Abstract

JUAREZ W., S.R.; MORALES S., A.  and  KIELANOWSKI, P.. Higgs mass and grand unification. Rev. mex. fis. [online]. 2004, vol.50, n.4, pp.401-405. ISSN 0035-001X.

The knowledge of the solution of the Renormalization Group Equation (RGE) for the quartic self-interaction of the Higgs scalar λ_H is crucial for the determination of the energy limits on the Higgs mass. λ_H is also important in order to solve the RGEs at the two loop level for other observables like the quark masses or the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We obtain an analytical and numerical (considering Grand Unification) solution to the one loop renormalization group evolution of the Higgs quartic coupling λ_H in the energy range [m_t, E_GU], where m_t is the mass of the top quark and E_GU = 10¹⁴ GeV. We find that depending on the value of λ_H (m_t) the solution for λ_H (E) may have singularities or zeros and become negative, in which case the Standard Model (SM) becomes inconsistent. We obtain that for 0.65 ≤ λ_H (m_t) ≤ 0.69 the SM is valid in the whole range [m_t, E_GU]. These values of λ_H (m_t) correspond to the following Higgs mass 198 ≤ mH ≤ 205 GeV.

Keywords : Standard model; Higgs; quartic self-interaction; Riccati equation.

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