Selection Rules for Hadronic Transitions ofXYZMesons

Abstract

Many of the XY Z mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (B-O) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XY Z mesons that are candidates for ground-state energy levels in the B-O potentials for charmonium hybrids and tetraquarks. A full decade has elapsed since the discovery of the first XY Z meson, the X(3872) [7], but no compelling explanation for the pattern of XY Z mesons has emerged. In simple constituent models, an XY Z meson consists of a heavy quark (Q) and antiquark (Q) and possibly additional constituents that could be gluons (g) or light quarks (q) and light antiquarks (q). The models that have been proposed can be classified according to how the constituents are clustered within the me- The B-O approximation is used in atomic and molecular physics to understand the binding of atoms into molecules. It exploits the large ratio of the time scale for the motion of the atomic nuclei to that for the electrons, which is a consequence of the large ratio of the nuclear and electron masses. The electrons respond almost instantaneously to the motion of the nuclei, which can be described by the Schroedinger equation in a B-O potential defined by the energy of the electrons in the presence of static electric charges. The B-O approximation for QQ mesons in QCD was developed by Juge, Kuti, and Morningstar [13]. It exploits the large ratio of the time scale for the motion of the Q andQ to that for the evolution of gluon fields, which is a consequence of the large ratio of the heavy-quark mass to the nonperturbative momentum scale Λ QCD . The gluon field responds almost instantaneously to the motion of the QQ pair, which can be described by the Schroedinger equation in a B-O potential defined by the energy of the gluon field in the presence of static color sources. Conventional quarkonia are energy levels of a QQ pair in the ground-state B-O potential. The energy levels in the excited-state B-O potentials are quarkonium hybrids. Juge, Kuti, and Morningstar calculated many of the B-O potentials using quenched lattice QCD [13]. They calculated the spectra of charmonium hybrids and bottomonium hybrids by

Hybrid static potential flux tubes from SU(2) and SU(3) lattice gauge theory

“…For the majority of computations for gauge group SU(2) we use the ensemble with (L/a) 3 × T /a = 24 4 . The ensemble with (L/a) 3 ×T /a = 18 4 is only used for exploring and excluding finite volume effects in section 4.1.3.…”

“…Also on the theoretical side there are many open questions concerning hybrid mesons (see e.g. the theoretical reviews [3][4][5][6]). They are difficult to study, because in QCD total angular momentum J and parity P are not separately conserved for gluons on the one hand and for the quarkantiquark pair on the other hand.…”

The hidden-charm pentaquark and tetraquark states

“…The selection rules for hadronic transitions between QQ mesons were investigated in Refs. [638,639] based on Born-Oppenheimer potentials, and the Born-Oppenheimer approximation was also used in Ref. [640] to study the four-quark bound states.…”

Heavy Hybrids: decay to and mixing with Heavy Quarkonium

“…In table 3 1 state. However, the three states have been observed to decay to vector quarkonium, which violates spin symmetry [13]. This is also so for Y b (10890).…”