^{1}

^{*}

^{1}

^{*}

^{2}

^{*}

The masses of the recently reported by LHCb two pentaquark charmonium states P
_{c}* (4380) and P
_{c}* (4450) which are suggested to possess pentaquark configuration (
) have been estimated considering a dihadronic state consisting of a meson
and a baryon (uud). The binding energies of the states have been estimated with a van der Walls type of molecular interaction between the hadrons. A spin interaction has also been considered. Masses of these two states are well reproduced with the aforesaid molecular interaction which indicates that the multiquarks P
_{c}* (4380) and P
_{c}* (4450) can be well described as meson-baryon bound states.

The existence of pentaquark charmonium states with the decay of

identified as sum of two up quarks, one down quark, one charm quark and one anti-charm quark with spin

study of the properties and dynamics of multiquark states [

In the present work pentaquark states

stituent hadrons [

has also been considered. Masses of

Assuming the pentaquark states as meson-baryon system the mass formula for the low-lying di-hadronic molecule runs as:

where M_{1}, M_{2} represent the masses of the constituent hadrons respectively, E_{BE} represents the binding energy of the di-hadronic system and E_{SD} represents the spin-dependent term.

The binding energy can be expressed as:

where r is the radius parameter of the di-hadronic molecule and V(r) is the di-hadronic molecular potential which is expressed as [

where k_{mol} [_{12} → ∞) of the residual confined one-gluon exchange interaction with strength k_{mol} [

Ψ(r) is the wave function of the di-hadronic state. To estimate E_{BE} we have used the wave functions for the ground state of the hadronic molecule from statistical model which runs as: [

corresponding to the linear type of background potential and harmonic type of background potential respectively [_{12} is the radius of the hadronic molecule and _{12} = r_{1} + r_{2}, where r_{1} and r_{2} represent the individual radii of the hadrons constituting the molecule respectively and using Equations (2), (3) and (4) we get E_{BE} as:

where_{mol} = 0.59 and 0.65 [^{−1} and 5.977 GeV^{−1} respectively. The radius of ^{−1}.

The spin hyperfine interaction can be expressed as [

where M_{1} and M_{2} are the masses of the constituent hadrons in the di-hadronic molecule, α_{s} is the strong interaction constant, S_{1} and S_{2} are the spins of the hadrons involved, _{s} = 0.59 [_{SD} has been estimated subsequently using the relation (8). The masses of _{1}) and baryon (M_{2}) [

In the present work we have estimated masses of particles

ing them as di-hadronic (meson-baryon) molecules. The masses have been obtained as 4171 MeV and 4492 MeV for

that the pentaquarks

Waals type of interaction between them. It is also pertinent to point out that the statistical model wave function is also very successful in describing the hadrons. The pentaquark state is one of the leading candidates for the study of the multiquark state. The description of pentaquark as diquark-diquark-antiquark state has been done by a number of authors [

allowed decay channels is given by

With ^{ } | With ^{ } | |||||
---|---|---|---|---|---|---|

Particle | State | E_{BE} + E_{SD} (MeV) | M (MeV) | E_{BE} + E_{SD} (MeV) | M (MeV) | M_{exp} (MeV) [ |

136 | 4171 | 133 | 4168 | 4380 ± 8 ± 29 | ||

163 | 4492 | 162 | 4491 | 4449.8 ± 1.7 ± 2.5 |

Authors are thankful to University Grants Commission, New Delhi, India for their financial supports.

Rismita Ghosh,Aparajita Bhattacharya,Ballari Chalrabarti, (2015) The Masses of P_{c}* (4380) and P_{c}* (4450) as Di-Hadronic States. Journal of Modern Physics,06,2070-2073. doi: 10.4236/jmp.2015.614213