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Register a new userPseudoscalar glueball mass: a window on three-gluon interactions
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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.
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We discuss properties of non-Abelian gauge theories that change significantly across the lower edge of the conformal window. Their probes are the topological observables, the meson spectrum and the scalar glueball operator. The way these quantities change tells about the way conformal symmetry is lost.
The task of mapping and explaining the spectrum of baryons and the structure of these states in terms of quarks and gluons is a longstanding challenge in hadron physics, which is likely to persist for another decade or more. We review the progress made in this topic using a functional method based on Dyson-Schwinger equations. This framework provides a non-perturbative, Poincare-covariant continuum formulation of Quantum Chromodynamics which is able to extract novel insight on baryon properties since the physics at the hadron level is directly related with the underlying quark-gluon substructure, via convolution of Green functions.
We show that the anomalous dimension $gamma_G$ of the scalar glueball operator contains information on the mechanism that leads to the onset of conformality at the lower edge of the conformal window in a non-Abelian gauge theory. In particular, it distinguishes whether the merging of an UV and an IR fixed point -- the simplest mechanism associated to a conformal phase transition and preconformal scaling -- does or does not occur. At the same time, we shed light on new analogies between QCD and its supersymmetric version. In SQCD, we derive an exact relation between $gamma_G$ and the mass anomalous dimension $gamma_m$, and we prove that the SQCD exact beta function is incompatible with merging as a consequence of the $a$-theorem; we also derive the general conditions that the latter imposes on the existence of fixed points, and prove the absence of an UV fixed point at nonzero coupling above the conformal window of SQCD. Perhaps not surprisingly, we then show that an exact relation between $gamma_G$ and $gamma_m$, fully analogous to SQCD, holds for the massless Veneziano limit of large-N QCD. We argue, based on the latter relation, the $a$-theorem, perturbation theory and physical arguments, that the incompatibility with merging may extend to QCD.
We report on new results on the infrared behaviour of the three-gluon vertex in quenched Quantum Chormodynamics, obtained from large-volume lattice simulations. The main focus of our study is the appearance of the characteristic infrared feature known as zero crossing, the origin of which is intimately connected with the nonperturbative masslessness of the Faddeev-Popov ghost. The appearance of this effect is clearly visible in one of the two kinematic configurations analyzed, and its theoretical origin is discussed in the framework of Schwinger-Dyson equations. The effective coupling in the momentum subtraction scheme that corresponds to the three-gluon vertex is constructed, revealing the vanishing of the effective interaction at the exact location of the zero crossing.
We present a detailed analysis of the kinetic and mass terms associated with the Landau gauge gluon propagator in the presence of dynamical quarks, and a comprehensive dynamical study of certain special kinematic limits of the three-gluon vertex. Our approach capitalizes on results from recent lattice simulations with (2+1) domain wall fermions, a novel nonlinear treatment of the gluon mass equation, and the nonperturbative reconstruction of the longitudinal three-gluon vertex from its fundamental Slavnov-Taylor identities. Particular emphasis is placed on the persistence of the suppression displayed by certain combinations of the vertex form factors at intermediate and low momenta, already known from numerous pure Yang-Mills studies. One of our central findings is that the inclusion of dynamical quarks moderates the intensity of this phenomenon only mildly, leaving the asymptotic low-momentum behavior unaltered, but displaces the characteristic zero crossing deeper into the infrared region. In addition, the effect of the three-gluon vertex is explored at the level of the renormalization-group invariant combination corresponding to the effective gauge coupling, whose size is considerably reduced with respect to its counterpart obtained from the ghost-gluon vertex. The main upshot of the above considerations is the further confirmation of the tightly interwoven dynamics between the two- and three-point sectors of QCD.
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