Spin structure of heavy-quark hybrids

Abstract

A unique feature of quantum chromodynamics (QCD), the theory of strong interactions, is the possibility for gluonic degrees of freedom to participate in the construction of physical hadrons, which are color singlets, in an analogous manner to valence quarks. Hadrons with no valence quarks are called glueballs, while hadrons where both gluons and valence quarks combine to form a color singlet are called hybrids. The unambiguous identification of such states among the experimental hadron spectrum has been thus far not possible. Glueballs are particularly difficult to establish experimentally since the lowest lying ones are expected to strongly mix with conventional mesons. On the other hand, hybrids should be easier to single out because the set of quantum numbers available to their lowest excitations may be exotic, i.e., not realized in conventional quark-antiquark systems. Particularly promising for discovery appear to be heavy hybrids, which are made of gluons and a heavy-quark-antiquark pair (charm or bottom). In the heavy-quark sector systematic tools can be used that are not available in the light-quark sector. In this paper we use a nonrelativistic effective field theory to uncover for the first time the full spin structure of heavy-quark hybrids up to 1/m 2 -terms in the heavy-quark-mass expansion. We show that such terms display novel characteristics at variance with our consolidated experience on the fine and hyperfine splittings in atomic, molecular and nuclear physics. We determine the nonperturbative contributions to the matching coefficients of the effective field theory by fitting our results to lattice-QCD determinations of the charmonium hybrid spectrum and extrapolate the results to the bottomonium hybrid sector where lattice-QCD determinations are still challenging.

The dynamical diquark model: fine structure and isospin

“…[18], they are expected to lie about 1 GeV above the Σ + g (1S) ground states (just like the gap between quarkonium hybrids and conventional quarkonium states). Nevertheless, were they to be considered in a model analogous to the one described here, yet further operators would need to be included, such as ones dependent upon not only quark spin, but the spin of the nontrivial glue degrees of freedom as well [42].…”

Novel implementation of the multipole expansion to quarkonium hadronic transitions

“…These double ratios are independent of β (21) r,b /β (21) r,c . We also expect several other uncertainties to cancel: The dependence on the light-quark masses cancels; In principle, we would also expect most of the effect due to unaccounted for O(α s ) corrections in the hadronization of the local operators vanish, since the phase space is similar.…”

“…In principle, we expect that for this ratio most of the neglected O(α s ) corrections in the hadronization of the local operators vanish. This observable can be considered a rough measure of β (21) r,b /β (21) r,c . The agreement with experiment is remarkable: below 20%, and could be accounted for by the quoted errors.…”

“…Again, the twist expansion would yield a different prediction for these ratios, and, again, these ratios can be considered a measure of β (21) r,b /β (21) r,c . The agreement with experiment is quite reasonable, with difference of the order of 30%.…”

“…In order to asses whether this error and the error of Eq. (81) is really related to β (21) r,b /β (21) r,c or to something else, one may consider the double ratios:…”