Quarkonium hybrids with nonrelativistic effective field theories

Charmonium spectrum with a Dirac potential model in the momentum space

“…However there exist other important resonances that are still under examination. These states, denoted as X, Y and Z, do not match the predictions of the nonrelativistic or semirelativistic qq potential models and some of them have been described as tetraquarks, molecules, glueballs and hybrids [3][4][5][6][7][12][13][14][15][16][17][18]. Another possible explanation suggests that some of these states may be the result of kinematic effects [19,20] that appear in the nearby of the thresholds of the open charm channels.…”

Heavy Hybrids: decay to and mixing with Heavy Quarkonium

“…The basic difference with respect to ref. [25] is that we fix the arbitrary constant in the potential through the heavy quarkonium spectrum whereas in that reference it is fixed through the RS heavy quark masses [27]. We identify a number of possible heavy hybrid states in table 3, which would correspond to spin zero hybrids.…”

Born-Oppenheimer approximation in EFT and quarkonium hybrids

“…We have reported [1] on the computation of the heavy hybrid masses using an EFT formulation that incorporates the energy gap between the gluonic and heavy-quark degrees of freedom. This EFT is constructed by a procedure analogous to the one used in the BO approximation for diatomic molecules.…”

“…x 1 and x 2 are the heavy quark positions and n labels the representations of D ∞h , the (0) superscript denotes the static limit for the heavy quarks (see [1,10] for further details). Then…”

“…We report on the results of [1] for the calculations of quarkonium hybrids. We have developed and Effective Field Theory (EFT) for quarkonium hybrids that systematically incorporates an expansion with respect to the adiabatic limit.…”