Possible Description of the Excited States of the Neutral Charmed Omega in Terms of a First-Order Pentaquark Mass Formula

Bevelacqua Resources,


Introduction
The possibility that hadrons could exist with structures beyond conventional qq or qqq quark configurations was noted by Gell-Mann 1 .Numerous data obtained by several collaborations (Belle, BABAR, LHCb, and BESII) produced exotic hadrons that appear to be inconsistent with the conventional quark model 2,3 .These structures have been suggested with a recent example noted in Ref. 4.
The LHCb Collaboration 4 , recently reported the observation of new Ω 0 c excited states decaying to a Ξ + c K¯ final state.
baryons masses in terms of effective quark masses.Within this formulation, quark wave functions are assumed to reside in their lowest S state.These mass formulas are used as the basis for deriving a first-order pentaquark mass formula.In particular, the model proposed in this paper assumes the pentaquark is partitioned between two and three quark clusters with the interaction between the clusters providing a minimal contribution to the pentaquark mass.
The meson (m) mass (M) formula of Refs.12 and 13 is: where m 1 (m 2 ) is the mass of the first (second) quark comprising the meson, m o is the average mass of a first generation quark 5,14 , and the σ i (i = 1 and 2) are the spin vectors for the quarks incorporated into the meson.The parameters δ m and b m are 40 MeV and 615 MeV, respectively 13 .
The last term in Eq. 1 represents the spin-spin interaction of the quarks and is the scalar product of the quark spin vectors.has the value -3/4 and +1/4 for pseudoscalar and vector mesons, respectively.
In a similar manner, the baryon (b) mass formula 12,13 is: where the m i labels the three baryon quarks (i = 1, 2, and 3) and δ b and b b are 230 MeV and 615 MeV, respectively 13 .For a particle with a total baryon spin 1/2, the following prescription is used if the baryon (comprised of three quarks q 1 , q 2 , and q 3 ) contains two identical quarks 13 q 2 , and q 3 σ 2 •σ 3 = 1/4 (3) For completeness, the reader should note that σ i •σ j has the value +1/4 for a J= 3/2 baryon.In addition, these basic σ i •σ j relationships must be modified if the baryon contains three different quarks.The methodology is detailed, and described in Ref. 13.
In formulating the pentaquark mass formula, effective quark masses provided by Griffiths 14 are utilized.These effective masses for d, u, s, c, b, and t quarks are 340, 336, 486, 1550, 4730, and 177000 MeV/c 2 , respectively.These masses are utilized in Eqs. 1 and 2.
The first-order mass formula used in this paper partitions the pentaquark into two clusters.The first cluster is a meson (m) and the remaining cluster is a baryon (b).Zero angular momentum is assumed between the two clusters.These simplifications are incorporated to minimize model complexity that is consistent with an initial first-order formulation.In particular, the pentaquark mass formula (M) is assumed to have the form: where Φ defines the interaction between the meson and baryon clusters.Within the scope of this mass formula, the meson-baryon cluster interaction is assumed to be weak and sufficiently small to be ignored.Accordingly, Eq. 5 represents a quasimolecular five quark system whose basic character is a weakly bound meson-baryon system.In the case of the sscqq-bar pentaquark system, the first cluster is a qq-bar meson and the remaining cluster is an ssc baryon.