We present new versions of the packages RunDec and CRunDec which can be used for the running and decoupling of the strong coupling constant and quark masses. Furthermore several conversion formulae for heavy quark masses are implemented. The new versions include fiveloop corrections of the QCD beta function and four-loop decoupling effects. Furthermore, various relations between the heavy quark mass defined in the MS and other short-distance schemes are implemented to next-to-next-to-next-to-leading order. We discuss in detail the improvements and provide several examples which show how RunDec and CRunDec can be used in frequently occurring situations.Nature of physical problem: The value for the coupling constant of Quantum Chromodynamics, αRestrictions on the complexity of the problem: It could be that for an unphysical choice of the input parameters the results are nonsensical.Typical running time: In general the run time for the individual operations is below a millisecond. In some cases it can increase to the order of a second.

We compute the beta functions for the three gauge couplings and the Yukawa matrices of a general two-Higgs-doublet model in the modified minimal subtraction scheme to three loops. The calculations are performed using Lorenz gauge in the unbroken phase. We discuss in detail the occurence of poles in anomalous dimensions and propose practical prescriptions to avoid them. We provide explicit results for the often used Z 2 -symmetric versions of the two-Higgs-doublet model of type I, II, X and Y. Furthermore, we provide the first independent cross-check of the three-loop Yukawa coupling beta functions of the Standard Model.One can match with the standard notation given in Eq.(2) and obtain the following relations K 11 = m 2 11 , K 12 = −m 2 12 , K 21 = −(m 2 12 ) * , λ 11,11 = λ 1 , λ 22,22 = λ 2 , λ 11,22 = λ 22,11 = λ 3 , λ 12,21 = λ 4 , λ 12,12 = λ 5 , λ 11,12 = λ 6 , λ 22,12 = λ 7 .The two tensors transform under the basis change given in Eq. (3) as

An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients C H and C HH for one and two Higgs bosons, respectively. In this work we calculate for the first time C HH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient C H for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU(N c ) colour factors. The latter are related to C H and C HH via low-energy theorems. 4524863

We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of γ5 in D = 4 − 2ǫ space-time dimensions is required; however, in our calculation we determine the γ5-dependent terms by exploiting relations with beta function coefficients at lower loop orders.

We compute the real-radiation corrections to Higgs boson pair production at next-to-next-to-leading order in QCD, in an expansion for large top quark mass. We concentrate on the radiative corrections to the interference contribution from the next-to-leading order one-particle reducible and the leading order amplitudes. This is a well defined and gauge invariant subset of the full real-virtual corrections to the inclusive cross section. We obtain analytic results for all phase-space master integrals both as an expansion around the threshold and in an exact manner in terms of Goncharov polylogarithms.