Uncertainty estimates of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>-pole determination by Padé approximants

Caprini, I.; Masjuan, Pere; Elvira, J. Ruiz de; Sanz-Cillero, Juan José

doi:10.1103/physrevd.93.076004

Cited by 27 publications

(26 citation statements)

References 50 publications

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“…In the third and fourth columns of Table 1 we also show the results obtained by following the same procedure with the Schenk [58] and Chew-Mandelstam (C-M) [59] parameterizations already used in [23] fitted to the CFD curve. For each parameterization we choose its best s 0 value.…”

Section: Scalar Resonancesmentioning

confidence: 99%

“…The explicit expression for the poles may be found in [23]. In the case of the κ, when using this M = 2 sequence of Padé series, we will see that one of the poles will converge to the pole associated to the resonance s p , whereas the other will simulate a branch cut.…”

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

“…These approximants can be calculated easily from the derivatives of the data fit with respect to the energy squared s. Thanks to the de Montessus de Ballore theorem these Padé approximants can be used to unfold the next continuous Riemann sheet of a scattering amplitude in order to search for resonance poles [21][22][23]. The relevant observation is that when they yield a pole they do not assume a model for the relation between its position and residue.…”

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

“…The relevant observation is that when they yield a pole they do not assume a model for the relation between its position and residue. Hence, in this sense the pole is model independent, although there is some residual dependence on the choice of parameterization for the data, from which the derivatives are obtained [23]. This will be taken into account into our systematic error estimation.…”

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

“…They are based on several approaches: conformal expansions to exploit the maximum analyticity domain of the amplitude [13][14][15], Laurent [16,17] or Laurent-Pietarinen [18][19][20] expansions, or Padé approximants [21][22][23]. They all determine the pole position without assuming a particular model for the relation between the mass, width and residue.…”

Section: Introductionmentioning

confidence: 99%

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Strange resonance poles from $$K\pi $$ K π scattering below 1.8 GeV

2017

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In this work we present a determination of the mass, width, and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar κ-meson, nowadays known as K * 0 (800), the scalar K * 0 (1430), the K * (892) and K * 1 (1410) vectors, the spin-two K * 2 (1430) as well as the spin-three K * 3 (1780). The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the K π scattering amplitudes obtained in a recent and precise data analysis constrained with dispersion relations, which were not well satisfied in previous analyses. This analytic continuation will be performed by means of Padé approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties.

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Section: Scalar Resonancesmentioning

confidence: 99%

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

Section: Pole Determination Using Padé Approximantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strange resonance poles from $$K\pi $$ K π scattering below 1.8 GeV

2017

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Probing the singularities of the Landau-Gauge gluon and ghost propagators with rational approximants

Boito

Cucchieri

London

et al. 2023

J. High Energ. Phys.

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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 ± 0.05stat± 0.08sys) ± i (0.66 ± 0.03stat± 0.02sys)] 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.

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Light- and strange-quark mass dependence of the ρ(770) meson revisited

Molina

Elvira

2020

J. High Energ. Phys.

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Recent lattice data on ππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the ρ(770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the ρ(770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the ρ(770) meson is studied.

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Uncertainty estimates of theσ-pole determination by Padé approximants

Cited by 27 publications

References 50 publications

Strange resonance poles from $$K\pi $$ K π scattering below 1.8 GeV

Strange resonance poles from $$K\pi $$ K π scattering below 1.8 GeV

Probing the singularities of the Landau-Gauge gluon and ghost propagators with rational approximants

Light- and strange-quark mass dependence of the ρ(770) meson revisited

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