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Aguilar, A. C., Ferreira, M. N., & Papavassiliou, J. (2021). Gluon dynamics from an ordinary differential equation. Eur. Phys. J. C, 81(1), 54–20pp.
Abstract: We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the aforementioned kinetic term are related by a partial Slavnov-Taylor identity. The main ingredients entering in the solution are projection of the three-gluon vertex and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a Schwinger-Dyson equation. Crucially, the requirement of a pole-free answer determines the initial condition, whose value is calculated from an integral containing the same ingredients as the solution itself. This feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients have been accurately evaluated. In practice, however, due to substantial uncertainties in the computation of the necessary inputs, certain crucial components need be adjusted by hand, in order to obtain self-consistent results. Furthermore, if the gluon propagator has been independently accessed from the lattice, the solution for the kinetic term facilitates the extraction of the momentum-dependent effective gluon mass. The practical implementation of this method is carried out in detail, and the required approximations and theoretical assumptions are duly highlighted.
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Aguilar, A. C., Ferreira, M. N., & Papavassiliou, J. (2020). Novel sum rules for the three-point sector of QCD. Eur. Phys. J. C, 80(9), 887–18pp.
Abstract: For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the “kinetic term” of the gluon propagator. The exact solutions of these equations exhibit poles at the origin, which are incompatible with the physical answer, known to diverge only logarithmically; their elimination hinges on the validity of two integral conditions that we denominate “asymmetric” and “symmetric” sum rules, depending on the kinematics employed in their derivation. The corresponding integrands contain components of the three-gluon vertex and the ghost-gluon kernel, whose dynamics are constrained when the sum rules are imposed. For the numerical treatment we single out the asymmetric sum rule, given that its support stems predominantly from low and intermediate energy regimes of the defining integral, which are physically more interesting. Adopting a combined approach based on Schwinger-Dyson equations and lattice simulations, we demonstrate how the sum rule clearly favors the suppression of an effective form factor entering in the definition of its kernel. The results of the present work offer an additional vantage point into the rich and complex structure of the three-point sector of QCD.
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Aguilar, A. C., Ferreira, M. N., Papavassiliou, J., & Santos, L. R. (2023). Planar degeneracy of the three-gluon vertex. Eur. Phys. J. C, 83(6), 549–20pp.
Abstract: We present a detailed exploration of certain outstanding features of the transversely-projected three-gluon vertex, using the corresponding Schwinger-Dyson equation in conjunction with key results obtained from quenched lattice simulations. The main goal of this study is the scrutiny of the approximate property denominated “planar degeneracy”, unveiled when the Bose symmetry of the vertex is properly exploited. The planar degeneracy leads to a particularly simple parametrization of the vertex, reducing its kinematic dependence to essentially a single variable. Our analysis, carried out in the absence of dynamical quarks, reveals that the planar degeneracy is particularly accurate for the description of the form factor associated with the classical tensor, for a wide array of arbitrary kinematic configurations. Instead, the remaining three form factors display considerable violations of this property. In addition, and in close connection with the previous point, we demonstrate the numerical dominance of the classical form factor over all others, except in the vicinity of the soft-gluon kinematics. The final upshot of these considerations is the emergence of a very compact description for the three-gluon vertex in general kinematics, which may simplify significantly nonperturbative applications involving this vertex.
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Aguilar-Saavedra, J. A., Bernabeu, J., Mitsou, V. A., & Segarra, A. (2017). The Z boson spin observables as messengers of new physics. Eur. Phys. J. C, 77(4), 234–6pp.
Abstract: We demonstrate that the eight multipole parameters describing the spin state of the Z boson are able to disentangle known Z production mechanisms and signals from new physics at the LHC. They can be extracted from appropriate asymmetries in the angular distribution of lepton pairs from the Z boson decay. The power of this analysis is illustrated by (1) the production of Z boson plus jets; (2) Z boson plus missing transverse energy; (3) W and Z bosons originating from the two-body decay of a heavy resonance.
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Aguilar-Saavedra, J. A., Boudreau, J., Escobar, C., & Mueller, J. (2017). The fully differential top decay distribution. Eur. Phys. J. C, 77(3), 200–8pp.
Abstract: We write down the four-dimensional fully differential decay distribution for the top quark decay t -> Wb -> l nu b. We discuss how its eight physical parameters can be measured, either with a global fit or with the use of selected one-dimensional distributions and asymmetries. We give expressions for the top decay amplitudes for a general tbW interaction, and show how the untangled measurement of the two components of the fraction of longitudinal W bosons – those with b quark helicities of 1/2 and -1/2, respectively – could improve the precision of a global fit to the tbW vertex.
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