Low energy reactions , , and the strangeness hyperons
Abstract
A combined study of the reactions , and at low energies is carried out with a chiral quarkmodel approach. Good descriptions of the experimental observations are obtained. The roles of the lowlying strangeness hyperon resonances in these processes are carefully analyzed. We find that: (i) In the process, both and play dominant roles. Significant contributions of and could be seen around their threshold; (ii) In the process, some obvious evidence of and could be found. Some hints of might exist in the reaction as well. and should correspond to the representations and , respectively; (iii) In the process, the dominant resonances are and . Some evidence of , and could be seen as well. A weak coupling of to should be needed in the reactions and . Furthermore, by analyzing these reactions, we also find that the , channel backgrounds and channel Born term play crucial roles in the reactions: (i) The angle distributions of are very sensitive to the , channel backgrounds and s channel pole; (ii) The reaction is dominated by the , channel backgrounds and the ground wave state ; (iii) While, the reaction is governed by the channel background, and also plays an important role in this reaction.
pacs:
12.39.Fe, 12.39.Jh,13.75.Jz,14.20.JnI Introduction
There exist many puzzles in the spectroscopies of and hyperons. To clearly see the status of these hyperon spectroscopies, we have collected all the strangeness hyperons classified in the quark model up to shell in Tab. 1. From the table, it is seen that only a few lowlying hyperons are established, while for most of them there is still no confirmed evidence found in experiments. Concretely, for the spectroscopy although a lot of states, such as , , and , have been listed by the Particle Data Group (PDG) PDG , they are not established at all. Their quantum numbers and structures are still unknown. Even for the wellestablished states with known quantum numbers, such as , it is questionable in the classification of them according to various quark models Chen:2009de ; Klempt:2009pi ; Melde:2007 ; Melde:2008 ; Isgur78 . For the spectroscopy, a little more knowledge is known compared with that of , however, the properties of some resonances with confirmed quantum numbers are still controversial. For example, it is still undetermined whether these states, such as , and , are excited three quark states or dynamically generated resonances, though their are welldetermined Klempt:2009pi . How to clarify these issues and extract information of the unestablished hyperon resonances from experimental data are still open questions.
To uncover the puzzles in the hyperon spectroscopies, many theoretical and experimental efforts have been performed. Theoretically, (i) the mass spectroscopes were predicted in various quark models Isgur78 ; Isgur:1977ky ; Capstick:1986bm ; Melde:2008 ; Gerasyuta:2007 ; Bijker:2000 ; Glozman:1997ag ; Loring:2001ky ; Schat:2001xr ; Goity:2002pu , large QCD approach Schat:2001xr ; Goity:2002pu and lattice QCD etc Menadue:2011pd ; Engel:2012qp ; (ii) the strong decays were studied within different models Koniuk:1979vy ; Melde:2006yw ; Melde:2008 ; Melde:2007 ; An:2010wb ; (iii) the properties of the individual resonances, such as , and , were attempted to extract from the scattering data with UPT approaches Hyodo:2011ur ; Oller:2005ig ; Roca:2006sz ; Oller:2006hx ; Borasoy:2005ie ; Hyodo:2003qa ; Oset:2001cn ; GarciaRecio:2002td ; Jido:2003cb ; Oller:2000fj ; Oset:1997it ; Oller:2006jw ; Borasoy:2006sr ; Roca:2008kr , BPT approaches Bouzasa;2008 , matrix methods Martin:1969ud ; D. M. Manley , large QCD method Lutz:2001yb , mesonexchange models Buttgen:1985yz ; Buettgen:1990yw ; MuellerGroeling:1990cw , quark model approaches Hamaie:1995wy ; Zhong:2009 , dispersion relations Gensini:1997fp ; Martin:1980qe , and the other hadronic models BS:2009 ; Gao:2012zh ; Gao:2010ve ; Liu:2011sw ; (iv) furthermore, the possible exotic properties of some strange baryons, such as two mesonsone baryon bound states, quark mass dependence, fivequark components, were also discussed in the literature Mart:2007x ; GarciaRecio:2003ks ; Zou:2008be . Experimentally, the information of the hyperon resonances was mainly obtained from the measurements of the reactions , , , , and Mast:1976 ; Baxter:1974zs ; Ponte:1975bt ; Conforto:1975nw ; Evans:1983hz ; Kim:1965 ; Jones:1974at ; AlstonGarnjost:1977cs ; AlstonGarnjost:1977ct ; Cameron:1980nv ; Ciborowski:1982et ; armen:1970zh ; London:1975av ; Olmsted:2004 ; Mast:1974sx ; Berley:1996zh ; Bangerter:1980px ; Starostin:2001zz ; Prakhov:2004an ; Zychor:2007gf . In recent years, some other new experiments, such as excited hyperon productions from and collisions, had been carried out at LEPS, JLAB and COSY to investigate the hyperon properties further Niiyama:2008rt ; Kohri:2009xe ; Zychor:2008ct ; Zychor:2006 .
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Recently, some higher precision data of the reactions Manweiler:2008zz ; Prakhov:2008 , and Prakhov:2008 at eight momentum beams between 514 and 750 MeV/c were reported, which provides us a good opportunity to study these lowlying and resonances systemically. In this work, we carry out a combined study of these reactions in a chiral quark model, where an effective chiral Lagrangian is introduced to account for the quarkmeson coupling. Since the quarkmeson coupling is invariant under the chiral transformation, some of the lowenergy properties of QCD are retained. The chiral quark model has been well developed and widely applied to meson photoproduction reactions qk1 ; qk2 ; qkk ; Li:1997gda ; zhaokstar ; qk3 ; qk4 ; qk5 ; He:2008ty ; Saghai:2001yd ; Zhong:2011ht . Its recent extension to describe the process of Zhong:2007fx and Zhong:2009 scattering, and the charmed hadron strong decays Zhong:2007gp ; Zhong:2010vq ; Liu:2012sj also turns out to be successful and inspiring.
Ii framework
The tree diagrams calculated in the chiral quark model have been shown in Fig. 1. The reaction amplitude can be expressed as the sum of the , , channel transition amplitudes:
(1) 
The  and channel transition amplitudes as shown in Fig. 1 are given by
(2)  
(3) 
where and stand for the incoming and outgoing mesonquark couplings, which might be described by the effective chiral Lagrangian Li:1997gda ; qk3
(4) 
where represents the th quark field in a hadron, and is the meson’s decay constant. The pseudoscalarmeson octet, , is written as
(5) 
In Eqs. (2) and (3), and are the energies of the incoming and outgoing mesons, respectively. , and stand for the initial, intermediate and final states, respectively, and their corresponding energies are , and , which are the eigenvalues of the nonrelativistic Hamiltonian of constituent quark model Isgur78 ; Isgur:1977ky .
The extracted transition amplitude for the channel is Zhong:2007fx ; Zhong:2009
(6)  
with
(7)  
(8) 
where , and is the light quark mass. The is defined as , and the factor is given by expanding the energy propagator in Eq. (6) which leads to
(9) 
where is the mass of the intermediate baryons in the th shell, while is the typical energy of the harmonic oscillator; and are the four momenta of the initial baryons and incoming mesons in the centerofmass (c.m.) system, respectively.
While the extracted transition amplitude for the channel is Zhong:2007fx ; Zhong:2009
(10)  
where, we have defined
(11)  
(12) 
with . The factor is given by
(13) 
where stands for the four momenta of the outgoing mesons in the c.m. system.
The factors appeared in the  and channel amplitudes are determined by Zhong:2009
(14)  
(15)  
(16)  
(17)  
(18)  
(19)  
(20)  
(21) 
where corresponds to the Pauli spin vector of the th quark in a hadron, and are the isospin operators of the initial and final mesons defined in Zhong:2009 .
These factors can be derived in the SU(6)O(3) symmetry limit. In Tab. 2, we have listed the factors for the reactions , and . From these factors, we can see some interesting features of these reactions. For example, it is found that in the reactions and , the  and mesons can not couple to the same quark of a channel intermediate state (i.e., ), which leads to a strong suppression of the channel contributions. However, for the channel the kaon and pion can couple to not only the same quark but also different quarks of a baryon. Thus, the channel could contribute a large background to these two processes. While for the chargeexchange reaction , there are no channel contributions (i.e., ), and only the channel amplitude survives for the isospin selection rule (i.e., ).
In this work, we consider the vectorexchange and the scalarexchange for the channel backgrounds. The vector mesonquark and scalar mesonquark couplings are given by
(22)  
(23) 
where and stands for the vector and scalar fields, respectively. The constants , and are the vector, tensor and scalar coupling constants, respectively. They are treated as free parameters in this work.
On the other hand, the and couplings ( stands for a pseudoscalarmeson) are adopted as PPV ; Wu:2007fc
(24)  
(25) 
where is the coupling constant to be determined by experimental data.
For the case of the vector meson exchange, the channel amplitude in the quark model is given by
(26) 
where is a form factor deduced from the quark model, and is the vectormeson mass. The amplitude is given by
(27)  
where we have defined
(28)  
(29)  
(30) 
with . The tensor term of the channel vectorexchange amplitude is less important than that of vector term. In the calculations, we find the results are insensitive to the tensor term, thus, its contributions are neglected for simplicity. In Eq.(27), we have defined , and , which can be deduced from the quark model, where, is the isospin operator of exchanged meson. For the processes, the vector exchange is considered, and for the process, the vector exchanged is considered.
While, for the case of the scalar meson exchange, the channel amplitude in the quark model is written as
(31) 
where is the scalarmeson mass, and the is given by
(32)  
with
(33)  
(34)  
(35) 
In Eq.(32), we have neglected the higher order terms. In this work, the scalar exchange is considered for the processes, while the scalar exchange is considered for the process.
Iii separation of the resonance contributions
It should be remarked that the amplitudes in terms of the harmonic oscillator principal quantum number are the sum of a set of SU(6) multiplets with the same . To see the contributions of an individual resonance listed in Tab. 1, we need to separate out the singleresonanceexcitation amplitudes within each principal number in the channel.
We have noticed that the transition amplitude has a unified form Hamilton:1963zz :
(36) 
where . The nonspinflip and spinflip amplitudes and can be expanded in terms of the familiar partial wave amplitudes for the states with :
(37)  
(38) 
Combining Eqs. (37) and (38), firstly, we can separate out the partial waves with different in the same . For example, in the shell, only the () wave contributes to the reaction; in the shell, both () and () waves contribute to the reaction; and in the shell, only the and waves are involved in the process. The separated partial amplitudes, , up to the shell are given by Zhong:2009 ; Zhong:2007fx
(39)  
(40)  
(41)  
(42)  
(43)  
Then, using the Eqs. (37) and (38) again, we can separate out the partial amplitudes for the states with different in the same as well. For example, we can separate out the resonance amplitudes with [i.e., ] and [i.e., ] from the amplitude .
Finally, we should sperate out the partial amplitudes with the same quantum numbers , , in the different representations of the constituent quark model. We notice that the resonance transition strengths in the spinflavor space are determined by the matrix element . Their relative strengths () can be explicitly determined by the following relation:
(44)  
At last, we obtain the singleresonanceexcitation amplitudes by the relation:
(45) 
In this work, the values of for the reactions , and have been derived in the symmetric quark model, which have been listed in Tab. 2.