Isis; an international review devoted to the history of science and its cultural influences, 2015
The history of the theory of general relativity presents unique features. After its discovery, th... more The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly di...
Isis; an international review devoted to the history of science and its cultural influences, 2015
The history of the theory of general relativity presents unique features. After its discovery, th... more The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly di...
Physical Review D Particles and Fields, Jun 26, 2007
Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, van... more Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, vanishing Ue3, and a nonmaximal atmospheric neutrino mixing angle θ23. We show that these values emerge naturally by the hypothesis of scaling in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the Le-Lμ-Lτ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing Ue3 and maximal atmospheric neutrino mixing are shown to be unlikely to lead to nonmaximal θ23 while simultaneously keeping Ue3 zero. We find a peculiar ratio of the branching ratios μ→eγ and τ→eγ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in τ→eγ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry D4×Z2 leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant CP phase is identical to the low energy Majorana phase, and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV.
In this paper we discuss how to extract information about physics beyond the Standard Model (SM) ... more In this paper we discuss how to extract information about physics beyond the Standard Model (SM) from searches for a light SM Higgs at Tevatron Run II and CERN LHC. We demonstrate that new (pseudo)scalar states predicted in both supersymmetric and dynamical models can have enhanced visibility in standard Higgs search channels, making them potentially discov- erable at Tevatron Run
This thesis deals with the possibility of describing the flavor sector of the Standard Model of P... more This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D4, the other describing quarks and employing the symmetry D14. In the latter model it is the quark mixing matrix element...
Studies In History and Philosophy of Science Part B Studies In History and Philosophy of Modern Physics
Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in ... more Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary.
In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order... more In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, interactions involving electrically neutral and doubly charged bosons are investigated. We also investigate flavour changes at 1-loop level. In all cases we find that the essential theoretical requirements can be reduced to a few basic conditions on the particle content and the coupling matrices. For 1-loop diagrams, we also investigate how exactly a GIM-suppression can occur that will strongly reduce the rates of lepton flavour violating effects even if they are in principle present in a certain theory. In all chapters, we apply our criteria to several models which can in general induce lepton flavour violation, e.g. LR-symmetric models or the MSSM. In the end we give a summarizing table of the obtained results, thereby demonstrating the applicability of our criteria to a large class of models beyond the Standard Model. *
The Standard Model (SM) of particle physics unifies the electromagnetic and the weak force under ... more The Standard Model (SM) of particle physics unifies the electromagnetic and the weak force under an SU(2) x U(1) gauge group. The fact that these forces are observed to be so different in strength and range is explained by spontaneous breaking of this symmetry, induced by the nonzero vacuum expectation value of a scalar Higgs field. There is however no experimental evidence for the Higgs field and there are also theoretical difficulties. In one class of extensions of the SM designed to deal with these problems, the electroweak symmetry is broken dynamically. This thesis provides a framework in which SM Higgs searches at Tevatron Run II and at the Large Hadron Collider (LHC) can be extended to new scalar or pseudoscalar states predicted in dynamical models of electroweak symmetry breaking. These states can have enhanced visibility in standard Higgs search channels, making them potentially discoverable at Tevatron Run II and definitely visible at the LHC. I discuss the likely sizes of the enhancements in the various search channels for each model and identify the model features having the largest influence on the degree of enhancement. I suggest the mass reaches of Higgs searches at Tevatron and LHC for these non-standard scalar states. I compare signals for the non-standard scalars across models and also with expectations in the SM and the Minimal Supersymmetric Model, another theory beyond the SM, to show how one could start to identify which state has actually been found.
In this paper we discuss how to extract information about physics beyond the Standard Model (SM) ... more In this paper we discuss how to extract information about physics beyond the Standard Model (SM) from searches for a light SM Higgs at Tevatron Run II and CERN LHC. We demonstrate that new (pseudo)scalar states predicted in both supersymmetric and dynamical models can have enhanced visibility in standard Higgs search channels, making them potentially discoverable at Tevatron Run II and CERN LHC. We discuss the likely sizes of the enhancements in the various search channels for each model and identify the model features having the largest influence on the degree of enhancement. We compare the key signals for the non-standard scalars across models and also with expectations in the SM, to show how one could start to identify which state has actually been found. In particular, we suggest the likely mass reach of the Higgs search in pp/pp → H → τ + τ − for each kind of non-standard scalar state and we demonstrate that pp/pp → H → γγ may cleanly distinguish the scalars of supersymmetric models from those of dynamical models. * MSUHEP-050608
Journal of High Energy Physics - J HIGH ENERGY PHYS, 2009
We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in \ci... more We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in \cite{GL1} which predicts theta23 maximal and theta13 = 0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 × Z2(aux) in the original model, to D4 × Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since theta23 maximal and theta13 = 0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of theta13 and theta23, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity |mee|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m3. The...
In it was shown how the flavor symmetry A 4 (or S 4 ) can arise if the three fermion generations ... more In it was shown how the flavor symmetry A 4 (or S 4 ) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincaré symmetry, after it is broken down to the 4-dimensional Poincaré symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from them. The symmetries we obtain from these orbifolds are, in addition to S 4 and A 4 , the groups D 3 , D 4 and D 6 ≃ D 3 × Z 2 which are all popular groups for flavored model building. *
We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying... more We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU (2) or SU (3) through spontaneous symmetry breaking. We consider all possible cases, where the continuous symmetry is broken by small representations. "Small" representations are these which couple at leading order to the Standard Model fermions transforming as twoor three-dimensional representations of the flavor group. We find that, given this limited representation content, the only non-abelian discrete group which can arise as a residual symmetry is the quaternion group D ′ 2 .
Best-fit values of recent global analyzes of neutrino data imply large solar neutrino mixing, van... more Best-fit values of recent global analyzes of neutrino data imply large solar neutrino mixing, vanishing U e3 and a non-maximal atmospheric neutrino mixing angle θ 23 . We show that these values emerge naturally by the hypothesis of "scaling" in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the L e − L µ − L τ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing U e3 and maximal atmospheric neutrino mixing are shown to be unlikely to lead to non-maximal θ 23 while keeping simultaneously U e3 zero. We find a peculiar ratio of the branching ratios µ → eγ and τ → eγ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in τ → eγ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry D 4 × Z 2 leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant CP phase is identical to the low energy Majorana phase and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV. *
We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element... more We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element |V ud | can take the value |V ud | = cos π 14 ≈ 0.97493 implying that the Cabibbo angle θ C is sin (θ C ) ≈ |V us | ≈ sin π 14 ≈ 0.2225. These values are very close to those observed in experiments. The value of |V ud | (θ C ) is based on the fact that different Z 2 subgroups of D 14 are conserved in the up and down quark sector. In order to achieve this, D 14 is accompanied by a Z 3 symmetry. The spontaneous breaking of D 14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D 14 and partly due to a Froggatt-Nielsen symmetry U (1) F N under which only the right-handed quarks transform. The model is completely natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for |V ud |. Out of these, only one of them leads to a phenomenological viable model. A study of the Z 2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow |V ud | (θ C ) to be well inside the small experimental error bars.
It has recently been speculated that the solar neutrino mixing angle is connected to the golden r... more It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio ϕ. Two such proposals have been made, cot θ 12 = ϕ and cos θ 12 = ϕ/2. We compare these Ansätze and discuss a model leading to cos θ 12 = ϕ/2 based on the dihedral group D 10 . This symmetry is a natural candidate because the angle in the expression cos θ 12 = ϕ/2 is simply π/5, or 36 degrees. This is the exterior angle of a decagon and D 10 is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions. * 1 Actually, prediction (A) would lie very slightly outside the 2σ range of Ref. , which is sin 2 θ 12 = 0.278 ÷ 0.352.
P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys. Lett. B 530, 167 (2002) [INSPEC][ADS][CAS ]... more P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys. Lett. B 530, 167 (2002) [INSPEC][ADS][CAS ]; P. F. Harrison and W. G. Scott, Phys. Lett. B 535, 163 (2002) [INSPEC][ADS][CAS]; Z. z. Xing, Phys. Lett. B 533, 85 (2002) [INSPEC][ADS][CAS]; P. F. Harrison and W. G. Scott, ...
Isis; an international review devoted to the history of science and its cultural influences, 2015
The history of the theory of general relativity presents unique features. After its discovery, th... more The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly di...
Isis; an international review devoted to the history of science and its cultural influences, 2015
The history of the theory of general relativity presents unique features. After its discovery, th... more The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly di...
Physical Review D Particles and Fields, Jun 26, 2007
Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, van... more Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, vanishing Ue3, and a nonmaximal atmospheric neutrino mixing angle θ23. We show that these values emerge naturally by the hypothesis of scaling in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the Le-Lμ-Lτ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing Ue3 and maximal atmospheric neutrino mixing are shown to be unlikely to lead to nonmaximal θ23 while simultaneously keeping Ue3 zero. We find a peculiar ratio of the branching ratios μ→eγ and τ→eγ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in τ→eγ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry D4×Z2 leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant CP phase is identical to the low energy Majorana phase, and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV.
In this paper we discuss how to extract information about physics beyond the Standard Model (SM) ... more In this paper we discuss how to extract information about physics beyond the Standard Model (SM) from searches for a light SM Higgs at Tevatron Run II and CERN LHC. We demonstrate that new (pseudo)scalar states predicted in both supersymmetric and dynamical models can have enhanced visibility in standard Higgs search channels, making them potentially discov- erable at Tevatron Run
This thesis deals with the possibility of describing the flavor sector of the Standard Model of P... more This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D4, the other describing quarks and employing the symmetry D14. In the latter model it is the quark mixing matrix element...
Studies In History and Philosophy of Science Part B Studies In History and Philosophy of Modern Physics
Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in ... more Sidney Dancoff׳s paper “On Radiative Corrections for Electron Scattering” is generally viewed in the secondary literature as a failed attempt to develop renormalized quantum electrodynamics (QED) a decade early, an attempt that failed because of a mistake that Dancoff made. I will discuss Dancoff׳s mistake and try to reconstruct why it occurred, by relating it to the usual practices of the quantum field theory of his time. I will also argue against the view that Dancoff was on the verge of developing renormalized QED and will highlight the conceptual divides that separate Dancoff׳s work from the QED of the late 1940s. I will finally discuss how the established view of Dancoff׳s paper came to be and how the reading of this specific anecdote relates to more general assessments of the conceptual advances of the late 1940s (covariant techniques, renormalization), in particular to their assessment as being conservative rather than revolutionary.
In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order... more In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, interactions involving electrically neutral and doubly charged bosons are investigated. We also investigate flavour changes at 1-loop level. In all cases we find that the essential theoretical requirements can be reduced to a few basic conditions on the particle content and the coupling matrices. For 1-loop diagrams, we also investigate how exactly a GIM-suppression can occur that will strongly reduce the rates of lepton flavour violating effects even if they are in principle present in a certain theory. In all chapters, we apply our criteria to several models which can in general induce lepton flavour violation, e.g. LR-symmetric models or the MSSM. In the end we give a summarizing table of the obtained results, thereby demonstrating the applicability of our criteria to a large class of models beyond the Standard Model. *
The Standard Model (SM) of particle physics unifies the electromagnetic and the weak force under ... more The Standard Model (SM) of particle physics unifies the electromagnetic and the weak force under an SU(2) x U(1) gauge group. The fact that these forces are observed to be so different in strength and range is explained by spontaneous breaking of this symmetry, induced by the nonzero vacuum expectation value of a scalar Higgs field. There is however no experimental evidence for the Higgs field and there are also theoretical difficulties. In one class of extensions of the SM designed to deal with these problems, the electroweak symmetry is broken dynamically. This thesis provides a framework in which SM Higgs searches at Tevatron Run II and at the Large Hadron Collider (LHC) can be extended to new scalar or pseudoscalar states predicted in dynamical models of electroweak symmetry breaking. These states can have enhanced visibility in standard Higgs search channels, making them potentially discoverable at Tevatron Run II and definitely visible at the LHC. I discuss the likely sizes of the enhancements in the various search channels for each model and identify the model features having the largest influence on the degree of enhancement. I suggest the mass reaches of Higgs searches at Tevatron and LHC for these non-standard scalar states. I compare signals for the non-standard scalars across models and also with expectations in the SM and the Minimal Supersymmetric Model, another theory beyond the SM, to show how one could start to identify which state has actually been found.
In this paper we discuss how to extract information about physics beyond the Standard Model (SM) ... more In this paper we discuss how to extract information about physics beyond the Standard Model (SM) from searches for a light SM Higgs at Tevatron Run II and CERN LHC. We demonstrate that new (pseudo)scalar states predicted in both supersymmetric and dynamical models can have enhanced visibility in standard Higgs search channels, making them potentially discoverable at Tevatron Run II and CERN LHC. We discuss the likely sizes of the enhancements in the various search channels for each model and identify the model features having the largest influence on the degree of enhancement. We compare the key signals for the non-standard scalars across models and also with expectations in the SM, to show how one could start to identify which state has actually been found. In particular, we suggest the likely mass reach of the Higgs search in pp/pp → H → τ + τ − for each kind of non-standard scalar state and we demonstrate that pp/pp → H → γγ may cleanly distinguish the scalars of supersymmetric models from those of dynamical models. * MSUHEP-050608
Journal of High Energy Physics - J HIGH ENERGY PHYS, 2009
We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in \ci... more We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in \cite{GL1} which predicts theta23 maximal and theta13 = 0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 × Z2(aux) in the original model, to D4 × Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since theta23 maximal and theta13 = 0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of theta13 and theta23, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity |mee|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m3. The...
In it was shown how the flavor symmetry A 4 (or S 4 ) can arise if the three fermion generations ... more In it was shown how the flavor symmetry A 4 (or S 4 ) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincaré symmetry, after it is broken down to the 4-dimensional Poincaré symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from them. The symmetries we obtain from these orbifolds are, in addition to S 4 and A 4 , the groups D 3 , D 4 and D 6 ≃ D 3 × Z 2 which are all popular groups for flavored model building. *
We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying... more We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU (2) or SU (3) through spontaneous symmetry breaking. We consider all possible cases, where the continuous symmetry is broken by small representations. "Small" representations are these which couple at leading order to the Standard Model fermions transforming as twoor three-dimensional representations of the flavor group. We find that, given this limited representation content, the only non-abelian discrete group which can arise as a residual symmetry is the quaternion group D ′ 2 .
Best-fit values of recent global analyzes of neutrino data imply large solar neutrino mixing, van... more Best-fit values of recent global analyzes of neutrino data imply large solar neutrino mixing, vanishing U e3 and a non-maximal atmospheric neutrino mixing angle θ 23 . We show that these values emerge naturally by the hypothesis of "scaling" in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the L e − L µ − L τ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing U e3 and maximal atmospheric neutrino mixing are shown to be unlikely to lead to non-maximal θ 23 while keeping simultaneously U e3 zero. We find a peculiar ratio of the branching ratios µ → eγ and τ → eγ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in τ → eγ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry D 4 × Z 2 leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant CP phase is identical to the low energy Majorana phase and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV. *
We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element... more We construct a supersymmetric model with the flavor symmetry D 14 in which the CKM matrix element |V ud | can take the value |V ud | = cos π 14 ≈ 0.97493 implying that the Cabibbo angle θ C is sin (θ C ) ≈ |V us | ≈ sin π 14 ≈ 0.2225. These values are very close to those observed in experiments. The value of |V ud | (θ C ) is based on the fact that different Z 2 subgroups of D 14 are conserved in the up and down quark sector. In order to achieve this, D 14 is accompanied by a Z 3 symmetry. The spontaneous breaking of D 14 is induced by flavons, which are scalar gauge singlets. The quark mass hierarchy is partly due to the flavor group D 14 and partly due to a Froggatt-Nielsen symmetry U (1) F N under which only the right-handed quarks transform. The model is completely natural in the sense that the hierarchies among the quark masses and mixing angles are generated with the help of symmetries. The issue of the vacuum alignment of the flavons is solved up to a small number of degeneracies, leaving four different possible values for |V ud |. Out of these, only one of them leads to a phenomenological viable model. A study of the Z 2 subgroup breaking terms shows that the results achieved in the symmetry limit are only slightly perturbed. At the same time they allow |V ud | (θ C ) to be well inside the small experimental error bars.
It has recently been speculated that the solar neutrino mixing angle is connected to the golden r... more It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio ϕ. Two such proposals have been made, cot θ 12 = ϕ and cos θ 12 = ϕ/2. We compare these Ansätze and discuss a model leading to cos θ 12 = ϕ/2 based on the dihedral group D 10 . This symmetry is a natural candidate because the angle in the expression cos θ 12 = ϕ/2 is simply π/5, or 36 degrees. This is the exterior angle of a decagon and D 10 is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions. * 1 Actually, prediction (A) would lie very slightly outside the 2σ range of Ref. , which is sin 2 θ 12 = 0.278 ÷ 0.352.
P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys. Lett. B 530, 167 (2002) [INSPEC][ADS][CAS ]... more P. F. Harrison, D. H. Perkins, and W. G. Scott, Phys. Lett. B 530, 167 (2002) [INSPEC][ADS][CAS ]; P. F. Harrison and W. G. Scott, Phys. Lett. B 535, 163 (2002) [INSPEC][ADS][CAS]; Z. z. Xing, Phys. Lett. B 533, 85 (2002) [INSPEC][ADS][CAS]; P. F. Harrison and W. G. Scott, ...
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Papers by Alexander Blum