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Title: Precise bounds on the Higgs boson mass

Abstract

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{submore » 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}.« less

Authors:
; ;  [1];  [2]
  1. Departamento de Fisica, Centro de Investigacion y Estudios Avanzados del IPN (Mexico)
  2. (Mexico)
Publication Date:
OSTI Identifier:
20713881
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.72.096003; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Kielanowski, P., Juarez W, S.R., Solis-Rodriguez, H.G., and Departamento de Fisica, Escuela Superior de Fisica y Matematicas, IPN. Precise bounds on the Higgs boson mass. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.096003.
Kielanowski, P., Juarez W, S.R., Solis-Rodriguez, H.G., & Departamento de Fisica, Escuela Superior de Fisica y Matematicas, IPN. Precise bounds on the Higgs boson mass. United States. doi:10.1103/PhysRevD.72.096003.
Kielanowski, P., Juarez W, S.R., Solis-Rodriguez, H.G., and Departamento de Fisica, Escuela Superior de Fisica y Matematicas, IPN. Tue . "Precise bounds on the Higgs boson mass". United States. doi:10.1103/PhysRevD.72.096003.
@article{osti_20713881,
title = {Precise bounds on the Higgs boson mass},
author = {Kielanowski, P. and Juarez W, S.R. and Solis-Rodriguez, H.G. and Departamento de Fisica, Escuela Superior de Fisica y Matematicas, IPN},
abstractNote = {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}.},
doi = {10.1103/PhysRevD.72.096003},
journal = {Physical Review. D, Particles Fields},
number = 9,
volume = 72,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • We reanalyze our recently proposed mass matrix model based on spontaneously broken discrete chiral family symmetry, taking into account the additional flavor changing neutral current constraint implied by the bound on the D{sub 1}{minus}D{sub 2} mass difference, and including several corrections to our earlier analysis. When combined, the K{sub 1}{minus}K{sub 2} and D{sub 1}{minus}D{sub 2} constraints force the masses of the Higgs particles that contribute most strongly to flavor changing neutral currents (the {phi} Higgs states) to lie above 17 TeV, well beyond the limit of validity of conventional perturbative Higgs physics. The analogous constraints on the masses of themore » {eta} Higgs states and the neutral pseudo Goldstone Higgs state depend on the mechanism for realizing small first family masses. If the {eta} Higgs states are the primary contributor to second family masses, the pseudo Goldstone and {eta} Higgs states must have masses above 220 GeV, with numerical fits suggesting masses above 1 TeV, while if the {eta} Higgs states are responsible solely for first family masses, the corresponding mass bounds drop to the range detectable at the CERN LHC. We show that naturalness of small first family masses favors the latter alternative, and give an illustrative mass matrix texture model. {copyright} {ital 1999} {ital The American Physical Society}« less
  • A Comment on the Letter by T. Uchiyama, Phys. Rev. Lett. 50, 946 (1983).
  • It is pointed out that the conditions used by Uchiyama can lead to additional values from the Higgs boson upper mass limit.
  • In the Glashow-Salam-Weinberg model with single Higgs doublet, upper bounds on the Higgs-boson mass and the coupling constant are obtained: m/sub H/< or =455 GeV, lambda< or =32.8 based on one-loop radiative corrections and the existence of the spontaneously broken absolute vacuum. Under two-loop radiative corrections, these bounds are improved to m/sub H/< or =320 GeV, lambda< or =9.35.
  • We study the effects of the one-loop matching conditions on Higgs boson and top quark masses on the triviality bounds on the Higgs boson mass using {beta}{sub {lambda}} with corrected two-loop coefficients. We obtain quite higher results than previous ones and observe that the triviality bounds are not nearly influenced by varying the top quark mass over the range measured at CDF and D0. The effects of typographical errors in {beta}{sub {lambda}}{sup (2)} and the one-loop matching condition on the top quark mass are negligible. We estimate the size of the effects on the triviality bounds from the one-loop matchingmore » condition on the Higgs boson mass. {copyright} {ital 1996 The American Physical Society.}« less