A non-Standard Standard Model
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866909522770001920 |
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| author | LaChapelle, J. |
| author_facet | LaChapelle, J. |
| contents | We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all electroweak gauge bosons interact with each other prior to symmetry breaking. This represents a crucial shift in the identification of physical gauge bosons: Unlike the Standard Model which posits a change of Lie algebra basis induced by spontaneous symmetry breaking, here the basis is unaltered and $A,\,Z^0,\,W^\pm$ represent the physical bosons both before and after spontaneous symmetry breaking. Our choice of $\mathfrak{u}_{EW}(2)$ requires some modification of the matter field representation of the Standard Model. For $U_{EW}(2)$, there are two pertinent representations ${\mathbf{2}}$ and its $U(2)$-conjugate ${\mathbf{2^c}}$ related by a global gauge transformation that squares to minus the identity. The product group structure calls for strong-electroweak degrees of freedom in the $(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},{\mathbf{2^c}})$ of $SU_C(3)\times U_{EW}(2)$ that possess integer electric charge just like leptons. These degrees of freedom play the role of quarks, and they lead to a modified Lagrangian that nevertheless reproduces transition rates and cross sections equivalent to the Standard Model. The close resemblance between quark and lepton electroweak doublets suggests a mechanism for a speculative phase transition between quarks and leptons that stems from the product structure of the symmetry group. Our hypothesis is that the strong and electroweak bosons see each other as a source of decoherence. In effect, lepton representations get identified with the $SU(3)$-trace-reduced quark representations. This mechanism allows for possible extensions of the Standard Model that don't require large inclusive multiplets of matter fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1709_04346 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A non-Standard Standard Model LaChapelle, J. General Physics We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all electroweak gauge bosons interact with each other prior to symmetry breaking. This represents a crucial shift in the identification of physical gauge bosons: Unlike the Standard Model which posits a change of Lie algebra basis induced by spontaneous symmetry breaking, here the basis is unaltered and $A,\,Z^0,\,W^\pm$ represent the physical bosons both before and after spontaneous symmetry breaking. Our choice of $\mathfrak{u}_{EW}(2)$ requires some modification of the matter field representation of the Standard Model. For $U_{EW}(2)$, there are two pertinent representations ${\mathbf{2}}$ and its $U(2)$-conjugate ${\mathbf{2^c}}$ related by a global gauge transformation that squares to minus the identity. The product group structure calls for strong-electroweak degrees of freedom in the $(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},{\mathbf{2^c}})$ of $SU_C(3)\times U_{EW}(2)$ that possess integer electric charge just like leptons. These degrees of freedom play the role of quarks, and they lead to a modified Lagrangian that nevertheless reproduces transition rates and cross sections equivalent to the Standard Model. The close resemblance between quark and lepton electroweak doublets suggests a mechanism for a speculative phase transition between quarks and leptons that stems from the product structure of the symmetry group. Our hypothesis is that the strong and electroweak bosons see each other as a source of decoherence. In effect, lepton representations get identified with the $SU(3)$-trace-reduced quark representations. This mechanism allows for possible extensions of the Standard Model that don't require large inclusive multiplets of matter fields. |
| title | A non-Standard Standard Model |
| topic | General Physics |
| url | https://arxiv.org/abs/1709.04346 |