Abstract
Abstract We propose a bottom-up approach in which a structure of high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that the magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be highly sensitive to a small variation of matrix elements, and it seems that the mass hierarchy occurs as a result of fine tuning.
Highlights
One of the most fascinating riddles in particle physics is the origin of the fermion mass hierarchy and flavor mixing in the standard model (SM)
We propose a bottom-up approach that a structure of a high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension
We adopt several assumptions. (a) A theory beyond the SM, which is referred to as high-energy theories (HETs), has higher gauge symmetries. It owns a seed of the flavor structure, and the form of Yukawa coupling matrices is determined by HET
Summary
One of the most fascinating riddles in particle physics is the origin of the fermion mass hierarchy and flavor mixing in the standard model (SM). We propose a bottom-up approach that a structure of a high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. Based on the bottom-up approach, we make conjectures on Yukawa couplings and pursue whether they are realized or not in an extension of the SM including heavy vector-like fermions, without specifying HETs beyond the extension. It comes from our expectation that the magnitude of dimensionless parameters on terms allowed by symmetries should be O(1) in a fundamental theory If it is true, the hierarchical structure of Yukawa couplings occurs after a transition from a HET to the extension of the SM or through a mechanism in some lower-energy physics.
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