A remark on the mathematics of the seesaw mechanism

Besnard, Fabien

doi:10.1088/2399-6528/aa7adb

Cited by 7 publications

(10 citation statements)

References 6 publications

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“…31) which does not rely on any perturbative arguments and we emphasise that these results are only valid for 'type-I like' scenarios where the entry diagonally opposite the dominant block is zero. Our results agree with the gap properties derived in [57] in the type-I limit which assumes m ee = (m EE ) T = m D and m Ee = m R and recovers the usual type-I hierarchy.…”

Section: Jhep05(2021)199supporting

confidence: 89%

“…Unlike the previous section which relied on an approximate block diagonalisation technique with neglected higher-order terms, the results below are exact statements that do not rely on any perturbative arguments. We closely follow the work presented in [57] which proved a similar gap property specifically for the type-I seesaw symmetric mass matrix, which we will generalise to an arbitrary complex matrix relevant to our charged-lepton seesaw. We state without proof three matrix properties related to the Courant-Fischer-Weyl min-max theorem:…”

Section: C3 Gap Properties Between the Charged Leptons And Down Quarksmentioning

confidence: 89%

“…Additional details including proofs for some of these properties can be found in [57]. We take the mass mixing matrix M eE to have the same structure as the case of an SU(2) R triplet defined in eq.…”

Section: Jhep05(2021)199mentioning

confidence: 99%

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Lowering the scale of Pati-Salam breaking through seesaw mixing

Dolan

Dutka

Volkas

2021

J. High Energ. Phys.

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We analyse the experimental limits on the breaking scale of Pati-Salam extensions of the Standard Model. These arise from the experimental limits on rare-meson decay processes mediated at tree-level by the vector leptoquark in the model. This leptoquark ordinarily couples to both left- and right-handed SM fermions and therefore the meson decays do not experience a helicity suppression. We find that the current limits vary from $$ \mathcal{O} $$ O (80–2500) TeV depending on the choice of matrix structure appearing in the relevant three-generational charged-current interactions. We extensively analyse scenarios where additional fermionic degrees of freedom are introduced, transforming as complete Pati-Salam multiplets. These can lower the scales of Pati-Salam breaking through mass-mixing within the charged-lepton and down-quark sectors, leading to a helicity suppression of the meson decay widths which constrain Pati-Salam breaking. We find four multiplets with varying degrees of viability for this purpose: an SU(2)L/R bidoublet, a pair of SU(4) decuplets and either an SU(2)L or SU(2)R triplet all of which contain heavy exotic versions of the SM charged leptons. We find that the Pati-Salam limits can be as low as $$ \mathcal{O} $$ O (5–150) TeV with the addition of these four multiplets. We also identify an interesting possible connection between the smallness of the neutrino masses and a helicity suppression of the Pati-Salam limits for three of the four multiplets.

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Section: Jhep05(2021)199supporting

confidence: 89%

Section: C3 Gap Properties Between the Charged Leptons And Down Quarksmentioning

confidence: 89%

See 1 more Smart Citation

Lowering the scale of Pati-Salam breaking through seesaw mixing

Dolan

Dutka

Volkas

2021

J. High Energ. Phys.

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show abstract

“…which does not rely on any perturbative arguments and we emphasise that these results are only valid for 'type-I like' scenarios where the entry diagonally opposite the dominant block is zero. Our results agree with the gap properties derived in [46] in the type-I limit which assumes m ee = (m EE ) T = m D and m Ee = m R and recovers the usual type-I hierarchy.…”

Section: A2 Singular Values For Multiple Generationssupporting

confidence: 89%

Lowering the scale of Pati-Salam breaking through seesaw mixing

Dolan,

Dutka,

Volkas

2020

Preprint

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We analyse the experimental limits on the breaking scale of Pati-Salam extensions of the Standard Model. These arise from the experimental limits on rare-meson decay processes mediated at tree-level by the vector leptoquark in the model. This leptoquark ordinarily couples to to both left-and right-handed SM fermions and therefore the meson decays do not experience a helicity suppression. We find that the current limits vary from O(80 − 2500) TeV depending on the choice of matrix structure appearing in the relevant three-generational charged-current interactions. We extensively analyse scenarios where additional fermionic degrees of freedom are introduced, transforming as complete Pati-Salam multiplets. These can lower the scales of Pati-Salam breaking through massmixing within the charged-lepton and down-quark sectors, leading to a helicity suppression of the meson decay widths which constrain Pati-Salam breaking. We find four multiplets with varying degrees of viability for this purpose: an SU (2) L/R bidoublet, a pair of SU (4) decuplets and either a SU (2) L or SU (2) R triplet all of which contain heavy exotic versions of the SM charged leptons. We find that the Pati-Salam limits can be as low as O(5 − 150) TeV with the addition of these four multiplets. We also identify an interesting possible connection between the smallness of the neutrino masses and a helicity suppression of the Pati-Salam limits for three of the four multiplets.

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“…In [15] the matrix theory has been applied to phenomenological studies and new limits on light-heavy neutrino mixings in the 3 + 1 model (three light, known neutrinos with one additional sterile neutrino) have been obtained. In another work where the matrix theory methods have been explored in the context of neutrino physics, conditions for the existence of the gap in the seesaw mass spectrum have been established and justified [16,17]. We should also mention that an interesting mathematical connection between eigenvalues and eigenvectors has been rediscovered in the context of neutrino oscillations in matter [18,19].…”

Section: Introductionmentioning

confidence: 94%

Geometry of the neutrino mixing space

Flieger,

Gluza

2022

Preprint

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We study a geometric structure of a physical region of neutrino mixing matrices as part of the unit ball of the spectral norm. Each matrix from the geometric region is a convex combination of unitary PMNS matrices. The disjoint subsets corresponding to a different minimal number of additional neutrinos are described as relative interiors of faces of the unit ball. We determined the Carathéodory's number showing that, at most, four unitary matrices of dimension three are necessary to represent any matrix from the neutrino geometric region. For matrices which correspond to scenarios with one and two additional neutrino states, the Carathéodory's number is two and three, respectively. Further, we discuss the volume associated with different mathematical structures, particularly with unitary and orthogonal groups, and the unit ball of the spectral norm. We compare the obtained volumes to the volume of the region of physically admissible mixing matrices for both the CP-conserving and CP-violating cases in the present scenario with three neutrino families and scenarios with the neutrino mixing matrix of dimension higher than three.

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A remark on the mathematics of the seesaw mechanism

Cited by 7 publications

References 6 publications

Lowering the scale of Pati-Salam breaking through seesaw mixing

Lowering the scale of Pati-Salam breaking through seesaw mixing

Lowering the scale of Pati-Salam breaking through seesaw mixing

Geometry of the neutrino mixing space

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