Chiral symmetry of heavy-light scalar mesons withUA(1)symmetry breaking

Abstract

In a previous paper, based on a calculation in the nonrelativistic quark model, we advanced the hypothesis that the D s ð2317Þ, D 0 ð2308Þ mesons are predominantly four-quark states lowered in mass by the flavor-dependent Kobayashi-Kubo-Maskawa 't Hooft U A ð1Þ symmetry breaking effective interaction. Here we show similar results and conclusions in a relativistic effective chiral model calculation, based on three-light-quark (i.e., two q plus one " q) local interpolators. To this end we classify the four-quark (three light plus one heavy quark) local interpolators according to their chiral transformation properties and then construct chiral invariant interactions. We evaluate the diagonal matrix elements of the Kobayashi-Kubo-Maskawa 't Hooft interaction between different interpolating fields and show that the lowest-lying one is always the (antisymmetric) SUð3Þ F antitriplet belonging to the chiral (3, 3) multiplet. We predict bottomstrange B s0 and the bottom-nonstrange B 0 scalar mesons with equal masses at 5720 MeV, the strange meson being some 100 MeV lower than in most of the quark potential models. We also predict the J P ¼ 1 þ bottom-nonstrange B 1 and the bottom-strange B s1 meson masses as 5732 MeV and 5765 MeV, respectively, using the Bardeen-Hill-Nowak-Rho-Zahed scalar-vector mass relation.

A review of the open charm and open bottom systems

“…Similar results and conclusions were obtained in Ref. [783] using a relativistic effective chiral model. In Ref.…”

Masses of scalar and axial-vector B mesons revisited

“…Evidently, mass degeneracy in the scalar D sector will repeat itself in the B system through heavy quark symmetry. Scrutiny of Table 4 shows that this degeneracy is respected only in few of the predictions such as [48,49,71,72,83,93]. Though the relations in Eq.…”

“…The predictions of their masses in the literature are collected in Table 4. They can be classified into the following categories: (i) relativistic quark potential model [7,8,[63][64][65][66][67], (ii) nonrelativistic quark model [68,69], (iii) heavy meson chiral perturbation theory [48,[70][71][72], (iv) unitarized chiral perturbation theory [73][74][75][76][77][78], (v) lattice QCD [79][80][81][82], (vi) potential model with one loop corrections [64,83,84], (vii) QCD sum rules [85], and (viii) others, such as the nonlinear chiral SU(3) model [86,87], the semi-relativistic quark potential model [88], the MIT bag model [89], the mixture of conventional P-wave quark-antiquark states with four-quark components [90], the chiral quark-pion Lagrangian with strong coupled channels [91], heavy quark symmetry and the assumption of flavor independence of mass differences between 0 + and 0 − states in [93].…”

Confirmation of the existence of an exotic state in the $πD$ system

“…If we follow the standard assignment, compact tetraquarks are made of compact diquarks in the colorantitriplet representation [15] although some works also discuss the color-sextet configuration [50,51]. Then, the Pauli principle demands that a [q q] diquark sits either in the strongly attractive flavor [3] irrep with spin 0 or the less attractive [ 6] with spin 1.…”

“…Note that in the tetraquark model of Ref. [52] the non-strange member of the [15] appears even lower in mass than that of the [6] as a consequence of the action of the t'Hooft force, although the actual ordering depends very much on the details of the model employed [50].…”