Electroweak $SU(2{)}_L\times U(1{)}_Y$ model with strong spontaneously fermion-mass-generating gauge dynamics

Abstract

Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor $SU(3{)}_f$ symmetry with scale $\hat{I}›$. Anomaly freedom requires addition of three $\hat{I}{½}_R$. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies $\hat{I}{\pounds }_f(p^2)$ has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) $\hat{I}{\pounds }_f(p^2)=M_{fR}^2/p$ where three Majorana masses $M_{fR}$ of $\hat{I}{½}_{fR}$ are of order $\hat{I}›$. (2) $\hat{I}{\pounds }_f(p^2)=m_f^2/p$ where three Dirac masses $m_f=m_{(0)}1+m_{(3)}\hat{I}{»}_3+m_{(8)}\hat{I}{»}_8$ of SM fermions are {\it exponentially suppressed w.r.t. $\hat{I}›$}, and {\it degenerate for all SM fermions in $f$}. (1) $M_{fR}$ break $SU(3{)}_f$ symmetry completely; $m_{(3)},m_{(8)}$ superimpose the tiny breaking to $U(1)\times U(1)$. All flavor gluons thus acquire self-consistently the masses $\sim \hat{I}›$. (2) All $m_f$ break the electroweak $SU(2{)}_L\times U(1{)}_Y$ to $U(1{)}_{em}$. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) Three $\hat{I}{½}_R$-composed Higgses $\ddot{I}{‡}_i$ with masses $\sim \hat{I}›$. (2) Two new SM-fermion-composed Higgses $h_3,h_8$ with masses $\sim m_{(3)},m_{(8)}$, respectively. (3) The SM-like SM-fermion-composed Higgs $h$ with mass $\sim m_{(0)}$, the effective Fermi scale. $\hat{I}{\pounds }_f(p^2)$-dependent vertices in the electroweak Ward-Takahashi identities imply: The axial-vector ones give rise to the $W$ and $Z$ masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in $f$. At the present exploratory stage the splitting comes out unrealistic.

19 pages, 1 figure