Precise bounds on the Higgs boson mass

Abstract

We study the renormalization group evolution of the Higgs quartic coupling ${\lambda }_H$ and the Higgs mass $m_H$ in the Standard Model. The one loop equation for ${\lambda }_H$ is non linear and it is of the Riccati type which we numerically and analytically solve in the energy range $[m_t,E_{GU}]$ where $m_t$ is the mass of the top quark and $E_{GU}=10^{14}$ GeV. We find that depending on the value of ${\lambda }_H(m_t)$ the solution for ${\lambda }_H(E)$ may have singularities or zeros and become negative in the former energy range so the ultra violet cut off of the standard model should be below the energy where the zero or singularity of ${\lambda }_H$ occurs. We find that for $0.369\le {\lambda }_H(m_t)\le 0.613$ the Standard Model is valid in the whole range $[m_t,E_{GU}]$. We consider two cases of the Higgs mass relation to the parameters of the standard model: (a) the effective potential method and (b) the tree level mass relations. The limits for ${\lambda }_H(m_t)$ correspond to the following Higgs mass relation $150\le m_H⪅193$ GeV. We also plot the dependence of the ultra violet cut off on the value of the Higgs mass. We analyze the evolution of the vacuum expectation value of the Higgs field and show that it depends on the value of the Higgs mass. The pattern of the energy behavior of the VEV is different for the cases (a) and (b). The behavior of ${\lambda }_H(E)$, $m_H(E)$ and $v(E)$ indicates the existence of a phase transition in the standard model. For the effective potential this phase transition occurs at the mass range $m_H\approx 180$ GeV and for the tree level mass relations at $m_H\approx 168$ GeV.

14 pages, 7 figures. Expanded the discussion of the Higgs mass relation between the parameters of the Standard Model. Included the method of the Higgs effective potential

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Cited by in corpus (8)

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• Aspects of Z'-mediated Supersymmetry Breaking
• Renormalization Group Equations for the CKM matrix
• Scaling of the Higgs Self-coupling and bounds on the Extra Dimension
• RG Invariance of the Pole Mass in the Minimal Subtraction Scheme
• Renormalization Group Invariance of the Pole Mass in the Multi-Higgs system
• Asymptotic properties of CP violation in the Standard Model
• Higgs boson self coupling from two-loop analysis