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We study pioninduced binary reactions for charmed baryons,
Observations of new hadrons have been stimulating diverse activities in hadron physics; see, for instance, Ref. [
So far, many of the new observations have been made for mesons. In contrast, not much progress has been achieved for baryons. In fact, the number of known heavy quark baryons is much less than that of light quark baryons. The study of charmed baryons is important not only for heavy but also for light quark dynamics, which in turn will be linked to the physics of the new hadrons and eventually to the unsolved problems of quantum chromodynamics (QCD).
From the above background, an experimental proposal is being made for the new pion beam facility at JPARC [
where
The purpose of this paper is to perform a theoretical study for the above reaction, while experimental feasibility is now under investigation. The study of such reactions is a challenging problem, because 1) not many studies have been performed so far, 2) production rates should reflect the structure of charmed baryons, and, furthermore, 3) the charm production mechanism from the threshold region to the region of a few GeV is not well understood.
The structure of charmed baryons has been studied in a quark model [
This paper is organized as follows. In Sect. 2, we estimate the rate of charm production using a Regge model in comparison with strangeness production. In Sect. 3, we compute the production rates of various charmed baryons
Let us consider forward angle scattering for the reaction (
Left: A
In the Regge theory [
The advantage of the Regge theory is that it determines the asymptotic behavior of the cross section of binary reactions,
For our present estimation, we employ Kaidalov's prescription for the vector Reggeon exchange [
In this paper, we use Eq. (
In Fig.
Forward differential cross sections
So far, we have estimated the total cross section indirectly by using the ratios for
In this section, baryons are described as twobody systems of a quark and a diquark. Charmed baryons are then composed of a heavy quark and a light diquark. The relative motion of the quark and diquark is described by the
Baryon masses
1116  1192  1385  
2286  2455  2520  
1  1/9  8/9  
1  0.04  0.210  
1  0.03  0.17  
1405  1520  1670  1690  1750  1750  1775  
2595  2625  2750  2800  2750  2820  2820  
1/3  2/3  1/27  2/27  2/27  56/135  2/5  
0.07  0.11  0.002  0.003  0.003  0.01  0.01  
0.93  1.75  0.02  0.04  0.05  0.21  0.21  
1890  1820  1840  1915  1880  2000 
2000 
2000 

2940  2880  1840  3000 
3000 
3000 
3000 
3000 

2/5  3/5  2/45  3/45  2/45  8/45  38/105  32/105  
0.02  0.04  0.003  0.001  0.001  0.001  0.001  0.001  
0.49  0.86  0.01  0.02  0.01  0.05  0.11  0.09 
As shown in Fig.
As in the previous section, we consider vector (
The cross section shows a forward peak. Therefore, we compute the differential cross sections only at the forward angle.
We focus on ratios of excited charmed baryon production as compared to groundstate production.
The main issue in this section is the computation of various baryon matrix elements and their ratios. For this purpose, we follow the standard prescription of the Reggeon calculation [
Let us first look at the matrix element of the
Next, we compute the baryon matrix element of
Now combining the matrix elements Eqs. (
To further simplify the computation, the quark momenta
We have computed the transition amplitudes
By using the baryon wave functions as summarized in Appendices B and C, the geometric factors
Herein below we make several observations.
In general the production rates for
Some excited
The above pairs of
We can similarly compute the amplitude for
So far, we have looked at
We have studied charm production induced by the highmomentum pion beam. This is a very challenging problem since no experiment has been performed for almost thirty years since the one at Brookhaven [
We first estimated that in the Regge model charm production is suppressed by a factor of
In the present study, we have used a simple quark and diquark model for baryons. In view of the successes of the constituent picture for lowlying states, we expect that some of the features should also persist in the charm production reactions. In particular, the identification of
Open Access funding:
We thank A. I. Titov, M. Oka, K. Sadato, and T. Yoshida for discussions. This work is supported in part by the GrantinAid for Science Research (C) 26400273. S.H.K. is supported by a Scholarship of the Ministry of Education, Culture, Science and Technology of Japan. The work of H.Ch.K. was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant Number: 2013S1A2A2035612).
Let us calculate the matrix elements
The total cross section is then proportional to the sum of squared amplitudes over possible spin states. For
First we consider the transition to
Similarly, we calculate the transitions to the groundstate
Let us first consider the transition to
The computations go in a completely similar manner to before, except for the radial matrix element
We summarize the baryon wave functions used in the present calculations [
For spin wave functions, using the notation for angular momentum coupling
Finally, the nucleon wave function is given as
We summarize some of the harmonic oscillator wave functions for lowlying states. Including the angular and radial parts, they are given as
The experimental total cross sections are