Excited flux tube from q¯g hybrid mesons

Abstract

Abstract. In the framework of quark models, hybrid mesons are either seen as two-body qq systems with an excited flux tube connecting the quark to the antiquark or as three-body qqg systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the qqg hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent qq potential. This equivalence between the excited flux tube and the constituent-gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account. The study of hybrid mesons is an active domain in theoretical and in experimental particle physics with future experiments BESIII, GLUEX and PANDA. From a theoretical point of view, they are interpreted as mesons in which the color field is in an excited state. Numerous lattice QCD calculations have been devoted to hybrid mesons [1,2], as well as many studies involving effective models. In particular, within the framework of quark models, there are two main approaches. In the first one, the quark and the antiquark are linked by a string, or flux tube, which is responsible for the confinement. In this stringy picture, it is possible for the flux tube to fluctuate, and thus to be in an excited state [3,4]. The second approach assumes that the hybrid meson is a three-body system formed of a quark, an antiquark, and a constituent gluon. Two straight strings then link the gluon to the quark and to the antiquark. This picture has been firstly studied in refs. but also in more recent works including effective models as well as lattice QCD calculations [6][7][8][9]. Very good descriptions of mesons and baryons, even light ones, are obtained within the framework of potential models with constituent quarks. Moreover, it has been recently shown that such models, with constituent gluons, give gg and ggg glueball spectra very similar to results predicted by lattice QCD works [10]. This picture of constituent particles is also validated by recent lattice calculations [9]. So it seems relevant to work in this framework. PACSIt was suggested in ref.[8] that, in the static quark limit, the constituent-gluon picture is equivalent to the excited flux tube one, the total energy of the constituent gluon being equal to the energy contained in the excited string. These results were extended in ref. [11], where the dynamics of the quarks has been taken into account. For further developments, it is useful to briefly sum up the key points of this last reference. Assuming the Casimir scaling hypothesis, it can be shown that the flux tubes in a qqg system are two fundamental straight strings linking the gluon to the quark and to the antiquark [7], in agreement with refs. [5,9].In this work, in order to simplify, we will neglect all short-range interactions between quarks and gluon and only consider the dominant confining potential. In this

Wave-function-based characteristics of hybrid mesons

“…), these are also not possible with this potential form and thus for many applications it has to be replaced by others of higher chisquare. Fig.4 shows the behaviour of string potential [34] σ 2 r 2 + 2πσ(N + 3 2 ) + w q (9) with N = 0, 1, 2. In this figure, the points represent the data taken from ref.…”

Lagrange-mesh calculations in momentum space

“…More rigorously, it is obtained from the covariant Bethe-Salpeter equation [22] with the following approximations: Elimination of any dependences on timelike variables and neglect of particle spin degrees of freedom as well as negative energy solutions [23]. The spinless Salpeter Hamiltonian is often used in hadronic physics to study bound states of quarks or gluons [24][25][26][27]. Within this formulation, the action of the kinetic operator is just an ordinary multiplication.…”

Instanton effect in QCD sum rules for the0++hybrid

“…Most studies have focused on hybrids with exotic quantum numbers (e.g., 1 Àþ ) because such states do not mix with ordinary " qq mesons. Less attention has been paid to the 0 þþ hybrid because it is experimentally very difficult to identify the composition of such a state, and it is also considered as a highly excited flux tube (e.g., some authors think the 0 þþ is one of the degenerate ground states in the flux tube model [13]). …”