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Binosi, D., Ibañez, D., & Papavassiliou, J. (2012). All-order equation of the effective gluon mass. Phys. Rev. D, 86(8), 085033–21pp.
Abstract: We present the general derivation of the full nonperturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of nonperturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The mass equation is obtained from a previously unexplored version of the Schwinger-Dyson equation for the gluon propagator, particular to the pinch technique-background field method formalism, which involves a reduced number of two-loop dressed diagrams, thus simplifying the calculational task considerably. The two-loop contributions turn out to be of paramount importance, modifying the qualitative features of the full mass equation and enabling the emergence of physically meaningful solutions. Specifically, the resulting homogeneous integral equation is solved numerically, subject to certain approximations, for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses.
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Athenodorou, A., Binosi, D., Boucaud, P., De Soto, F., Papavassiliou, J., Rodriguez-Quintero, J., et al. (2016). On the zero crossing of the three-gluon vertex. Phys. Lett. B, 761, 444–449.
Abstract: We report on new results on the infrared behavior of the three-gluon vertex in quenched Quantum Chromodynamics, 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.
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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2010). Nonperturbative gluon and ghost propagators for d=3 Yang-Mills theory. Phys. Rev. D, 81(12), 125025–13pp.
Abstract: We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the non-perturbative dynamics of the gluon and ghost propagators in d = 3 Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in d = 3), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of SU(2) lattice simulations.
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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2013). Gluon mass generation in the presence of dynamical quarks. Phys. Rev. D, 88(7), 074010–12pp.
Abstract: We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Aguilar et al. [Phys. Rev. D 86, 014032 (2012)], where the behavior of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirms the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.
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Binosi, D., Mezrag, C., Papavassiliou, J., Roberts, C. D., & Rodriguez-Quintero, J. (2017). Process-independent strong running coupling. Phys. Rev. D, 96(5), 054026–7pp.
Abstract: We unify two widely different approaches to understanding the infrared behavior of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realized via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann-Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be a near direct means by which to gain empirical insight into QCD's Gell-Mann-Low effective charge.
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