^{1}

^{*}

^{2}

^{†}

^{2}

^{‡}

sekihara@post.j-parc.jp

yuki.kamiya@yukawa.kyoto-u.ac.jp

hyodo@yukawa.kyoto-u.ac.jp

^{3}.

Based on a baryon-baryon interaction model with meson exchanges, we investigate the origin of the strong attraction in the

Existence and properties of dibaryons have been one of the major topics in hadron physics. Here dibaryons stand for states of baryon number

Historically, dibaryons were first discussed in theoretical studies. In the early stage, dibaryons analogous to the deuteron were predicted in Ref.

In this study, we focus on yet another dibaryon system, the

The aim of our study is to understand the origin of the strong attraction in the

This paper is organized as follows: First, in Sec.

First of all, we formulate the

As for the elastic

Feynman diagrams for the

There are several inelastic channels which can couple to

Baryon-baryon channels coupling to

The vertices in Fig.

The

The Lagrangian for the

Similarly, the Lagrangian for the

Finally, we employ a spin-independent form for the contact

In the following we construct the

The

To formulate the correlated two-meson exchange term

Now our task is to evaluate the coefficients

Feynman diagram for the

In this study we formulate the

Particles in the intermediate states of the diagram in Fig.

We fix the cutoff

Lorentz invariant amplitudes

The contact term

The interaction terms above are constructed in terms of the helicity eigenstates in momentum space as

In this study we focus on the

Channels for the

The evaluation of the inelastic contributions proceeds as follows: We first calculate a coupled-channel partial-wave projected interaction of the process ^{1}

The

The transition to inelastic channels with the

As we explained in Sec.

The

One of the most important quantities calculated with this interaction is the

From the on-shell

Next, we would like to fix the model parameters in our potential: cutoff ^{2}

We would like to thank T. Iritani and HAL QCD collaboration for providing us with the numerical value of the scattering length

For the hadron masses in the lattice QCD simulations, we adopt

In this condition, we obtain the scattering length

Now that we have fixed parameters in our model, we discuss the properties of the

First we investigate properties of the

The elastic contributions to the

To estimate the strength of the attraction, we calculate the volume integral of the interaction in the momentum space:

Volume integral

In addition to the

The

The

To quantify the smallness of the

Based on these results, in the following discussions we neglect the

Next we investigate the effects of the inelastic channels to the

The contributions

The inelastic contributions to the

We calculate the volume integral

We then calculate the on-shell

The

Inverse of scattering amplitude

Finally, by using the full

In general, when one takes into account the imaginary part of the potential to represent absorption into open channels, the binding energy of a bound state in quantum mechanics decreases. In particular, a shallow bound state may disappear above the threshold. In the present case, the pole position of the

The

To investigate the properties of the

From the wave function

The norm

Besides, using the weak-binding relation derived by Weinberg

We then plot the density distribution

Real and imaginary parts of the density distribution

We also estimate the shift of the binding energy by the Coulomb interaction in the

The existence of the

We consider a local potential in the

where

The

We set the cutoff as the same value with

Parameters

Now we check that the local potential

First, we solve the Schrödinger equation

Let us switch on the Coulomb potential

Second, we calculate the

We show in Fig.

Equivalent local

In this study we have investigated the

The constructed

We have discussed how the different mechanisms contribute to the

We have constructed an equivalent local

Finally, we remark on the possibility of the experimental investigation of the

The authors acknowledge A. Ohnishi, F.-K. Guo, and E. Oset for fruitful discussions on the recent studies of the

In this study we use isospin symmetric masses for hadrons

In this Appendix we summarize our conventions of baryons used in this study.

Throughout this study the metric in four-dimensional Minkowski space is

The Dirac spinors for a positive-energy solution are expressed as

Next,

Finally, the Rarita–Schwinger spinors for the spin-

and satisfy the following relations:

In this Appendix we show formulas of the projection of baryon-baryon interactions to general partial waves. Here the baryon-baryon scatterings are denoted by

We calculate the partial-wave matrix elements of the interaction

Finally, the interaction used for the Lippmann–Schwinger equation

Note that the orbital angular momentum ^{3}

Note that all baryons in this study have positive parity.

In this Appendix we summarize our formulation of the correlated two-meson exchange, for which we concentrate on the exchange of the scalar-isoscalar channel

Let us formulate the

To calculate

In general,

Now our task is to calculate the scattering amplitudes of the

The

Diagrammatic equation for the

With appendixes

Frazer–Fulco amplitude

Finally, we evaluate

Feynman box diagram for the

In Fig.

Next, we use the dispersion relation

Here we show the explicit forms of the Born terms for the

First, the

Next, the

In this study we describe the

We employ the leading-order terms of chiral perturbation theory for the interaction kernel