Absorptive one-loop corrections and the complex-mass prescription for the Δ resonance propagator

Barbero, César Alberto; Mariano, A.; Castro, G. López

doi:10.1088/0954-3899/39/8/085011

Cited by 9 publications

(11 citation statements)

References 30 publications

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“…we will assume as in Ref. [12] that the parameter m ∆ represents the 'renormalized' mass of ∆. We place quotation marks as a reminder that the Lagrangian is not renormalizable; only the absorptive corrections are finite in this case.…”

Section: Resonancesmentioning

confidence: 99%

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Weak pion-production and the second resonance region

2022

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In this work we report the calculation of the total cross section for pion-production by the dispersion of neutrinos on nucleons. We use a consistent formalism for the intermediate resonance states of spin 3 2 , taking care on the conditions imposed by the invariance on contact transformations and using the Sachs parametrization for the form factors. In addition, we incorporate states in the second resonance region up to 1.6 GeV and implement different approaches for all the dressed resonance propagators. In addition to the ∆(1232), we include the N * (1440),N * (1535)and N * (1520) resonance contributions, and it is shown that this inclusion improve the description of the total cross section regards a model where only the ∆(1230) resonance is considered. Also results for antineutrinos are properly described.

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Section: Resonancesmentioning

confidence: 99%

“…( 26), and the dressed propagator can be finally obtained (for details see Ref. [12]). Now, we discuss some approximations commonly adopted.…”

Section: Resonancesmentioning

confidence: 99%

Weak pion-production and the second resonance region

2022

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“…of the energy dependent ∆ self-energy taking into account the ∆ mixing with πN states at one or higher loop bubbles to all order [12]. Nevertheless, since we are interested in the qualitative behavior of the different components of the πN ∆ interaction, we use the simpler CMS scheme.…”

Section: Numeric Calculationsmentioning

confidence: 99%

Higher derivative terms in the πΔN interaction: Some phenomenological consequences

et al. 2019

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In this paper we implement for the first time the use of a πN ∆(1232) vertex interaction containing both first and second order derivative terms, as required by renormalization considerations. As as was previously shown both interactions present formal problems, but can be implemented pertubatively. We put an end point to the discussion of which type of interaction is the apropriate one: both the usual pi-derivative and the "spin 3/2" gauge invariant that include also a derivative in the Delta field should be included in amplitude calculations. We show that when working within a tree level approach the description of total πN scattering in the different channels is improved.

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“…This propagator, including one-loop self-energy contributions (figure 1(a)), has been deduced in [5] together with a discussion about some approximated forms and reads…”

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confidence: 99%

About the validity of complex mass scheme for the Δ resonance and higher energy region approaches

Barbero

Mariano

2015

J. Phys. G: Nucl. Part. Phys.

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It is a well known fact that when a resonance (R) is produced and decays, its unperturbed propagator will be singular at when it appears in an s-type Feynman pole graph. Nevertheless this is not a problem, since it must be dressed by the successive re-interactions of the resonance with itself to all orders through the non-pole T-matrix, which we include in this work for the self-energy one-loop pion–nucleon contributions. Recently, we have shown that within the one-loop approximation for the absorptive part it is possible to justify the use of the complex-mass description over the unperturbed propagator, adopted in previous calculations to treat pion–nucleon elastic and radiative scattering, and photo and weak pion production in the resonance region. Here we discuss the limits of the validity of this approximation, since in actual calculations we must go over this range. We show that, when the resonance energy is increased above , this approach becomes invalid and an alternative approximation should be considered. In addition, we discuss the usual energy dependent width approximation, present in several actual isobar models used to analyze the last neutrino scattering experiments, and show that also it could be unappropriate.

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Absorptive one-loop corrections and the complex-mass prescription for the Δ resonance propagator

Cited by 9 publications

References 30 publications

Weak pion-production and the second resonance region

Weak pion-production and the second resonance region

Higher derivative terms in the πΔN interaction: Some phenomenological consequences

About the validity of complex mass scheme for the Δ resonance and higher energy region approaches

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