Abstract
We present scheme-independent calculations of the derivative of the beta function, denoted $\beta'_{IR}$, at a conformally invariant infrared (IR) fixed point, in several asymptotically free chiral gauge theories, namely SO($4k+2$) with $2 \le k \le 4$ with respective numbers $N_f$ of fermions in the spinor representation, and E$_6$ with fermions in the fundamental representation.
Highlights
A weakly coupled chiral gauge theory associated with the GEW 1⁄4 SUð2ÞL ⊗ Uð1ÞY electroweak gauge symmetry plays a crucial role in nature, comprising the electroweak sector of the Standard Model (SM)
For our SOðNÞ theories with N 1⁄4 4k þ 2, we find that the signs of d4 and d5 depend on N; they are both negative for SO(10); they are mixed for SO(14); and they are both positive for SO(18)
In [41] we carried out corresponding scheme-independent calculations of the dj coefficients for vectorial gauge theories based on the gauge groups SOðNÞ with N ≥ 3 [the SOð2Þ ≈ Uð1Þ
Summary
A weakly coupled chiral gauge theory ( χGT) associated with the GEW 1⁄4 SUð2ÞL ⊗ Uð1ÞY electroweak gauge symmetry plays a crucial role in nature, comprising the electroweak sector of the Standard Model (SM). EWSB models should exhibit quasiconformal behavior, which can occur naturally in the presence of an approximate infrared fixed point (IRFP) of the renormalization group (RG) at a value of the gauge coupling that is sufficiently strong to eventually cause the bilinear fermion condensate formation. Since this spontaneously breaks the approximate scale (dilatation) invariance, this can lead to a resultant light dilatonlike scalar, with Higgs-like properties (some papers on this include [10,11,12,13,14,15]). VI and some relevant group-theoretic formulas in the Appendix
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