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Register a new userGlueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of the glueball spectrum
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In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from the QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the $0^{++},0^{-+},1^{++},1^{-+},2^{++}$ and $2^{-+text{}}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulation
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A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Greens functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations.
Brief review of the status of the glueball spectrum in the deformed conifold background. Talk based on work done with R. Hernandez and X. Amador.
In pure-glue QCD, gluon-gluon scattering in the $J^{PC}=0^{-+}$ channel is described by a very simple equation, especially if one considers just the leading contribution to the scattering kernel. Of all components in this kernel, only the three-gluon vertex, $V_{mu urho}$, is poorly constrained by contemporary analyses; hence, calculations of $0^{-+}$ glueball properties serve as a clear window onto the character and form of $V_{mu urho}$. This is important given that many modern calculations of $V_{mu urho}$ predict the appearance of an infrared suppression in the scalar function which comes to modulate the bare vertex after the nonperturbative resummation of interactions. Such behaviour is a peculiar prediction; but we find that such suppression is essential if one is to achieve agreement with lattice-QCD predictions for the $0^{-+}$ glueball mass. It is likely, therefore, that this novel feature of $V_{mu urho}$ is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states.
We use a variational technique to study heavy glueballs on gauge configurations generated with 2+1 flavours of ASQTAD improved staggered fermions. The variational technique includes glueball scattering states. The measurements were made using 2150 configurations at 0.092 fm with a pion mass of 360 MeV. We report masses for 10 glueball states. We discuss the prospects for unquenched lattice QCD calculations of the oddballs.
Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $sigma$ and $eta-eta$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $Lambda$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.
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