δ + of 1232 MeV, we obtain this excited energy value of 293.43 MeV. Table 6       At this point in our argument, we notice that the binding energy between quarks becomes smaller as the mass of each bound quark becomes heavier.
Thus, we set the binding energy for cc to be nearly 0. A meson pair of c Σ baryons is determined using the following argument. c + Σ is originally considered as a pair of D + and η 0 because Σ + is composed by π + and η 0 . However, the exis-  Table 7 shows the properties of heavy baryons with spin 1 2 composed by b quarks.
The determination of binding energy is based on the same considerations used in the charm baryon case.
The reason that the strangeness of b and that of κ − (κ + ) is −1 (+1) so that the total of strangeness becomes 0. Table 8 shows the properties of heavy baryons with spin 3 2 composed by c quarks. Table 9 shows the properties of heavy baryons with spin 3 2 composed by b quarks.
In the case that Λ 0 is described as + − π + κ , the decay mode is made obvious by noticing the fact that κ − decays to + − − π + π + π or 0 − π + π . The mass difference between the original baryon (in this case Σ + ) and the generated baryon (in this case n 0 ) is not large enough for two pions.

Conclusions
In Section 2 and Section 3, we show the qualitative aspects of baryons described as a meson pair. From Tables 4-9, we can demonstrate that all baryons satisfy the generalized Gell-Mann-Nishijima relation Equation (5)

Discussion
During the presentation of Table 6, we mention that the reason we omit cc + Ξ and cc − Ξ is for the consistency of the isospin argument. To be precise, the other 1 2 isospin case shows that a positive charge particle has an I 3 of 1 2 and the negative charge particle has an I 3 of 1 2 − , as is the case for c   D + π is that a neutron is composed of π + and π − . We derived the charge distribution function of a neutron in a previous paper [7]. Because we consider that any neutral baryons should have a charge distribution, we adopt this mixture instead of that of a pair of neutral mesons.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.