The Production of Singly Charmed Pentaquark $\bar c q qqq$ from Bottom Baryon

In the paper, we study the production of pentaquark $\bar{c}q qqq$ from singly bottom baryon. The tensor representations of pentaquark $\bar{c}q qqq$ are completed at first. Under the light quark symmetry analysis, we decompose the singly charmed pentaquarks into $6$, $15$ and $15'$ multiple states, and deduce the representations of these states. Then we construct the production Hamiltonian of the multiple states in proper order. For completeness, we systematically study the production channels of pentaquark states, including the possible production amplitudes and cross section relations between different channels. Ultimately, we screen out some advantageous channels, which expected to be fairly valuable supports for future search experiments.

possible existence, mass spectrums and possible decay behaviors of the singly charmed pentaquark have been discussed on many occasions.
Although the theoretical studies devoted to the singly charmed pentaquark have achieved remarkable results, there is no conclusive consensus on the properties, e.g, the masses and stability were determined by differences [15,[18][19][20]. In the present work, we will not discuss the differences, instead, the production processes of the singly charmed pentaquarkcqqqq with less controversy are the attentions. In principle, the light quark flavor SU(3) symmetry, a model independent method, has been successfully used to meson and baryon system [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], consequently to be a convincing tool dealing withcqqqq. Though the SU(3) breaking effects might be sizable, the results can still behave well comparing with the experimental data in a global viewpoint [30,37]. Referring to the LHC experiment, we consider the initial baryon with bqq components, which can form multiple states3 and 6 in SU(3) symmetry. Therefore, the singly charmed pentaquarkcqqqq, grouped into6, 15 and 15 ′ multiple states, can be produced by b-quark weak decay in initial baryon. Accordingly, we could make a systematical investigation on the pentaquarkcqqqq, constructing the possible Hamiltonian of production, and screening out several advantageous production channels for the examination in experiment.
The rest of the paper is organized as follows. In Sec.II, we deduce the tensor representations of multiple pentaquark states. We construct the possible production Hamiltonian of multiple pentaquark states in Section III, which including the production from singly bottom baryon T b3 or T b6 in initial state, for definiteness, we still present a collection of the golden channels. We make a short summary in the end.

II. REPRESENTATIONS OF PENTAQUARKcqqqq
Light quark SU(3) flavor symmetry is a good symmetry, especially at the level of hadrons. Aided by the language of group theory, the hadrons can be classified into different group representations, respectively matching with individual spin or orbital quantum number. The singly charmed pentaquark with four light quarkcqqqq can then be transformed under the SU(3) symmetry.
The irreducible representations of new combination states6, 15 and 15 ′ , arising from group decomposition above, can be shown clearly with tensor reduction, expressing as different tensor forms.
We deduce the tensor decomposition of pentaquark labeled with T ijkl , the coefficients of irreducible representations: (

III. HAMILTONIAN OF PRODUCTIONS
The strategy of SU(3) symmetry analysis needs more representations of hadrons and transition operators, which are pretty easy to achieve. For the singly bottom baryon in initial state, the representations can be decomposed into3 and 6, found as [38,39] In the meson sector, singly charmed mesons form an SU(3) triplet or anti-triplet, light mesons form an octet plus singlet, all multiplets are collected as [35,40]  States Name Tensor I 3 Y Name Tensor The productions in quark level are the transition of b → ccd/s and b → ucd/s, which can be decomposed into the operators H3 and H 6 , as (H3

A.6 states
Since the representations of hadrons and transition operators have been determined, we can directly construct the possible Hamiltonian for the production of pentaquark6, 15 and 15 ′ states, from the singly bottom baryon, on the hadronic level under the SU(3) symmetry frame. The initial baryon which form multiple state T b3 or T b6 can produce pentaquark anti-sextetP 6 and meson. Accordingly, we construct the possible Hamiltonian for the production of anti-sextetP 6 , given as follows.
Here, the independent parameters, a 1 ,ā 1 , d 1 , . . ., represent non-perturbative effection, T b3 or T b6 We expand the Hamiltonian and harvest the possible amplitude results, aggregating into Tab. II. Typically, the Cabibbo allowed production channels, may receive the largest contribution. Meanwhile, the charged final light meson possesses high detection efficiency. Consequently, we extract these channels and suggest them as golden channels for the studying in the future experiment, see Tab III. There is no simply way to estimate the size of production cross section, but the relations between different cross sections can be further deduced, when we approximately ignore the phase space differences. Our calculations show the relations given as follows.

B. 15 states
Similarly, we construct the possible Hamiltonian for the production of pentaquark 15 state from the singly bottom baryon.
The corresponding Feynman diagrams are shown in Fig. 2. We collect the possible channels and amplitude results into Tab IV and Tab V. Several golden channels for producing pentaquark 15 state are arranged in Tab III. For convenience, the cross section relations between different channels with anti-triplet or sextet baryon T b3 /T b6 in initial state are reorganized in Appendix A.

C. 15' states
The possible Hamiltonian for the production of pentaquark 15 ′ state on the hadronic level under the SU(3) symmetry frame are constructed as below.
We draw the Feynman diagrams in Fig. 2. It should be noted that one anti-triplet baryon T b3 can not produce the pentaquark 15 ′ state, because the symmetry and anti-symmetry indexes in the production, we obtain cross sections of different production channels, as well as the relations between different channels. For definiteness, we suggest several golden channels for searching the singly charmed pentaquark in future experiments. The establishment the existence of these states means a remarkable progress in hadron physics.

Appendix A: tables and relations
We collect some results in the appendix. The tables of possible channels and amplitudes with the pentaquark multiplets 15 and 15 ′ are grouped into Tab IV, Tab V and Tab VI. Further more, for the relations between different channels, we deduce the cross section relations of 15 state according to the amplitudes in Tab IV and Tab V, shown as below.
The cross section relations of 15 ′ state are given as follows.

Appendix B: tensor forms
The pentaquark statecqqqq(T ijkl ) can be decomposed into different tensor representations upon the SU(3) flavor symmetry.
The tensor reduction Eq. (2) can tell the representations of irreducible tensorsT 3 ,T6, T 15 , . . ., with the way of projection. In addition, the traceless tensor 15 indicates the following equations.
Here, filtering out redundant mathematical calculations, we directly list the tensor representations