Gluons in glueballs: Spin or helicity?

Abstract

In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show in particular that this helicity formalism exactly reproduces the J P C numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as it is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.

The SUSY Yang–Mills plasma in a T-matrix approach

“…This notation follows the pioneering work [52] and is used in [53]. In the special case of identical particles, the helicity states must also be eigenstates of the operatorŜ = [1 + (−1)…”

“…For completeness, the ones considered in this paper are recalled here. [52,53], with the corresponding quantum numbers and some averaged operators.…”

“…The general forms of the two-gluon states have been presented in [53]. Some properties are given in Table VIII, as well as the average value of some operators, computed with these states.…”

The glueball spectrum from constituent gluon model

“…When applying it to two-gluon glueballs, we remarked that the Bose symmetry (and the parity) implies selection rules. Three families were identified [12]: (2k) ++ , (2k + 3) ++ , (2k + 2) −+ with k ∈ N. One easily checks that no spurious J = 1 states appear. Moreover, with this special construction, the orbital-spin part of all states is now expressed through a given linear combination of spectroscopic states.…”

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.…”