Open access peer-reviewed chapter

Spectrosopic Study of Baryons

By Zalak Shah and Ajay Kumar Rai

Reviewed: April 8th 2021Published: May 10th 2021

DOI: 10.5772/intechopen.97639

Downloaded: 141

Abstract

Baryons are the combination of three quarks(antiquarks) configured by qqq(q¯q¯q¯). They are fermions and obey the Pauli’s principal so that the total wave function must be anti-symmetric. The SU(5) flavor group includes all types of baryons containing zero, one, two or three heavy quarks. The Particle Data Froup (PDG) listed the ground states of most of these baryons and many excited states in their summary Table. The radial and orbital excited states of the baryons are important to calculate, from that the Regge trajectories will be constructed. The quantum numbers will be determined from these slopes and intersects. Thus, we can help experiments to determine the masses of unknown states. The other hadronic properties like decays, magnetic moments can also play a very important role to emphasize the baryons. It is also interesting to determine the properties of exotic baryons nowadays.

Keywords

  • baryons
  • potential model
  • mass spectra
  • Regge trajectories
  • decays

1. Introduction

The particle physics has a remarkable track record of success by discovering the basic building blocks of matter and their interactions. Everything in the observed universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. All of these are encapsulated in the Standard Model (SM). The Standard Model has been established in early 1970s and so far it is the most precise theory ever made by mankind. In the Standard Model elementary particles are considered to be the constituents of all observed matter. These elementary particles are quarks and leptons and the force carrying particles, such as gluons and W, Z bosons. All stable matter in the universe is made from particles that belong to the first generation; any heavier particles quickly decay to the next most stable level. The concept of the quark was first proposed by Murray Gell-Mann and George Zweig in 1937. The quarks have very strong interaction with each other, that is a reason, they always stuck inside composite system. But quarks interact with leptons weakly, the best example of this is protons, neutrons and electrons of atomic nuclei. The flavored quarks combine together in various aggregates called hadrons. The Standard Model includes 12 elementary particles of half-spin known as fermions. They follow the Pauli exclusion principle and each of them have a corresponding anti-particle. There are also twelve integer-spin particles which mediate interactions between these particles known as Bosons. They obey the Bose-Einstein statistics. The classification of bosons and fermions along with hadrons are drawn in Figure 1.

Figure 1.

The classifications of particles.

The Quantum Chromodynamics (QCD) as the theory of strong interactions was successfully used to explore spectroscopic parameters and decay channels of hadrons during last five decades. The interaction is governed by massless spin 1 objects called gluons. Quarks inside the hadrons exchange gluons and create a very strong color force field. To conserve color charge, quarks constantly change their color by exchanging gluons with other quarks. As the quarks within a hadron get closer together, the force of containment gets weaker so that it asymptotically approaches zero for close confinement. The quarks in close confinement are completely free to move about. This condition is referred to as “asymptotic freedom”. An essential requirements for the progress in hadronic physics is the full usage of present facilities and development of new ones, with a clear focous on experiments that provide geniune insight into the inner workings of QCD.

Hadron spectroscopy is a tool to reveal the dynamics of the quark interactions within the composite systems. The short-lived hadrons and missing excited states could be identified through the possible decays of the resonance state. The experimentally discovered states are listed in summary tables of Particle Data Group [1]. The worldwide experiments such as LHCb, BELLE, BARBAR, CDF, CLEO are main source of identification of heavy baryons so far and especially LHCb and Belle experiments have provided the new excited states in heavy baryon sector recently [2]. The various phenomenological approaches for spectroscopy is all about to use the potential and establish the excited resonances. These approches are, relativistic quark model, HQET, QCD Sum rules, Lattice-QCD, Regge Phenomology, and many Phenomenological models [3, 4, 5, 6, 7, 8]. An overview to the current status of research in the field of baryon physics from an experimental and theoretical aspects with a view to provide motivation and scope for the present chapter. The present study covers the baryons with one heavy and two light quarks [9, 10, 11, 12, 13]; two heavy and one light quark [14, 15] as well as three heavy quarks [16, 17, 18]. We also like to discuss the spectroscopy of nucleons [19, 20]. The decay properties, magnetic moments and Regge Trajectories are also discussed.

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2. Light, heavy flavored baryons and exotics

In the case of baryons, when three same quark combines, definitely their electric charge, spin, orbital momentum would be same. This might violates the Pauli exclusion principal stated “no two identical fermions can be found in the same quantum state at the same time”. However, the color quantum number of each quark is different so that the exclusion principle would not be violated. One of the most significant aspects of the baryon spectrum is the existence of almost degenerate levels of different charges which have all the characteristics of isospin multiplets, quartets, triplets, doublets and singlets. A more general charge formula that encompasses all these nearly degenerate multiplets is

Q=I3+12Y,Y=B+S+C/BE1

where Q, I3, Y, B, C, S, B′ are referred as charge, isospin, hypercharge, baryon number, charm, strangeness and bottomness,respectively. The strangeness of baryon is always negative.

The baryons are strongly interacting fermions made up of three quarks and have 12integer spin. They obey the Pauli exclusion principle, thus the total wave function must be anti-symmetric under the interchange of any two quarks. Since all observed hadrons are color singlets, the color component of the wave function must be completely anti-symmetric.

For Octet,suss+sdss=1symmetricsuss+sdss=0antisymmetric
For Decuplet,suss+sdss=12symmetricsuss+sdss=32antisymmetric

Here, su, sdand ssare spin of u,d,squarks.

It was considered that u, d and s are the sole elementary quarks. The symmetry group to consider three flavors of quark is done by SU(3) symmetry group. SU(3) flavor symmetry of light quarks. Each of these symmetries refers to an underlying threefold symmetry in strong interaction physics. SU(3) is the group symmetry transformations of the 3-vector wavefunction that maintain the physical constraint that the total probability for finding the particle in one of the three possible states equals 1. A Young diagram is the best way to represnts the symmetriesconsists of an array of boxes arranged in one or more left-justified rows, with each row being at least as long as the row beneath. The correspondence between a diagram and a multiplet label is: The top row juts out αboxes to the right past the end of the second row, the second row juts out βboxes to the right past the end of the third row, etc. The representation is shown in Figures 2 and 3.

Figure 2.

The representation of the multiplets (1,0), (0,1), (0,0), (1,1), and (3,0) in SU(3) diagrams.

Figure 3.

A standard young tableaux forN= 3.

The flavor wave functions of baryon states can then be constructed to be members of SU(3) multiplets as [5].

333=10S8M8M1A

Murray Gell-Mann introduced the Eightfold geometrical pattern for mesons and baryons in 1962 [21]. The eight lighest baryons fit into the hexagonal array with two particle in center are called baryon octet. A triangular array with 10 particles are called the baryon decuplet. Moreover, the antibaryon octet and decuplet also exist with opposite charge and strangeness [22]. Baryons having only uand dquarks are called nucleons Nand Δresonances. The protonand neutronhave spin (I3=12) and Δparticles have spin (I3=32). The four possible four combinations of the symmetric wave function gives four Δparticles; Δ++(uuu, I3=3/2), Δ+(uud, I3=1/2), Δ0(udd, I3=1/2) and Δ(ddd, I3=3/2). Particles with combination of u, dand squarks are called hyperons; Λ, Σ, Ξand Ω. While discussing heavy sector baryons, we need baryons having heavy quark(s) combination. Any squark(s) of hyperon baryons can be replaced by heavy quark (c, b) in heavy baryon particles. The added heavy quark(s) will be added to the suffix of the particular baryon. The particles are also depend on isospin quantum number, such that Σand Ξbaryons have isospin triplets and doublets, respectively. Λcand Σc(Λband Σb) are formed by replacing one squark. For Ξbaryon, replacement of one s quark gives Ξc(Ξb) and the particles Ξcc, Ξbband Ξbcfound while replacing two squarks. The biggest family is found for Ωparticle. Replacement of one squark gives Ωc(Ωb); two squarks replace to provide Ωcc, Ωbband Ωbc; all three quark replacement with squark give Ωccc, Ωbbb, Ωbbcand Ωccbparticles.

SU(4) group includes all of the baryons containing zero, one, two or three heavy Q(charm or beauty) quarks with light u, d and s quarks. The number of particles in a multiplet, N=N(α,β,γ) is

N=α+11β+11γ+11α+β+22(β+γ+2)2α+β+γ+33E2

It is clear from Eq. (2) that multiplets that are conjugate to one another have the same number of particles, but so can other multiplets. The multiplets (3,0,0) and (1,1,0) each have 20 particles. This multiplet structure is expected to be repeated for every combination of spin and parity which provides a very rich spectrum of baryonic states. The multiplet numerology of the tensor product of three fundamental representation is given as:

444=202012024¯.E3

Representation shows totally symmetric 20-plet, the mixed symmetric 20′-plet and the total anti-symmetric 4¯multiplet. The charm baryon multiplets are presented in Figure 4. The ground levels of SU(4) group multiplets are SU(3) decuplet, octet, and singlet, respectively. These baryon states can be further decomposed according to the heavy quark content inside. According to the symmetry, the heavy baryons belong to two different SU(3) flavor representations: the symmetric sextet 6sand anti-symmetric anti-triplet 3¯A. It can also be represented by young tableaux (refer Figure 2). The observed resonances of all light and heavy baryons are listed in PDG (2020) baryon summary Table 1.

Figure 4.

The baryon multiplets in SU(4) group. (a) the spin 3/2 20-plet, (b) the spin 1/2 20′-plet and (c)4¯singlet [1].

NamesExp. Mass (GeV) [1]Predicted Mass (GeV)Baryon State
Λc+27652180832766.6±2.4267822S12
Λc+29402939.31.5+1.42927,291022P12,22P32
Σc++280028016+42856,279112P32,14P52
Σc+280027925+142805,278312P32,14P52
Σc028002806±8±102799,277812P32,14P52
Ξc29302931±3±52750,273312P32,12P52
Ξc+29702971.4±3.32944,305922S12,24S32
Ξc029702968.0±2.62903,285922S12,24S32
Ξc+30553054.2±1.2±0.5308812D32
Ξc+30803077.0±0.4306212D52
Ξc030803079.9±1.43162,299712D32, 14D32
Ξc+31233122.9±1.3±0.3303912D72
Ξcc+35203518.9±0.9352012S12

Table 1.

Our predicted baryonic states are compared with experimental unknown (JP) excited states.

2.1 Exotics: non-conventional hadrons

Apart from the simplest pairings of quarks-anti quarks in formation of mesons and baryons, there are many observed states that do not fit into this picture. Numerous states have recently been found and some of those have exotic quark structures. Some of these exotics states are experimentally explained as tetraquarks(contains two-quarks and two anti-quarks) and pentaquarks(contains four-quarks plus an anti-quark) states with active gluonic degrees of freedom (hybrids), and even states of pure glue (glueballs) so far. Many experiments Belle, Barabar, CLEO, BESIII, LHCb, ATLAS, CMS and DO collaborations are working on the investigation of these exotic states. The theoretical approaches such as effective field theories of QCD, various quark moels, Sum rules, Lattice QCD, etc. also preicted many states of the exotic states.

The two pentaquarks Pc+4380and Pc+4450, discovered in 2015 by the LHCb collaboration, in the J/ψpKinvarnt mass distribution [23]. The newly observed states, Pc+4440, Pc+4457, Pc+4312were investigated via different methods in 2019 by LHCb. These states are considered in various recent studies and the majority suggested as negative spin parity quantum number [24]. The investigations of pentaquark states resulted in support of different possibilities for their sub-substructures leaving their structures still ambiguous. Therefore to discriminate their sub-structure we need further theoretical and experimental investigations.

R. Jaffe obtained six-quark states built of only light u, d, and s quarks called as dibaryonor hexaquarkthat belong to flavor group SUf3. Using for analysis the MIT quark-bag model, Jaffe predicted existence of a H-dibaryon, i.e., a flavor-singlet and neutral six-quark uuddss bound state with isospin–spin-parity IJP=00+[25]. In the past fifteen years, new states have been observed called the XYZ states, different from the ordinary hadrons. Some of them, like the charged states, are undoubtedly exotic. Theoretical study include the phenomenological quark model to exotics, non-relativistic effective field theories and lattice QCD calculations and enormous experimental studies we can see on XYZ states.

As a hadronic molecule [26, 27], deuteron has been well-established loosely bound state of a proton and a neutron. Ideally, the large masses of the heavy baryons reduce the kinetic energy of the systems, which makes it easier to form bound states. Such a system is approximately non- relativistic. Therefore, it is very interesting to study the binding of two heavy baryons dibaryonand a combination of heavy baryon and an antibaryon baryonium.

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3. Specroscopic properties

Hadron spectroscopy is a key to strong interactions in the region of quark confinement and very useful for understanding the hadron as a bound state of quarks and gluons. Any system within a standard model becomes difficult to deal considering all the interaction of quark-quark, quark-gluon and gluon-gluon. This is the reason for using constituent quark mass incorporating all the other effects in the form of some parameters. The bound state heavy baryons can be studied in the QCD motivated potential models treating to the non relativistic Quantum mechanics. A Constituent Quark Model is a modelization of a baryon as a system of three quarks or anti-quarks bound by some kind of confining interaction. The present study deals with the Hypercentral Constituent Quark Model(hCQM), an effective way to study three body systems is through consideration of Jacobi coordinates.

The hypercentral approach has been applied to solve bound states and scattering problems in many different fields of physics and chemistry. The basic idea of the hypercentral approach to three-body systems is very simple. The two relative coordinates are rewritten into a single six dimensional vector and the non-relativistic Schrödingerequation in the six dimensional space is solved. The potential expressed in terms of the hypercentral radial co-ordinate, takes care of the three body interactions effectively [28]. The ground states and some of the excited states of light baryons has also been affirmed theoretically by this scheme. It is interesting to identify the mass spectrum of heavy baryons(singly, doubly and triply) in charm as well as bottom sector and then to the light sector. We consider a nonrelativistic Hamiltonian given by

H=Px22m+VxE4

where, m=2mρmλmρ+mλ, is the reduced mass and mρand mλare reduced masses of Jacobi co-ordinates ρand λ. xis the six dimensional radial hyper central coordinate of the three body system. Non-relativistically, this interaction potential, Vxconsists of a central term Vcrand spin dependent part VSDr. The central part Vcris given in terms of vector (Couloumb) plus scalar (confining) terms as

Vcr=VV+VS=23αsr+βrνE5

The short-distance part of the static three-quark system, arising from one-gluon exchange within baryon, is of Coulombic shape. Here, we can observe that the strong running coupling constant (αs) becomes smaller as we decrease the distance, the effective potential approaches the lowest order one-gluon exchange potential given in Eq. (4) as r 0. So, for short distances, one can use the one gluon exchange potential, taking into account the running coupling constant αs. We employ the Coulomb plus power potential (CPPv) with varying power index ν, as there is no definite indication for the choices of νthat works at different hadronic sector. The values of potential index νis varying from 0.5 to 2.0; in other words, S.R (1/2), linear (1.0), 3/2 power- law (1.5) and quadratic (2.0) potentials are taken into account in case of singly heavy baryon. The hypercentral potential V(x) as the color coulomb plus power potential with first order correction and spin-dependent interactionare written as,

Vx=V0x+1mρ+1mλV1x+VSDxE6

where V0xis given by the sum of hyper Coulomb(hC) interaction and a confinement term

V0x=τx+βxνE7

and first order correction as similar to the one given by [29],

V1x=CFCAαs24x2E8

Here, CFand CAare the Casimir charges of the fundamental and adjoint representation. For computing the mass difference between different degenerate baryonic states, we consider the spin dependent part of the usual one gluon exchange potential (OGEP). The spin-dependent part, VSDxcontains three types of the interaction terms, such as the spin–spin term VSSx, the spin-orbit term VγSxand tensor term VTx. Considering all isospin splittings, the ground and excited state masses are determined for all heavy baryon system. The radial excited states from 2S–5S and orbital excited states from 1P-5P, 1D-4D and 1F–2F are calculated using the hCQM formalism. These mass spectra can be found in our Refs. [10, 11, 12, 13, 14, 15, 16, 17, 18].

The correction used in the potential have its dominant effect on potential energy. In our calculation, the effect of the correction to the potential energy part is decreasing as mass of the system increasing. For example, if noticed the maximum effect of heavy Ξbaryon family then, for the radial excited states of Ξbaryons are Ξc(3.0%) >Ξcc(3.0%) >Ξb(0.41%) >Ξbc(0.3%)>Ξbb(0.16%). The orbital excited states are (1.4–3.5%) for Ξc, (0.1–0.4%) for Ξband in case of doubly heavy region the error is rising in order of baryons Ξbb>Ξbc>Ξcc. Singly heavy baryons show the effect from (0.1–1.7%), Doubly heavy baryons show the effect from (0.1–1.0%) and Triply heavy baryons show the effect from (0.2–0.9%) in orbital excited states. For better idea, we shown the effect of masses with and without first order corrections in case of Σcbaryon (See, Figure 5). In the Figure, we plotted the graph of potenial index vs. mass. The radial excited states 2S–5S and the orbital excited states 1P-5P are shown for Σc++,Σc0and Σc+baryons.

Figure 5.

Spectra ofΣtriplets in S and P state with and without first order correction [13].

Recently, we calculate the masses of Nand Δresonances using the hCQM model by adding the first-order correction to the potential. The complete mass spectra with individual states graphically compared with the experimental states in Figure 6. We can observe that, many states are in accordance with the experimental resonances. We also predicted the JPvalues of unknown states.

Figure 6.

The resonances are predicted from the first radial excited state (2S) to the orbital excited state (2F) forNbaryons [19].

3.1 Regge trajectoy

We can say that, the mass spectra of hadrons can be conveniently described through Regge trajectories. These trajectories will aid in identifying the quantum number of particular resonance states. The important three properties of Regge Trajectories are: Linearity, Divergence and Parallelism.The higher excited radial and orbital states mass calculation enable to construct the Regge trajectories in the (n, M2) and (J, M2) planes. These graphical representation is useful in assigning JPvalue to the experimental unkown states. We are getting almost linear, parallel and equidistance lines in each case of the baryons.

Some of the obtained masses are plotted in accordance with quantum number as well as with natural and unnatural parities. For the singly heavy baryons, the trajectory is shown for Ξcdoublets baryons (See, Figure 7). For the doubly heavy baryons, the spectra of Ξbcand Ωbcare less determined till the date. Thus, we plotted their trajetories in Figure 8. The natural and unnatural parities are shown in (J, M2) for all triply heavy baryons; Ωccc, Ωbbb, Ωbbcand Ωccb(See, Figures 9 and 10). The rest trajetories of all heavy baryon families in both planes can be found in our articles.

Figure 7.

Variation of mass forΞc0andΞc+with different states. The (M2n) Regge trajectories forJPvalues1+2,12and5+2are shown from bottom to top. Available experimental data are also given with particle names [13].

Figure 8.

The doubly charm-beauty baryons in (M2n) plane [14,15].

Figure 9.

The triply charm and triply bottom Regge trajectories in (J,M2) plane [16].

Figure 10.

Parent and daughter (J,M2) Regge trajectories for triply heavy charm-beauty baryons with natural (first) and unnatural (second) parities [17,18].

3.2 Decays: strong, radiative and weak

The particles which are known to us decay by a similar sort of dissipation. Those who decay rapidly are unstable and take a long time are metastable. Some particles, like electron, three lightest neutrinos(and their antiparticles), the photon are stable partices (neverdecays). The observations of decays of baryon and meson resonances afford a valuable guidance in assigning to the correct places in various symmetry schemes. The correct isotopic spin assignment is likely to be implied by the experimental branching ratio into different charge states of particles produced by the decay,while experimental decay widths provide a means of extracting phenomenological coupling constants. For the success of a particular model, it is required to produce not only the mass spectra but also the decay properties of these baryons.

For the success of a particular model, it is required to produce not only the mass spectra but also the decay properties of these baryons. The masses obtained from the hypercentral Constitute Quark Model (hCQM) are used to calculate the radiative and the strong decay widths. Such calculated widths are reasonably close to other model predictions and experimental observations (where available) [30]. The effective coupling constant of the heavy baryons is small, which leads to their strong interactions perturbatively and makes it easier to understand the systems containing only light quarks. The Heavy Hadron Chiral Perturbation Theory (HHCPT) describes the strong interactions in the low-energy regime by an exchange of light Goldstone boson. Some of the strong P -wave couplings among the s-wave baryons and S-wave couplings between the s-wave and p-wave baryons are shown in Table 2 with PDG values.

Decay modePresentPDG
Pwave transitionsΣc++12S12Λc+π+1.721.890.18+0.09
Pwave transitionsΣc+12S12Λc+π01.60<4.6
Pwave transitionsΣc012S12Λc+π1.171.830.19+0.11
Swave transitionsΣc++12P12Λc+π+68.197517+22
Swave transitionsΣc+12P12Λc+π062.926240+60
Swave transitionsΣc012P12Λc+π66.447215+22
Swave transitionsΛc+12P12Σc0π+4.452.6 ± 0.6

Table 2.

Several strong one-pion decay rates (in MeV) [30].

The electromagnetic properties are one of the essential key tools in understanding the internal structure and geometric shapes of hadrons. In the present study, the magnetic moments of heavy flavor and light flavor baryons are computed based on the non-relativistic hypercentral constituent quark model using the spin-flavor wave functions of the constituent quark and their effective masses [11, 13]. Generally, the meaning of the constituent quark mass corresponds to the energy that the quarks have inside the color singlet hadrons, we call it as the effective mass. The magnetic moment of baryons are obtained in terms of the spin, charge and effective mass of the bound quarks. The study has been performed for all singly, doubly and triply heavy baryon systems for positive parity JP=12+,3+2.

μB=iϕsfμizϕsfE9

where

μi=eiσi2mieffE10

eiis a charge and σiis the spin of the respective constituent quark corresponds to the spin flavor wave function of the baryonic state. The effective mass for each of the constituting quark mieffcan be defined as [31].

mieff=mi1+HimiE11

where, H= E + Vspin. Using these equations, we calculate magnetic moments of singly, doubly and triply heavy baryons. The spin flavor wave function [32] ϕsfof all computed heavy flavor baryons are given in Table 3.

BaryonsfunctionOurBaryonsfunctionOur
nudd43μd13μu−1.997Δ2μu+ μd2.28
Σc++uuc43μu13μc1.834Σc++2μu+ μc3.263
Σc0udc43μd13μc−1.091Σc+μu+ μd+ μc1.1359
Σc+ddc23μu+ 23μd13μc0.690Σc02μd+ μc−1.017
Ξc0dsc23μd+ 23μs13μc−1.011Ξc0μd+ μs+ μc−0.825
Ξc+usc23μu+ 23μs13μc0.559Ξc+μu+ μs+ μc1.329
Ωc0ssc43μs13μc−0.842Ωc02 μs+ μc−0.625
Σb+uub43μu13μb2.288Σb+2μu+ μb3.343
Σbddb43μd13μb−1.079Σb2μd+ μb−1.709
Ξb0usb23μu+ 23μs13μb0.798Ξb0μu+ μs+ μb1.072
Ξbdsb23μd+ 23μs13μb−0.943Ξbμd+ μs+ μb−1.471
Ωbssb43μs13μb0.761Ωb2 μs+ μb−1.228
Ξcc+dcc43μc13μd0.784Ξcc+2 μc+ μd0.068
Ξcc++ucc43μc13μu0.031Ξcc++2 μc+ μu2.218
Ξbbdbb43μb13μd0.196Ξbb2 μb+ μd−1.737
Ξbb0ubb43μb13μu−0.662Ξbb02 μb+ μu1.6071
Ξbc0dbc23μb+ 23μc13μd0.527Ξbc0μb+ μc+ μd−0.448
Ξbc+ubc23μb+ 23μc13μu−0.304Ξbc+μb+ μc+ μu2.107
Ωcc+ccs43μc13μs0.692Ωcc+2 μc+ μs0.285
Ωbb(bbs)43μb13μs0.108Ωbb2 μb+ μs−1.239
Ωbc0(bcs)23μb+ 23μc13μs0.439Ωbc0μb+ μc+ μs−0.181
Ωbcc+bcc43μc13μb0.606Ωbcc+μb+ 2μc0.8198
Ωbbc0bbc43μb13μc−0.233Ωbbc+2μb+ μc0.228

Table 3.

Magnetic moments (in nuclear magnetons) with spin-flavor wavefunctions of JP=1+2,3+2are listed for nucleons(light) and singly, doubly, triply(heavy) baryons.

The electromagnetic radiative decay width is mainly the function of radiative transition magnetic moment μBCBc(in μN) and photon energy (k) [12] as

Γγ=k34π22J+1emp2μBcBc2E12

where mpis the mass of proton, Jis the total angular momentum of the initial baryon Bc. Some radiative decays are mentioned below:

  • Σc0Σc0: 1.553

  • ΞcΞc0: 0.906

  • Ωc0Ωc0: 1.441

  • Σc0Λc+: 213.3

Weak decays of heavy hadrons play a crucial role to understand the heavy quark physics. In these decays the heavy quark acts as a spectator and the light quark inside heavy hadron decays in weak interaction [33]. The transition can be suor dudepending on the available phase space. Since the heavy quark is spectator in such case, one can investigate the behavior of light quark system. These kind of small phase space transition could be possible in semi-electronic, semi-muonic and non leptonic decays of the heavy baryons and mesons. We calculate here, the semi-electronic decays for strange-charm heavy flavor baryons Ωc, Ξc, Ξband Ξbusing our spectral parameters.

The differential decay rates for exclusive semi-electronic decays are given by [33],

dΓdw=GF2M5VCKM2192π3w21PwE13

where Pwcontains the hadronic and leptonic tensor. Assuming that the form factors are slowly varying functions of the kinematic variables, we may replace all form factors by their values at variable w=1. The calculated semi-electronic decays for Ξc, Ωc, Ξband Ωbbaryons are listed in Table 4. We can observe that our results are in accorance with ref. [33] for singly heavy baryons.

ModeJPJP'Decay Rates(GeV)Ref. [33]
Ξc0Λc+eν¯1+21+27.839×10197.839×10197.91×1019
Ξc0Σc+eν¯1+21+24.416×10237.023×10246.97×1024
Ωc0Ξc+eν¯1+21+22.143×10182.290×10182.26×1018
Ωc0Ξc+eν¯1+23+22.057×10282.436×10281.49×1029
ΞbΛb0eν¯1+21+25.928×10196.16×1019
ΩbΞb0eν¯1+21+24.007×10184.05×1018
ΩbΞb0eν¯1+23+21.675×10263.27×1028

Table 4.

Semi-electronic decays in sutransition for charm baryons are listed [13].

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4. Current cenario in the field of baryons

Baryons with heavy quarks provide a beautiful laboratory to test our ideas of QCD. As the heavy quarks mass increases its motion decreases and the baryons properties are increasingly governed by the dynamics of the light quark and approach a universal limit. As we discussed, many theoretically approaches are calculating and obtaning the masses and decay widths of heavy baryons. We study the mass spectroscopy of ligt and heavy baryons and their properties. A few number of excited states for the singly heavy baryons have also been reported along with their ground states. The singly charmed baryons are, Λc2286+, Λc2595+, Λc2625+, Λc2880+, Λc2940+, Λc2765+,Λc2860+, Σc2455++,+,0, Σc2520++,+,0, Σc2800++,+,0,Ξc2468+,0, Ξc'2580+,0, Ξc'2645+,0, Ξc2790+,0, Ξc2815+,0, Ξc'29300, Ξc2980+,0, Ξc3055+, Ξc3080+,0, Ξc'3123+, Ωc26950, Ωc27700. The singly beauty baryons are Λb56190, Λb59120, Λb59200, Σb5811+, Σb5816, Σb5832+, Σb5835, Ξb5790,0, Ξb59450, Ξb5955, Ξb5935'. And now, LHCb experiment has identified new resonances(excited states) for singly heavy baryons (See, Table 5). The experimental state and masses are in first two columns. The third column shows our predicted masees and in the forth column we assign the states with JPvalues. We can observe that, apart from first radial and orbital excited states, we also have D state resonances in heavy sector. According to the SU(3) symmetry we also have doubly and triply baryons in charm as well as bottom sector. Among which, the evidence of 1S state for doubly heavy baryons Ξcc+and Ξcc++are observed by the SELEX and the LHCb experiments respectively. The Belle and CDF collaboration had also observed some of the particles. The fulture experiments like Panda, Belle-II and BES-II are expected to give more results soon.

NamesExp. Mass (MeV) [2]Predicted Mass (MeV)Baryon State
Λc+28602756.1 ± 0.5284212D32
Ωc300003000.4 ± 0.2 ± 0.10.50.32976,299312P32,14P32
Ωc305003050.4 ± 0.1 ± 0.10.50.33011,302812P12,14P12
Ωc306603065.6 ± 0.1 ± 0.30.50.3294714P52
Ωc309003090.2 ± 0.3 ± 0.50.50.33011,302812P12,14P12
Ωc311903119.1 ± 0.3 ± 0.90.50.33100,312622S12,22S12
Ξcc++36203521.4 ± 0.99351112S12
Ξc029652964.88 ± 0.262903,294012S12
Λb+60726072.3 ± 2.9606622S12
Λb+61466146.17 ± 0.33612112D32
Λb+61526152.51 ± 0.26611912D52
Σb+60976098 ± 1.7612212P12
Σb6097+6095.8 ± 1.7613112P12
Ωb63166315.64 ± 0.31 ± 0.07631314P52
Ωb63306330.3 ± 0.28 ± 0.07633112P12,14P12
Ωb63406339.71 ± 0.26 ± 0.05632112P32
Ωb63506349.88 ± 0.35 ± 0.05632614P32
Ξb622706227.11.51.4±0.56193,630922S12,24S32

Table 5.

The newly observed baryonic states are listed with the observed mass in column 1 & 2. Our predicted baryonic states are compared with JPvalue and masses.

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zalak Shah and Ajay Kumar Rai (May 10th 2021). Spectrosopic Study of Baryons, Quantum Chromodynamic, Zbigniew Piotr Szadkowski, IntechOpen, DOI: 10.5772/intechopen.97639. Available from:

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