On-shell renormalization of the mixing matrices in Majorana neutrino theories

Almasy, Andrea A.; Kniehl, Bernd A.; Sirlin, A.

doi:10.1016/j.nuclphysb.2009.03.025

Cited by 10 publications

(16 citation statements)

References 46 publications

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“…The counterparts of Eqs. (26) and (27) for unstable Dirac fermions read [22,23] Ψ 0 (x) =Ψ(x)Z 1 /2 (38)…”

Section: Renormalized Dressed Propagator Matrixmentioning

confidence: 99%

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Propagator mixing renormalization for Majorana fermions

Kniehl

2014

Phys. Rev. D

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We consider a mixed system of unstable Majorana fermions in a general paritynonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the wave-function renormalization matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.

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“…The counterparts of Eqs. (26) and (27) for unstable Dirac fermions read [22,23] Ψ 0 (x) =Ψ(x)Z 1 /2 (38)…”

Section: Renormalized Dressed Propagator Matrixmentioning

confidence: 99%

“…As for the flavor mixing matrices of Majorana fermions, various renormalization prescriptions have been proposed at one loop for the case of stability [24,25,26]. Specifically, the approach of Ref.…”

mentioning

confidence: 99%

Propagator mixing renormalization for Majorana fermions

Kniehl

2014

Phys. Rev. D

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“…In an attempt to be more general than [4], we obtain the formula for the loop correction to the mass of a Majorana fermion, like in [5][6][7][8]. We do not include tadpoles in the contribution from scalars as the tadpole couplings to ζ 1,2 vanish.…”

Section: Generating Mmentioning

confidence: 99%

Constraints on the Higgs Sector from Radiative Mass Generation of Neutrinos

Gajdosik¹,

Juodagalvis²,

Jurčiukonis³

et al. 2015

Acta Phys. Pol. B

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Adding a single gauge singlet and a second Higgs doublet to the original Standard Model allows an explanation of the observed smallness of the neutrino masses using the seesaw mechanism. This model predicts two neutral fermions with vanishing mass. But the one-loop contribution to the neutral fermion masses due to the second Higgs doublet lifts this degeneracy and allows to fit the model parameters to the observed neutrino mass differences. We present the determination of the additional Yukawa couplings that appear in our model by requiring that our model predicts the correct mass differences and mixings in the neutrino sector.

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“…Various renormalization prescriptions for mixing matrices of Dirac [12][13][14] and Majorana [15,16] fermions were proposed in the literature, some of which naturally extend to all orders. As pointed out in Ref.…”

Section: Introductionmentioning

confidence: 99%

All-order renormalization of propagator matrix for unstable Dirac fermions

Kniehl

2014

Phys. Rev. D

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We consider a system of unstable Dirac fermions in a general parity-nonconserving theory with intergeneration mixing and explain how to renormalize its propagator matrix to all orders in perturbation theory. We work in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted according to the Lehmann-Symanzik-Zimmermann reduction formalism. The unit-residue property is explicitly verified for the renormalized dressed propagator matrix. Closed analytic expressions for the pole-mass counterterms and WFR matrices in terms of the self-energy functions are presented. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exploit them. We demonstrate that, in the presence of instability, the WFR matrices of the in and out states bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. The well-known one-and two-loop results for stable fermions are recovered. The all-order renormalized propagator of a single unstable fermion takes a particularly compact form. We also briefly discuss Dirac spinors for unstable fermions.

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On-shell renormalization of the mixing matrices in Majorana neutrino theories

Cited by 10 publications

References 46 publications

Propagator mixing renormalization for Majorana fermions

Propagator mixing renormalization for Majorana fermions

Constraints on the Higgs Sector from Radiative Mass Generation of Neutrinos

All-order renormalization of propagator matrix for unstable Dirac fermions

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