Masses of the Doubly-heavy Tetraquarks in a Constituent Quark Model

Abstract

We perform a constituent quark model analysis for the masses of the doubly heavy tetraquark states TQQ after we fix the parameters to fit the masses of the newly observed Ξ ++ cc and hadrons involving heavy quarks relevant to the stability of these states. We investigate in detail how the relative distances between quark pairs vary as we change the quark content and how they affect the various contributions to the total tetraquark masses. We also find that our full calculations give in general less binding compared to simplified quark model calculations that treat quark dynamics inside the tetraquark the same as that inside a baryon. We trace the main origin to be the differences in the number of relative kinetic energies which increases as one goes from meson, baryon and tetraquarks. We also compare our new results with previous works using less constrained parameters and find that the tetraquark state T bb (udbb) and T bb (usbb) are bound by 120.56 MeV and 7.3 MeV respectively.

Masses of doubly heavy tetraquarks $T_{QQ^\prime}$ in a relativized quark model

“…[25,35,46,49,66,67], and others predicted a state near the open bottom thresholds[30,63]. Our results show that the lowest {bb}[ ū s] state is about 40 MeV above the Bs B * and B * s B thresholds.…”

Fully heavy pentaquark states in constituent quark model

“…Moreover, in order to understand the composition of the total energy of the pentaquark states in comparison to the lowest meson-baryon threshold, it is important to understand the relative lengths between quarks for the pentaquark states. These determine the magnitude of the various kinetic energies and the potential energies between quarks [58]. Here, we also define the V C : the sum of Coulomb potential and linear potential.…”

“…Here, we also define the V C : the sum of Coulomb potential and linear potential. In most of the multiquark configurations, the contributions to the bound state from the parts of V C and kinetic energy are repulsive, and therefore the contribution from the color spin interaction becomes important in these circumstances [58]. However, the hyperfine potential is far smaller compared to other contributions in fully heavy pentaquark system from corresponding tables because the hyperfine potential part is inversely proportional to the quark masses.…”

“…The qq Q Q states have been investigated via the variational method based on simple Gaussian trial function [46], and a good stable candidate, the lowest I(J P ) = 0(1 + ) ud bb state, was predicated and supported by other works [47][48][49][50][51][52][53][54]. Park et.al improved the potential terms in the constituent model and systemically calculated the P c states, the doubly heavy tetraquark states, and many dibaryons with different configurations [55][56][57][58][59][60]. It is interesting to extend the constituent quark model to fully heavy pentaquark states.…”

“…( 2) and (3) are chosen from Ref. [58] and given in Table I. Now we construct the wave function satisfied with Pauli Principle for fully heavy pentaquark states.…”