João N . Esteves | Universidade de Lisboa (original) (raw)
Uploads
Papers by João N . Esteves
Álgebras and Representation Theory , 2024
We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y ∞ ], based on the Topologic... more We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y ∞ ], based on the Topological Recursion formula of Eynard and Orantin. We have shown in previous works that the Loday-Ronco Hopf algebra of planar binary trees is a space of solutions for the genus 0 version of Topological Recursion, and that an extension of the Loday Ronco Hopf algebra as to include some new graphs with loops is the correct setting to find a solution space for arbitrary genus. Here we show that this new algebra k[Y ∞ ] h is still a Hopf algebra that can be seen in some sense to be made precise in the text as a quantization of the Hopf algebra of planar binary trees, and that the solution space of Topological Recursion A h TopRec is a subalgebra of a quotient algebra A h Reg obtained from k[Y ∞ ] h that nevertheless doesn't inherit the Hopf algebra structure. We end the paper with a discussion on the cohomology of A h TopRec in low degree.
We study the Maslov correction to semiclassical states by using a K\"ahler regularized BKS p... more We study the Maslov correction to semiclassical states by using a K\"ahler regularized BKS pairing map from the energy representation to the Schr\"odinger representation. For general semiclassical states, the existence of this regularization is based on recently found families of K\"ahler polarizations degenerating to singular real polarizations and corresponding to special geodesic rays in the space of K\"ahler metrics. In the case of the one-dimensional harmonic oscillator, we show that the correct phases associated with caustic points of the projection of the Lagrangian curves to the configuration space are correctly reproduced.
Journal of Physics A: Mathematical and Theoretical, 2015
We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y^∞], based on the Topologica... more We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y^∞], based on the Topological Recursion formula of Eynard and Orantin. We have shown in previous works that the Loday-Ronco Hopf algebra of planar binary trees is a space of solutions for the genus 0 version of Topological Recursion, and that an extension of the Loday Ronco Hopf algebra as to include some new graphs with loops is the correct setting to find a solution space for arbitrary genus. Here we show that this new algebra k[Y^∞]_h is still a Hopf algebra that can be seen in some sense to be made precise in the text as a quantization of the Hopf algebra of planar binary trees, and that the solution space of Topological Recursion is a sub-algebra 𝒜^h_TopRec⊂ k[Y^∞]_h that nevertheless doesn't inherit the Hopf algebra structure. We end the paper with a discussion on the cohomology of 𝒜^h_TopRec in low degree.
The use of graphs, in particular of trees, binary trees and planar binary trees, in mathematical ... more The use of graphs, in particular of trees, binary trees and planar binary trees, in mathematical physics has a long tradition. The canonical examples are perhaps Feynman diagrams but the connection with Hopf Algebras of trees started with the works of Connes and Kreimer [6, 7, 8] that describe the combinatorics of the procedure of extracting sub-divergences in Quantum Field Theory known as the BPHZ renormalization procedure [5]. Another approach to the use of graphs in QFT and in particular in QED, considering binary trees, planar or
Lepton flavour violation and neutrino masses are a signal for new Physics beyond the Standard Mod... more Lepton flavour violation and neutrino masses are a signal for new Physics beyond the Standard Model and are deeply related. The minimal extension of the Standard Model to make it include neutrino masses is not satisfactory from a conceptual point of view, since it requires a severe fine-tuning of Yukawa couplings. See-saw models provide a consistent and natural mechanism to generate neutrino masses and require Physics beyond the Standard Model. In this thesis, the connections between models for neutrino masses and processes that violate lepton flavour are explored. The reconstruction of high energy parameters from neutrino data is partially possible within the framework of these see-saw models and it is enhanced by the knowledge of phenomena outside the neutrino sector, as it is the case of lepton number violation processes. Grand Unification SUSY models offer a consistent theoretical framework for Type I, Type II and Type III see-saw models. On the other hand, Type II see-saw has t...
Journal of High Energy Physics, 2009
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010
We propose an A 4 flavor-symmetric SU(3) ⊗ SU(2) ⊗ U(1) seesaw model where lepton number is broke... more We propose an A 4 flavor-symmetric SU(3) ⊗ SU(2) ⊗ U(1) seesaw model where lepton number is broken spontaneously. A consistent two-zero texture pattern of neutrino masses and mixing emerges from the interplay of type-I and type-II seesaw contributions, with important phenomenological predictions. We show that, if the Majoron becomes massive, such seesaw scenario provides a viable candidate for decaying dark matter, consistent with cosmic microwave background lifetime constraints that follow from current WMAP observations. We also calculate the sub-leading one-loop-induced decay into photons which leads to a mono-energetic emission line that may be observed in future X-ray missions such as Xenia.
Journal of High Energy Physics, 2010
We review Lepton Flavour Violation (LFV) in the supersymmetric version of the seesaw mechanism (t... more We review Lepton Flavour Violation (LFV) in the supersymmetric version of the seesaw mechanism (type I, II, III) and in Left-Right models. The LFV needed to explain neutrino masses and mixings is the only source of LFV and has experimental implications both in lowenergy experiments where we search for the radiative decays of leptons, and at the LHC where we look at its imprint on the LFV decays of the sparticles and on slepton mass splittings. We discuss how this confrontation between high-and low-energy LFV observables may provide information about the underlying mechanism of LFV.
Journal of High Energy Physics, 2012
Left-right symmetric extensions of the Minimal Supersymmetric Standard Model can explain neutrino... more Left-right symmetric extensions of the Minimal Supersymmetric Standard Model can explain neutrino data and have potentially interesting phenomenology beyond that found in minimal SUSY seesaw models. Here we study a SUSY model in which the left-right symmetry is broken by triplets at a high scale, but significantly below the GUT scale. Sparticle spectra in this model differ from the usual constrained MSSM expectations and these changes affect the relic abundance of the lightest neutralino. We discuss changes for the standard stau (and stop) co-annihilation and for the Higgs funnel regions. The model has potentially large lepton flavour violation in both, left and right, scalar leptons and thus allows, in principle, also for flavoured co-annihilation. We also discuss lepton flavour signals due to violating decays of the second lightest neutralino at the LHC, which can be as large as 20 fb −1 at √ s = 14 TeV.
Physical Review D, 2013
We study a supersymmetric version of the seesaw mechanism type-III. The model consists of the MSS... more We study a supersymmetric version of the seesaw mechanism type-III. The model consists of the MSSM particle content plus three copies of 24 superfields. The fermionic part of the SU (2) triplet contained in the 24 is responsible for the type-III seesaw, which is used to explain the observed neutrino masses and mixings. Complete copies of 24 are introduced to maintain gauge coupling unification. These additional states change the beta functions of the gauge couplings above the seesaw scale. Using mSUGRA boundary conditions we calculate the resulting supersymmetric mass spectra at the electro-weak scale using full 2-loop renormalization group equations. We show that the resulting spectrum can be quite different compared to the usual mSUGRA spectrum. We discuss how this might be used to obtain information on the seesaw scale from mass measurements. Constraints on the model space due to limits on lepton flavour violating decays are discussed. The main constraints come from the bounds on µ → eγ but there are also regions where the decay τ → µγ gives stronger constraints. We also calculate the regions allowed by the dark matter constraint. For the sake of completeness, we compare our results with those for the supersymmetric seesaw type-II and, to some extent, with type-I.
Journal of Physics: Conference Series, 2010
Journal of Physics A: Mathematical and Theoretical, 2015
We study the Maslov correction to semiclassical states by using a Kähler regularized BKS pairing ... more We study the Maslov correction to semiclassical states by using a Kähler regularized BKS pairing map from the energy representation to the Schrödinger representation. For general semiclassical states, the existence of this regularization is based on recently found families of Kähler polarizations degenerating to singular real polarizations and corresponding to special geodesic rays in the space of Kähler metrics. In the case of the one-dimensional harmonic oscillator, we show that the correct phases associated with caustic points of the projection of the Lagrangian curves to the configuration space are correctly reproduced. Contents 1 Introduction 1 2 Preliminaries 2 3 Kähler regularizations 3 4 Schrödinger semiclassical states and Maslov phases 4 4.
We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of... more We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf Algebra by identifying pairs of nearest neighbor leaves and thus producing graphs with loops we obtain the full recursion formula of Eynard and Orantin.
Álgebras and Representation Theory , 2024
We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y ∞ ], based on the Topologic... more We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y ∞ ], based on the Topological Recursion formula of Eynard and Orantin. We have shown in previous works that the Loday-Ronco Hopf algebra of planar binary trees is a space of solutions for the genus 0 version of Topological Recursion, and that an extension of the Loday Ronco Hopf algebra as to include some new graphs with loops is the correct setting to find a solution space for arbitrary genus. Here we show that this new algebra k[Y ∞ ] h is still a Hopf algebra that can be seen in some sense to be made precise in the text as a quantization of the Hopf algebra of planar binary trees, and that the solution space of Topological Recursion A h TopRec is a subalgebra of a quotient algebra A h Reg obtained from k[Y ∞ ] h that nevertheless doesn't inherit the Hopf algebra structure. We end the paper with a discussion on the cohomology of A h TopRec in low degree.
We study the Maslov correction to semiclassical states by using a K\"ahler regularized BKS p... more We study the Maslov correction to semiclassical states by using a K\"ahler regularized BKS pairing map from the energy representation to the Schr\"odinger representation. For general semiclassical states, the existence of this regularization is based on recently found families of K\"ahler polarizations degenerating to singular real polarizations and corresponding to special geodesic rays in the space of K\"ahler metrics. In the case of the one-dimensional harmonic oscillator, we show that the correct phases associated with caustic points of the projection of the Lagrangian curves to the configuration space are correctly reproduced.
Journal of Physics A: Mathematical and Theoretical, 2015
We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y^∞], based on the Topologica... more We propose a quantization algebra of the Loday-Ronco Hopf algebra k[Y^∞], based on the Topological Recursion formula of Eynard and Orantin. We have shown in previous works that the Loday-Ronco Hopf algebra of planar binary trees is a space of solutions for the genus 0 version of Topological Recursion, and that an extension of the Loday Ronco Hopf algebra as to include some new graphs with loops is the correct setting to find a solution space for arbitrary genus. Here we show that this new algebra k[Y^∞]_h is still a Hopf algebra that can be seen in some sense to be made precise in the text as a quantization of the Hopf algebra of planar binary trees, and that the solution space of Topological Recursion is a sub-algebra 𝒜^h_TopRec⊂ k[Y^∞]_h that nevertheless doesn't inherit the Hopf algebra structure. We end the paper with a discussion on the cohomology of 𝒜^h_TopRec in low degree.
The use of graphs, in particular of trees, binary trees and planar binary trees, in mathematical ... more The use of graphs, in particular of trees, binary trees and planar binary trees, in mathematical physics has a long tradition. The canonical examples are perhaps Feynman diagrams but the connection with Hopf Algebras of trees started with the works of Connes and Kreimer [6, 7, 8] that describe the combinatorics of the procedure of extracting sub-divergences in Quantum Field Theory known as the BPHZ renormalization procedure [5]. Another approach to the use of graphs in QFT and in particular in QED, considering binary trees, planar or
Lepton flavour violation and neutrino masses are a signal for new Physics beyond the Standard Mod... more Lepton flavour violation and neutrino masses are a signal for new Physics beyond the Standard Model and are deeply related. The minimal extension of the Standard Model to make it include neutrino masses is not satisfactory from a conceptual point of view, since it requires a severe fine-tuning of Yukawa couplings. See-saw models provide a consistent and natural mechanism to generate neutrino masses and require Physics beyond the Standard Model. In this thesis, the connections between models for neutrino masses and processes that violate lepton flavour are explored. The reconstruction of high energy parameters from neutrino data is partially possible within the framework of these see-saw models and it is enhanced by the knowledge of phenomena outside the neutrino sector, as it is the case of lepton number violation processes. Grand Unification SUSY models offer a consistent theoretical framework for Type I, Type II and Type III see-saw models. On the other hand, Type II see-saw has t...
Journal of High Energy Physics, 2009
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2010
We propose an A 4 flavor-symmetric SU(3) ⊗ SU(2) ⊗ U(1) seesaw model where lepton number is broke... more We propose an A 4 flavor-symmetric SU(3) ⊗ SU(2) ⊗ U(1) seesaw model where lepton number is broken spontaneously. A consistent two-zero texture pattern of neutrino masses and mixing emerges from the interplay of type-I and type-II seesaw contributions, with important phenomenological predictions. We show that, if the Majoron becomes massive, such seesaw scenario provides a viable candidate for decaying dark matter, consistent with cosmic microwave background lifetime constraints that follow from current WMAP observations. We also calculate the sub-leading one-loop-induced decay into photons which leads to a mono-energetic emission line that may be observed in future X-ray missions such as Xenia.
Journal of High Energy Physics, 2010
We review Lepton Flavour Violation (LFV) in the supersymmetric version of the seesaw mechanism (t... more We review Lepton Flavour Violation (LFV) in the supersymmetric version of the seesaw mechanism (type I, II, III) and in Left-Right models. The LFV needed to explain neutrino masses and mixings is the only source of LFV and has experimental implications both in lowenergy experiments where we search for the radiative decays of leptons, and at the LHC where we look at its imprint on the LFV decays of the sparticles and on slepton mass splittings. We discuss how this confrontation between high-and low-energy LFV observables may provide information about the underlying mechanism of LFV.
Journal of High Energy Physics, 2012
Left-right symmetric extensions of the Minimal Supersymmetric Standard Model can explain neutrino... more Left-right symmetric extensions of the Minimal Supersymmetric Standard Model can explain neutrino data and have potentially interesting phenomenology beyond that found in minimal SUSY seesaw models. Here we study a SUSY model in which the left-right symmetry is broken by triplets at a high scale, but significantly below the GUT scale. Sparticle spectra in this model differ from the usual constrained MSSM expectations and these changes affect the relic abundance of the lightest neutralino. We discuss changes for the standard stau (and stop) co-annihilation and for the Higgs funnel regions. The model has potentially large lepton flavour violation in both, left and right, scalar leptons and thus allows, in principle, also for flavoured co-annihilation. We also discuss lepton flavour signals due to violating decays of the second lightest neutralino at the LHC, which can be as large as 20 fb −1 at √ s = 14 TeV.
Physical Review D, 2013
We study a supersymmetric version of the seesaw mechanism type-III. The model consists of the MSS... more We study a supersymmetric version of the seesaw mechanism type-III. The model consists of the MSSM particle content plus three copies of 24 superfields. The fermionic part of the SU (2) triplet contained in the 24 is responsible for the type-III seesaw, which is used to explain the observed neutrino masses and mixings. Complete copies of 24 are introduced to maintain gauge coupling unification. These additional states change the beta functions of the gauge couplings above the seesaw scale. Using mSUGRA boundary conditions we calculate the resulting supersymmetric mass spectra at the electro-weak scale using full 2-loop renormalization group equations. We show that the resulting spectrum can be quite different compared to the usual mSUGRA spectrum. We discuss how this might be used to obtain information on the seesaw scale from mass measurements. Constraints on the model space due to limits on lepton flavour violating decays are discussed. The main constraints come from the bounds on µ → eγ but there are also regions where the decay τ → µγ gives stronger constraints. We also calculate the regions allowed by the dark matter constraint. For the sake of completeness, we compare our results with those for the supersymmetric seesaw type-II and, to some extent, with type-I.
Journal of Physics: Conference Series, 2010
Journal of Physics A: Mathematical and Theoretical, 2015
We study the Maslov correction to semiclassical states by using a Kähler regularized BKS pairing ... more We study the Maslov correction to semiclassical states by using a Kähler regularized BKS pairing map from the energy representation to the Schrödinger representation. For general semiclassical states, the existence of this regularization is based on recently found families of Kähler polarizations degenerating to singular real polarizations and corresponding to special geodesic rays in the space of Kähler metrics. In the case of the one-dimensional harmonic oscillator, we show that the correct phases associated with caustic points of the projection of the Lagrangian curves to the configuration space are correctly reproduced. Contents 1 Introduction 1 2 Preliminaries 2 3 Kähler regularizations 3 4 Schrödinger semiclassical states and Maslov phases 4 4.
We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of... more We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf Algebra by identifying pairs of nearest neighbor leaves and thus producing graphs with loops we obtain the full recursion formula of Eynard and Orantin.