Standard and ǫ - finite Master Integrals for the ρ - Parameter
نویسندگان
چکیده
We have constructed an ǫ-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak ρ-parameter. Using transformation rules from the ǫ-finite basis to the standard " minimal-number-of-lines " basis, we obtain as a by-product analytical expressions for few leading terms of the ǫ-expansion of all members of the standard basis. The new master integrals have been computed with the help of the Padé method and by use of difference equations independently .
منابع مشابه
Master integrals with one massive propagator for the two - loop electroweak form factor
We compute the master integrals containing one massive propagator entering the two-loop electroweak form factor, i.e. the process f ¯ f → X, where f ¯ f is an on-shell massless fermion pair and X is a singlet particle under SU (2) L × U (1) Y , such as a virtual gluon or an hypothetical Z ′. The method used is that of the differential equation in the evolution variable x = −s/m 2 , where s is t...
متن کاملMaster Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional toN F , NF ·N , andNF /N . Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in ǫ, containing Γ-functions and hyperge...
متن کاملǫ-Finite Basis of Master Integrals for the Integration-By-Parts Method
It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we expli...
متن کاملNine-Propagator Master Integrals for Massless Three-Loop Form Factors
We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in ǫ. Using Riemann ζ functions of up to weight six, we give fully analyt...
متن کاملMaster Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
We compute the master integrals for massless two-loop vertex graphs with three offshell legs. These master integrals are relevant for the QCD corrections to H → V V ∗ (where V = W , Z) and for two-loop studies of the triple gluon (and quark-gluon) vertex. We employ the differential equation technique to provide series expansions in ǫ for the various master integrals. The results are analytic an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006