Electroweak symmetry breaking in Higgs mechanism with composite operators and solution of naturalness

Abstract

Introducing a source for a bi-local composite operator motivated by the perturbative expansion in gauge couplings, we calculate its effective potential in the renormalization group of Standard Model with no involvement of technicolor. The potential indicates the breaking of electroweak symmetry below a scale M due to a nonzero vacuum expectation value of neutral component for the SU(2)-doublet operator. At virtualities below a cut off \Lambda we introduce the local higgs approximation for the effective fields of sources coupled to the composite operators. The value of \Lambda\approx 600 GeV is fixed by the measured masses of gauge vector bosons. The exploration of equations for infrared fixed points of calculated Yukawa constants allows us to evaluate the masses of heaviest fermion generation with a good accuracy, so that m_t(m_t) = 165\pm 4 GeV, m_b(m_b) = 4.18\pm 0.38 GeV and m_\tau(m_\tau) = 1.78\pm 0.27 GeV. After a finite renormalization of effective fields for the sources of composite operators, the parameters of effective Higgs field potential are calculated at the scale of matching with the local theory \Lambda. The fixed point for the Yukawa constant of t quark and the matching condition for the null effective potential at M drive the M value to the GUT scale. The equation for the infrared fixed point of quartic self-action allows us to get estimates for two almost degenerate scalar particles with m_H= 306\pm 5 GeV, while third scalar coupled with the tau lepton is more heavy: m_{H_\tau} = 552\pm 9 GeV. Some phenomenological implications of the offered approach describing the effective scalar field, and a problem on three fermion generations are discussed.