Self-consistent variational approach to the minimal left-right symmetric model of electroweak interactions

The problem of mass generation is addressed by a Gaussian variational method for the minimal left-right symmetric model of electroweak interactions. Without any scalar bidoublet, the Gaussian effective potential is shown to have a minimum for a broken symmetry vacuum with a finite expectation value for both the scalar Higgs doublets. The symmetry is broken by the fermionic coupling that destabilizes the symmetric vacuum, yielding a self-consistent fermionic mass. In this framework a light Higgs is only compatible with the existence of a new high energy mass scale below 2 TeV.

Figure 1

The free parameters $\lambda$ (solid line) and $\eta$ (dashed line) evaluated by Eqs. (14, 15) as functions of the Higgs mass $\Omega$ at the scale $v_R=1500\mathrm{GeV}$ ($v_R/v_L\approx 6$). Since $\eta \ll \lambda$, the parameter $\eta$ has been rescaled by a factor 100. For comparison the standard [19] GEP ${\lambda }_S$ is also reported (dotted line). The constraint $\lambda ,\eta >0$ is only satisfied for $170<\Omega <253\mathrm{GeV}$ for this choice of $v_R$.

Figure 2

The allowed range for the Higgs mass $\Omega$ (vertical bars) are reported for several choices of the ratio $v_R/v_L$ between high energy and low-energy mass scales ($v_L$ is fixed at the Fermi value $v_{\mathrm{Fermi}}=247\mathrm{GeV}$).

Figure 3

The Gaussian effective potential according to Eq. (8) for several choices of the Higgs mass and the high energy scale $v_R$. From the top: $\Omega =140\mathrm{GeV}$, $v_R=1000\mathrm{GeV}$ (solid line); $\Omega =200\mathrm{GeV}$, $v_R=1500\mathrm{GeV}$ (dashed line); $\Omega =260\mathrm{GeV}$, $v_R=2000\mathrm{GeV}$ (dotted line); $\Omega =320\mathrm{GeV}$, $v_R=2500\mathrm{GeV}$ (dot-dash). For each value of the shift $\phi$ the GEP is evaluated by inserting in Eq. (8) the self-consistent masses $\Omega$, $m$ which solve the gap equations Eqs. (11, 12). The minimum point $\phi =v_L$ does not change as it is fixed at the phenomenological value $v_{\mathrm{Fermi}}=247\mathrm{GeV}$.