Abstract: It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of h... more Abstract: It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half–integer conformal weights. This yields representations of fermionic 2–point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. I employ this observation to determine the general structure of the corresponding Lorentz covariant correlators by methods similar to the methods employed in conformal field theory to determine 2 – and 3– point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic 2–point functions of 2D CFT up to a function of the product of momenta. The construction also permits for the formulation of covariant meromorphy constraints on spinors in 3+1 dimensions.
We discuss a dark family of lepton-like particles with their own "private" gauge bosons... more We discuss a dark family of lepton-like particles with their own "private" gauge bosons under a local SU'(2)xU'(1) symmetry. The product of dark and visible gauge groups SU'(2)xU'(1)xSU_w(2)xU_Y(1) is broken dynamically to the diagonal (vector-like) subgroup SU(2)xU(1) through the coupling of two scalar fields M_i to the Higgs field and the dark lepton-like particles. After substituting vacuum expectation values for the fields M_i, the Higgs doublet couples in the standard way to the left-handed SU'(2) doublet and right-handed singlets of the dark gauge group, but not to the extra gauge bosons. This defines a new Higgs portal, where the "dark leptons" can contribute to the dark matter and interact with Standard Model matter through Higgs exchange. It also defines a dark matter model with internal interactions. At low energies, the Standard Model Higgs boson aligns the two electroweak-type symmetry groups in the visible and dark sectors and gen...
In the standard dark matter creation scenario, dark matter arises from freeze-out due to decoupli... more In the standard dark matter creation scenario, dark matter arises from freeze-out due to decoupling from the thermal heat bath in the early universe. On the other hand, topological solitons can also emerge during phase transitions through the Kibble–Zurek mechanism or through bubble nucleation. In particular, Murayama and Shu found that the Kibble–Zurek mechanism can produce topological defects up to about 10 PeV, and Bramante et al. had recently pointed out that direct search constraints can be extrapolated to very large masses. Motivated by these observations, we examine direct search constraints for PeV scale dark skyrmions with a Higgs portal coupling to baryons. We find abundance constraints on the combination $$g_V^2M_S$$gV2MS of Skyrme coupling $$g_V$$gV and skyrmion mass $$M_S$$MS. We also find that extrapolation of the direct search constraints from XENON1T to very high masses constrains the combination $$g_{wh}/g_V^4$$gwh/gV4 as a function of $$M_S$$MS, where $$g_{wh}$$gwh...
We review predictions and constraints for nuclear recoil signals from Higgs portal dark matter un... more We review predictions and constraints for nuclear recoil signals from Higgs portal dark matter under the assumption of standard thermal creation from freeze-out. Thermally created scalar and vector Higgs portal dark matter masses are constrained to be in the resonance region near half the Higgs mass, [Formula: see text], or above several TeV. The resonance region for these models will be tested by XENONnT and LZ. The full mass range up to the unitarity limit can be tested by DarkSide-20k and DARWIN. Fermionic Higgs portal dark matter with a pure CP odd coupling is constrained by the Higgs decay width, but has strongly suppressed recoil cross sections which cannot be tested with upcoming experiments. Fermionic Higgs portal dark matter with a combination of CP even and odd Higgs couplings can be constrained by the direct search experiments.
Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we... more Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we determine densities of states in materials with low dimensional substructures and relativistic dispersion relations. We find that these dimensionally hybrid systems yield quasi-relativistic densities of states that are a superposition of the corresponding two- and three-dimensional densities of states.
We examine consequences of the stabilization of the dilaton through the axion. An estimate of the... more We examine consequences of the stabilization of the dilaton through the axion. An estimate of the resulting dilaton potential yields a relation between the axion parameter $m_a f_{PQ}$ and the average instanton radius, and predicts the ratio between the dilaton mass $m_\phi$ and the axion mass $m_a$. If we identify the string axion with a Peccei--Quinn axion, then $m_\phi m_{Pl}
In this talk I present recent results on Lorentz covariant correlation functions $\langle q(p_1)\... more In this talk I present recent results on Lorentz covariant correlation functions $\langle q(p_1)\overline{q}(p_2)\rangle$ on the cone $p^2=0$. In particular, chiral symmetry breaking terms are constructed which resemble fermionic 2--point functions of 2--D CFT up to a scalar factor.
From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields... more From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields of weights [Formula: see text] and [Formula: see text], where the weights are defined with respect to diffeomorphisms of a sphere in momentum space. The Weyl equation thus appears as a consequence of the transformation behavior of local sections of half-canonical bundles under a change of charts. As a consequence, it is possible to impose covariant constraints on spinors of negative (positive) helicity in terms of (anti-)holomorphy conditions. Furthermore, the identification with half-differentials is employed to determine possible extensions of fermion propagators compatible with Lorentz covariance.
Abstract: It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of h... more Abstract: It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half–integer conformal weights. This yields representations of fermionic 2–point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. I employ this observation to determine the general structure of the corresponding Lorentz covariant correlators by methods similar to the methods employed in conformal field theory to determine 2 – and 3– point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic 2–point functions of 2D CFT up to a function of the product of momenta. The construction also permits for the formulation of covariant meromorphy constraints on spinors in 3+1 dimensions.
We discuss a dark family of lepton-like particles with their own "private" gauge bosons... more We discuss a dark family of lepton-like particles with their own "private" gauge bosons under a local SU'(2)xU'(1) symmetry. The product of dark and visible gauge groups SU'(2)xU'(1)xSU_w(2)xU_Y(1) is broken dynamically to the diagonal (vector-like) subgroup SU(2)xU(1) through the coupling of two scalar fields M_i to the Higgs field and the dark lepton-like particles. After substituting vacuum expectation values for the fields M_i, the Higgs doublet couples in the standard way to the left-handed SU'(2) doublet and right-handed singlets of the dark gauge group, but not to the extra gauge bosons. This defines a new Higgs portal, where the "dark leptons" can contribute to the dark matter and interact with Standard Model matter through Higgs exchange. It also defines a dark matter model with internal interactions. At low energies, the Standard Model Higgs boson aligns the two electroweak-type symmetry groups in the visible and dark sectors and gen...
In the standard dark matter creation scenario, dark matter arises from freeze-out due to decoupli... more In the standard dark matter creation scenario, dark matter arises from freeze-out due to decoupling from the thermal heat bath in the early universe. On the other hand, topological solitons can also emerge during phase transitions through the Kibble–Zurek mechanism or through bubble nucleation. In particular, Murayama and Shu found that the Kibble–Zurek mechanism can produce topological defects up to about 10 PeV, and Bramante et al. had recently pointed out that direct search constraints can be extrapolated to very large masses. Motivated by these observations, we examine direct search constraints for PeV scale dark skyrmions with a Higgs portal coupling to baryons. We find abundance constraints on the combination $$g_V^2M_S$$gV2MS of Skyrme coupling $$g_V$$gV and skyrmion mass $$M_S$$MS. We also find that extrapolation of the direct search constraints from XENON1T to very high masses constrains the combination $$g_{wh}/g_V^4$$gwh/gV4 as a function of $$M_S$$MS, where $$g_{wh}$$gwh...
We review predictions and constraints for nuclear recoil signals from Higgs portal dark matter un... more We review predictions and constraints for nuclear recoil signals from Higgs portal dark matter under the assumption of standard thermal creation from freeze-out. Thermally created scalar and vector Higgs portal dark matter masses are constrained to be in the resonance region near half the Higgs mass, [Formula: see text], or above several TeV. The resonance region for these models will be tested by XENONnT and LZ. The full mass range up to the unitarity limit can be tested by DarkSide-20k and DARWIN. Fermionic Higgs portal dark matter with a pure CP odd coupling is constrained by the Higgs decay width, but has strongly suppressed recoil cross sections which cannot be tested with upcoming experiments. Fermionic Higgs portal dark matter with a combination of CP even and odd Higgs couplings can be constrained by the direct search experiments.
Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we... more Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we determine densities of states in materials with low dimensional substructures and relativistic dispersion relations. We find that these dimensionally hybrid systems yield quasi-relativistic densities of states that are a superposition of the corresponding two- and three-dimensional densities of states.
We examine consequences of the stabilization of the dilaton through the axion. An estimate of the... more We examine consequences of the stabilization of the dilaton through the axion. An estimate of the resulting dilaton potential yields a relation between the axion parameter $m_a f_{PQ}$ and the average instanton radius, and predicts the ratio between the dilaton mass $m_\phi$ and the axion mass $m_a$. If we identify the string axion with a Peccei--Quinn axion, then $m_\phi m_{Pl}
In this talk I present recent results on Lorentz covariant correlation functions $\langle q(p_1)\... more In this talk I present recent results on Lorentz covariant correlation functions $\langle q(p_1)\overline{q}(p_2)\rangle$ on the cone $p^2=0$. In particular, chiral symmetry breaking terms are constructed which resemble fermionic 2--point functions of 2--D CFT up to a scalar factor.
From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields... more From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields of weights [Formula: see text] and [Formula: see text], where the weights are defined with respect to diffeomorphisms of a sphere in momentum space. The Weyl equation thus appears as a consequence of the transformation behavior of local sections of half-canonical bundles under a change of charts. As a consequence, it is possible to impose covariant constraints on spinors of negative (positive) helicity in terms of (anti-)holomorphy conditions. Furthermore, the identification with half-differentials is employed to determine possible extensions of fermion propagators compatible with Lorentz covariance.
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Papers by Rainer Dick