Mass of the lightest supersymmetric Higgs boson beyond the leading logarithm approximation.

We examine the radiative corrections to the mass of the lightest Higgs boson in the minimal supersymmetric extension of the standard model. We use the renormalization-group improved effective potential which includes the next-to-leading-order contributions. We find that, contrary to the result of Espinosa and Quirós, the higher-order corrections to the lightest Higgs boson mass are non-negligible, adding 3− 11 GeV (3− 9 GeV) to the result in the leading logarithm approximation for the range of top quark mass 100GeV < mt < 200GeV and for the supersymmetric breaking scale MSUSY = 1TeV (MSUSY = 10TeV). Also we find that our result is stable under the change of the renormalization parameter t. HUPD-9316 YNU-HEPTh-93-102 November 1993 Work partially supported by the Monbusho Grant-in-Aid for Scientific Research (C) No. 05640351. Fellow of the Japan Society for the Promotion of Science for Japanese Junior Scientist. Work partially supported by the Monbusho Grant-in-Aid for Scientific Research No. 050076. e-mail address: [email protected] Although the standard model (SM) is highly successful and in excellent agreement with all the measurements at the present energies, it is widely believed that SM is not the final theory for the world of elementary particles. The minimal supersymmetric extention of the standard model (MSSM) is one of the most promising candidates beyond the SM. The MSSM possesses in its physical spectrum three neutral and two charged Higgs bosons, and there exists a tree-level relation which implies that at least one neutral Higgs boson is lighter than the Z mass (MZ). Radiative corrections to the masses of these Higgs bosons have been calculated by several groups [1] [14], who found that they are quite significant, depending strongly on the top quark mass and the scale of supersymmetry breaking (MSUSY) or the squark masses. All the above works except ref. [6] considered the one-loop radiative corrections to Higgs boson masses. Now that the one-loop corrections have been found to be significantly large, it is quite natural to ask next how large the higher-order corrections would be. Indeed Espinosa and Quirós [6] have analyzed the “two-loop” radiative corrections to the mass of the lightest Higgs boson in the minimal and non-minimal (including a gauge singlet) supersymmetric standard model. They used the effective potential (EP) in the leading logarithm approximation and examined the evolution of the Higgs quartic coupling λ by the renormalization group (RG) techniques with the oneand two-loop β functions. They found that the “two-loop” correction is negative and stays within a few percent even in cases where the one-loop correction is larger than the tree-level mass. Recently there appeared interesting papers [15] [17] which discussed about the improvement of EP by using the renormalization group equation (RGE) . It was shown there that to improve EP which satisfies the RGE with up to the twoloop β functions and anomalous dimension γ, one should include the one-looplevel potential with the running parameters into the solution. In this respect, the work of Espinosa and Quirós [6] seems unsatisfactory: they used the EP in the leading logarithm approximation, which is the tree-level potential with the running parameters, and they made use of the two-loop β functions only to determine the evolution of these parameters. In this paper we reanalyze the mass of the lightest