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We calculate the double charmonium production cross-section within the framework of

One of the challenging problems in heavy-quark physics is the process of double charmonium production in electron-positron annihilation at B-factories [

In these calculations, we make use of the Bethe-Salpeter Equation (BSE) approach [

In our recent works [

This paper is organized as follows. In Section

We start from the lowest-order Feynman diagrams for the process,

Leading-order Feynman diagrams for the production of double charmonium in

The relativistic amplitude

The relativistic BS wave function of pseudoscalar and vector charmonium is taken from our recent papers [

for

and

where

where

where

Applying the trace theorem and evaluating trace over the gamma matrices, one can obtain the expression:

After some mathematical steps, we can get the following expression:

Thus we can express the amplitude

The full amplitude for the process

The total amplitude,

After integration over the phase space, the total cross-section for vector and pseudoscalar charmonium production is

The algebraic expressions of the wave functions of pseudoscalar and vector charmonium,

where the inverse range parameter

Input parameters for this study.

| | | | |
---|---|---|---|---|

0.210 | 0.150 | 0.200 | 0.010 | 1.490 |

Using these input parameters listed in Table

The total cross-sections of pseudoscalar and vector charmonium production for ground and first excited states with experimental data and other theoretical models (in units of fb).

Production Process | |||||||
---|---|---|---|---|---|---|---|

| 20.770 | 25.6 | 17.6 | 26.7 | 22.2 | 22.3 | 21.75 |

| 11.643 | 16.3 | 16.3 | 15.3 | |||

| 11.177 | 16.5 | 16.4 | 26.6 | 16.4 | ||

| 6.266 | 16.0 | 14.5 | 9.6 |

We wish to mention here that the

The total cross-sections of pseudoscalar and vector bottomonium production for their ground states with predictions of other theoretical models (in units of fb).

Production Process | | | | |
---|---|---|---|---|

| 0.155-0.058 | 0.16-0.06 |

Our main aim in this paper was to study the cross-section for double charmonium production in electron-positron collisions at center of mass energies,

Further, the exclusive production of double heavy charmonia in

This process has also been studied in Relativistic Quark Model [

We wish to mention that, in our framework of

The main objective of this study was to test the validation of our approach, which provides a much deeper insight than the purely numerical calculations in

This calculation involving production of double charmonia in electron-positron annihilation can be easily extended to studies on other processes (involving the exchange of a single virtual photon) observed at B-factories such as

These processes that we intend to study next are quite involved, and the dynamical equation based approaches such as BSE are a promising approach. And since these processes involve quark-triangle diagrams, we make use of the techniques we used for handling such diagrams recently done in [

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was carried out at Samara University, Ethiopia, and at Chandigarh University, India. The authors thank these institutions for the facilities provided during the course of this work.

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