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Register a new userSemi-numerical evaluation of one-loop corrections
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G.Zanderighi
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We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.
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We present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with up to five external legs and massless internal lines, although the method is more generally applicable. Tensor integrals are reduced to generalized scalar integrals, which in turn are reduced to a set of known basis integrals using recursion relations. The reduction algorithm is modified near exceptional configurations to ensure numerical stability. To test the procedure we apply these techniques to one-loop corrections to the Higgs to four quark process for which analytic results have recently become available.
SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability.
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numerical integration routine with an extrapolation method, together with a multi-precision library, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as $10^{-150}$ GeV in the infrared vertex diagram.
A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU(2), and local (gauge), U(1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is of 90 degrees. The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.
We discuss the ${cal O}(alpha_s)$ supersymmetric QCD corrections to neutralino-stop coannihilation into a top quark and a gluon in the Minimal Supersymmetric Standard Model (MSSM). This particular channel can be numerically important in wide ranges of the MSSM parameter space with rather light stops. We discuss technical details such as the renormalization scheme and the phase-space slicing method with two cutoffs. We also comment on improvements with respect to earlier works on the given process. Further, we study for the first time the phenomenologically very interesting interplay of neutralino-stop coannihilation with neutralino-pair annihilation into quark pairs taking the full next-to-leading order SUSY-QCD corrections into account. We demonstrate that the numerical impact of these corrections on the total (co)annihilation cross section and finally on the theoretically predicted neutralino relic density is significant.
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