Precise bounds on the Higgs boson mass

Journal Article · Tue Nov 01 00:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.096003· OSTI ID:20713881

Kielanowski, P; Juarez W, S R; Solis-Rodriguez, H G ^[1]

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1. Departamento de Fisica, Centro de Investigacion y Estudios Avanzados del IPN (Mexico)

We study the renormalization group evolution of the Higgs quartic coupling {lambda}{sub H}. The one loop equation for {lambda}{sub H} is nonlinear and it is of the Riccati type which we analytically and numerically solve in the energy range [m{sub t},E{sub GU}] where m{sub t} is the mass of the top quark and E{sub GU}=10{sup 14} GeV. We find that depending on the value of {lambda}{sub H}(m{sub t}) the solution for {lambda}{sub H}(E) may have a singularity or a zero and become negative in the former energy range so the ultraviolet cutoff of the standard model should be below or equal to the energy where the zero or singularity of {lambda}{sub H} occurs. We then numerically solve the two loop renormalization group equation for {lambda}{sub H} and compare it with the one loop solution. We find that the two loop running of {lambda}{sub H} is very sensitive to the evolution of the top quark Yukawa coupling Y{sub t}. This implies a strong dependence on the top quark mass m{sub t} and suggests that the choice of m{sub t} as the renormalization point, that we use, reduces theoretical errors. We find that in the approximation of one loop for 0.397{<=}{lambda}{sub H}(m{sub t}){<=}0.618 the standard model is valid in the whole range [m{sub t},E{sub GU}] while for two loops the bound is 0.368{<=}{lambda}{sub H}(m{sub t}){<=}0.621. From the properties of {lambda}{sub H} we then study the predictions for the Higgs mass. We use the effective potential to derive the relation between the Higgs mass and {lambda}{sub H} and obtain that this relation is not very sensitive to the particular choice of the effective potential but for the large Higgs masses the two loop corrections are significant. We determine that the standard model is valid in the whole range [m{sub t},E{sub GU}] for the Higgs masses 153.5{<=}M{sub H}{<=}191.1 for one loop case and 148.5{<=}M{sub H}{<=}193.1 for two loops. The pattern of the behavior of {lambda}{sub H}(E) for different values of {lambda}{sub H}(m{sub t}) indicates the existence of a phase transition in the standard model for {lambda}{sub H}(m{sub t})=0.5 which corresponds to the value of the Higgs mass M{sub H}=m{sub t}.

• OSTI ID: 20713881
• Journal Information: Physical Review. D, Particles Fields, Vol. 72, Issue 9; Other Information: DOI: 10.1103/PhysRevD.72.096003; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPARATIVE EVALUATIONS
CORRECTIONS
COUPLING
ERRORS
GEV RANGE
HIGGS BOSONS
HIGGS MODEL
INTERMEDIATE BOSONS
MASS RENORMALIZATION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PHASE TRANSFORMATIONS
REST MASS
RICCATI EQUATION
SINGULARITY
STANDARD MODEL
T QUARKS
ULTRAVIOLET RADIATION
YUKAWA POTENTIAL