Cristiane Yumi London

We employ Padé approximants in the study of the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at $$ {p}_{\textrm{pole}}^2 $$p pole 2 = [(−0.37 ± 0.05_stat± 0.08_sys) ± i (0.66 ± 0.03_stat± 0.02_sys)] GeV², where the first error is statistical and the second systematic. The existence of this pair of complex poles, already hinted upon in previous works, is thus put onto a firmer basis, thanks to the model independence and to the careful error propagation of our analysis. For the ghost propagator, the Padés indicate the existence of a single pole at p² = 0, as expected. In this case, our results also show evidence of a branch cut along the negative real axis of p². This is corroborated with another type of approximant, the D-Log Padés, which are better suited to studying functions with a branch cut and are applied here for the first time in this context. Due to particular features and limited statistics of the gluon-propagator data, our analysis is inconclusive regarding the presence of a branch cut in the gluon case.

We employ Pad\'e approximants in the study of the analytic structure of the four-dimensional $SU(2)$ Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, serve as fitting functions for the lattice data. We carefully propagate the uncertainties due to the fitting procedure, taking into account all possible correlations. For the gluon-propagator data, we confirm the presence of a pair of complex poles at $p_{\rm pole}^2 = \left[(-0.37 \,\pm\, 0.05_{\rm stat}\,\pm\, 0.08_{\rm sys}) \pm i\,(0.66\, \pm\, 0.03_{\rm stat}\, \pm\, 0.02_{\rm sys})\right]\, \mathrm{GeV}^2$, where the first error is statistical and the second systematic. The existence of this pair of complex poles, already hinted upon in previous works, is thus put onto a firmer basis, thanks to the model independence and to the careful error propagation of our analysis. For the ghost propagator, the Pad\'es indicate the existence of a single pole at $p^2 = 0$, as expected. In this case, our results also show evidence of a branch cut along the negative real axis of $p^2$. This is corroborated with another type of approximant, the D-Log Pad\'es, which are better suited to studying functions with a branch cut and are applied here for the first time in this context. Due to particular features and limited statistics of the gluon-propagator data, our analysis is inconclusive regarding the presence of a branch cut in the gluon case.

We employ the method of Padé approximants to study the higher-order corrections of the massless scalar-current quark correlator. We begin by testing this method in the large-$\beta_0$ limit of QCD, where the perturbative series is known to all orders, using it as a testing ground to determine the best strategy to build the series at higher orders using only the first four coefficients. Applying the procedure in QCD, we estimate the yet unknown coefficient $c_5$ of order $\alpha_s^5$ (six loops) of the imaginary part of the correlator, directly related to $\Gamma(H \to b \bar{b})$, in a model-independent way as $c_5=-6900 \pm 1400$. We conclude that with this correction the series is almost insensitive to renormalization scale variations. This corroborates that the QCD corrections to this decay are under excellent control and the uncertainty of $\Gamma(H \to b \bar{b})$ will continue to be dominated by the Standard Model parameters in the near future, mainly the strong coupling and the bottom-quark mass.

Pad\'e approximants are employed in order to study the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, are used as fitting functions to lattice data for the propagators, carefully propagating uncertainties due to the fit procedure and taking into account all possible correlations. Applying this procedure systematically to the gluon-propagator data, we observe the presence of a pair of complex poles at $p^2_{\mathrm{pole}} = (-0.37 \pm 0.05_{\mathrm{stat}} \pm 0.08_{\mathrm{sys}}) \pm \, i\, (0.66 \pm 0.03_{\mathrm{stat}} \pm 0.02_{\mathrm{sys}}) \, \mathrm{GeV}^2$, where ``stat'' represents the statistical error and ``sys'' the systematic one. We also find a zero on the negative real axis of $p^2$, at $p^2_{\mathrm{zero}} = (-2.9 \pm 0.4_{\mathrm{stat}} \pm 0.9_{\mathrm{sys}}) \, \mathrm{GeV}^2$. We thus note that our procedure -- which is based on a model-independent approach and includes careful error propagation -- confirms the presence of a pair of complex poles in the gluon propagator, in agreement with previous works. For the ghost propagator, the Pad\'es indicate the existence of the single pole at $p^2 = 0$, as expected. We also find evidence of a branch cut on the negative real axis. Through the use of the so-called D-Log Pad\'e method, which is designed to approximate functions with cuts, we corroborate the existence of this cut for the ghost propagator.

Padé approximants are employed in order to study the analytic structure of the four-dimensional SU(2) Landau-gauge gluon and ghost propagators in the infrared regime. The approximants, which are model independent, are used as fitting functions to lattice data for the propagators, carefully propagating uncertainties due to the fit procedure and taking into account all possible correlations. Applying this procedure systematically to the gluon-propagator data, we observe the presence of a pair of complex poles at $p^2_{\mathrm{pole}} = (-0.37 \pm 0.05_{\mathrm{stat}} \pm 0.08_{\mathrm{sys}}) \pm \, i\, (0.66 \pm 0.03_{\mathrm{stat}}\pm 0.02_{\mathrm{sys}}) \, \mathrm{GeV}^2$, where ''stat'' represents the statistical error and ''sys'' the systematic one. We also find a zero on the negative real axis of $p^2$, at $p^2_{\mathrm{zero}} = (-2.9 \pm 0.4_{\mathrm{stat}} \pm 0.9_{\mathrm{sys}}) \, \mathrm{GeV}^2$. We thus note that our procedure --- which is based on a model-independent approach and includes careful error propagation --- confirms the presence of a pair of complex poles in the gluon propagator, in agreement with previous works. For the ghost propagator, the Padés indicate the existence of the single pole at $p^2 = 0$, as expected. We also find evidence of a branch cut on the negative real axis. Through the use of the so-called D-Log Padé method, which is designed to approximate functions with cuts, we corroborate the existence of this cut for the ghost propagator.

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to Γ(H → b $$ \overline{b} $$b ¯ ), to be c₅ = −6900 ± 1400. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → b $$ \overline{b} $$b ¯ ) will remain largely dominated by the Standard Model parameters.

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to $\Gamma(H\to b \bar b)$, to be $c_5=-6900\pm 1400$. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in $\Gamma(H\to b \bar b)$ will remain largely dominated by the Standard Model parameters.