The two-loop renormalization of the Yukawa sector for an arbitrary renormalizable field theory

The two-loop Yukawa coupling constant renormalization and the mass renormalization of the fermion for an arbitrary renormalizable field theory, including vector, scalar and of course fermion fields, has been calculated. This has been done in two different regularization schemes, i.e. dimensional regularization and dimensional reduction. Both calculations were done in the conventional way, and not with the use of the so-called background-field method. Only the reduction scheme is shown to preserve supersymmetry up to this level.Furthermore a simple example of a gauge theory is given to show that in general it is not possible to give an explicit transformation of the coupling constants in such a way that all β-functions become the same for the two regularization schemes, which proves that dimensional reduction, treated this way, is not a good regularization scheme.     

General background field calculations with fermion fields

Background field calculations including fermion background fields are undertaken to determine one- and two-loop counterterms, and β-functions, for a general vector, scalar, spinor field gauge theory. Dimensional regularisation, and also the dimensional reduction variant, with a non-perturbative treatment of the background fields are used. In the dimensional reduction case two alternative forms are given for the results depending on the precise treatment of ε-scalars.     

MSSM Higgs-boson mass predictions and two-loop non-supersymmetric counterterms

The evaluation of Yukawa-enhanced two-loop contributions to the MSSM Higgs-boson mass is considered. We prove the common assumption that regularization by dimensional reduction preserves supersymmetry at the required level. Thus generating counterterms by multiplicative renormalization is correct. Technically, we identify a suitable Slavnov–Taylor identity, use a recently developed method to evaluate it at the two-loop level, and show that it is valid in dimensional reduction.     

Evaluation of higher-order effective potentials with dimensional regularization

A new and simple method for evaluating high-order effective potentials is presented. It is based on the renormalization procedure of 't Hooft and Veltman used in conjunction with the scheme of dimensional regularization. Explicit calculations of the effective potential of a scalar field in two-loop approximation are carried out.     

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, $\text{spin}\text{-}\text{1}\text{2}$, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (^?MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).     

Two-loop relevant parts ofD-dimensional massive scalar one-loop integrals

The calculation of two-loop Feynman integrals within the dimensional regularization scheme requires the knowledge of scalar one-loop integrals up to the linear term inD-4. We give the corresponding explicit expressions in terms of polylogarithms for the general one-, two-and three-point function and for a special case of the fourpoint function needed for vertex corrections. Our results are valid in all kinematical regions for real masses and momenta.     

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.     

Tensor reduction of two-loop vacuum diagrams and projectors for expanding three-point functions

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators (projectors) extracting the coefficients of the momentum expansion of massive scalar three-point functions (with any number of loops), so the solution to the latter problem is also given.     

Precise prediction for the mass of the lightest Higgs boson in the MSSM

The leading diagrammatic two-loop corrections are incorporated into the prediction for the mass of the lightest Higgs boson, m_h, in the Minimal Supersymmetric Standard Model (MSSM). The results, containing the complete diagrammatic one-loop corrections, the new two-loop result and refinement terms incorporating leading electroweak two-loop and higher-order QCD contributions, are discussed and compared with results obtained by renormalization group calculations. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account.     

SU (5) + adjoint Higgs model at finite temperature

A three-dimensional effective theory of the finite-temperature SU(5) + adjoint Higgs model is constructed using the method of dimensional reduction. The resulting theory can be used for computer simulations of the GUT phase transition of the early universe. In this paper the transition is analyzed at two-loop level in perturbation theory. The structure of the effective theory does not essentially depend on the matter contents of the original four-dimensional one. Therefore the analysis of this paper applies also to more realistic theories.     

Two-loop QCD amplitude for gg-->h, H in the minimal supersymmetric standard model

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the minimal supersymmetric standard model (MSSM). We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet, and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the standard model.     

Higgs-boson two-loop contributions to electric dipole moments in the MSSM

The complete set of Higgs-boson two-loop contributions to electric dipole moments of the electron and neutron is calculated in the minimal supersymmetric standard model. The electric dipole moments are induced by CP-violating trilinear couplings of the `CP-odd' and charged Higgs bosons to the scalar top and bottom quarks. Numerical estimates of the individual two-loop contributions to electric dipole moments are given.     

Renormalization group equation for the vacuum energy of a scalar field in curved space-time

The renormalization group equation is formulated for the vacuum energy of a scalar field. We calculate the two-loop functions and study the asymptotic behavior of the vacuum energy.     

The master two-loop diagram with masses

In every mass case needed for QCD and QED two-point functions, the most difficult two-loop scalar Feynman diagram is reduced, by a systematic dispersive method, to a single integral of logarithms, whose expansion is obtained for large and, when appropriate, small momenta. The new results for the case with an intermediate state comprising three massive particles are needed for the two-loop calculation of fermion propagators.     

Lepton flavor-changing scalar interactions and <Emphasis Type="Italic">g</Emphasis>-2 of the muon

A systematic investigation on the muon's anomalous magnetic moment and a related lepton flavor-violating process such as , and is made at the two-loop level in the models with flavor-changing scalar interactions. The two-loop diagrams with double scalar exchanges are studied and their contributions are found to be compatible with the ones from the Barr-Zee diagram. By comparing with the latest data, the allowed ranges for the relevant Yukawa couplings Y_ij in the lepton sector are obtained. The results show the hierarchical structure in the physical basis if is found to be . It deviates from the widely used ansatz in which the off-diagonal elements are proportional to the square root of the products of the related fermion masses. An alternative Yukawa coupling matrix in the lepton sector is suggested to understand the current data. With such a reasonable Yukawa coupling ansatz, the decay rate of is found to be near the current experiment upper bound. Received: 5 September 2002 / Revised version: 11 January 2003 / Published online: 26 February 2003 RID="a" ID="a" e-mail: zhou@theorie.physik.uni-muenchen.de RID="b" ID="b" e-mail: ylwu@itp.ac.cn     

Fermion Corrections to Mass of Scalar Glueball in QCD Sum Rule

Contributions of fermions to the mass of the scalar glueball 0⁺⁺ are calculated at two-loop level in the framework of QCD sum rules. It slightly changes the coefficients in the operator product expansion (OPE) and shifts the mass of glueball to 1.72 ±0.07 GeV.     

QGP有效微扰论中纯规范场的二圈热力学势

使用基于硬热圈(HTL)的重求和方法,计算了QGP中纯规范场的二圈热力学势及其重整化,得到了包含集体效应的结果.     

Low-energy theorems in Higgs physics

We present low-energy theorems for the calculation of loop amplitudes with external scalar or pseudoscalar Higgs bosons which are light compared to the loop particles. Starting from existing lowest-order versions of these theorems, we show how their applicability may be extended to the two-loop level. To illustrate the usefulness of these theorems, we discuss a number of applications to Higgs production and decay at and beyond the one-loop order.     

The masses of the neutral {\cal CP}-even Higgs bosons in the MSSM: Accurate analysis at the two-loop level

We present detailed results of a diagrammatic calculation of the leading two-loop QCD corrections to the masses of the neutral -even Higgs bosons in the Minimal Supersymmetric Standard Model (MSSM). The two-loop corrections are incorporated into the full diagrammatic one-loop result and supplemented with refinement terms that take into account leading electroweak two-loop and higher-order QCD contributions. The dependence of the results for the Higgs-boson masses on the various MSSM parameters is analyzed in detail, with a particular focus on the part of the parameter space accessible at LEP2 and the upgraded Tevatron. For the mass of the lightest Higgs boson, , a parameter scan has been performed, yielding an upper limit on which depends only on . The results for the Higgs-boson masses are compared with results obtained by renormalization group methods. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account. Received: 11 January 1999 / Published online: 28 May 1999