Consistent on shell renormalisation of electroweakinos in the complex MSSM: LHC and LC predictions

Abstract

Abstract:We extend the formalism developed in ref. [53] for the renormalisation of the chargino-neutralino sector to the most general case of the MSSM with complex parameters. We show that products of imaginary parts arising from MSSM parameters and from absorptive parts of loop integrals can already contribute to predictions for physical observables at the one-loop level, and demonstrate that the consistent treatment of such contributions gives rise to non-trivial structure, either in the field renormalisation constants or the corrections associated with the external legs of the considered diagrams. We furthermore point out that the phases of the parameters in the chargino-neutralino sector do not need to be renormalised at the one-loop level, and demonstrate that the appropriate choice for the mass parameters used as input for the on-shell conditions depends both on the process and the region of MSSM parameter space under consideration. As an application, we compute the complete one-loop results in the MSSM with complex parameters for the process h a →χ + iχ − j (Higgs-propagator corrections have been incorporated up to the two-loop level), which may be of interest for SUSY Higgs searches at the LHC, and for chargino pair-production at an e + e − Linear Collider, e + e − →χ + iχ − j . We investigate the dependence of the theoretical predictions on the phases of the MSSM parameters, analysing in particular the numerical relevance of the absorptive parts of loop integrals.

One-loop effects on MSSM parameter determination via chargino production at the LC

“…In ref. [15,19], it was shown that in the CP violating case, the 1-loop corrections to the phases of M 1 and µ, i.e. φ M 1 and φ µ respectively 1 are UV finite.…”

“…[19], within the complex MSSM; examples for the contributing self-energy, vertex and box diagrams are shown in fig. 2.…”

“…Since we intend to extend the current study to the case of complex parameters, here we follow the approach of refs. [14,19] closely, where a dedicated on-shell renormalization scheme for the chargino and neutralino sector of the MSSM with complex parameters was developed. In the following we will therefore only discuss the parameter renormalization of the chargino and neutralino sector briefly, and for further details about the chargino field renormalization and the renormalization of other sectors we refer the reader to refs.…”

“…In the following we will therefore only discuss the parameter renormalization of the chargino and neutralino sector briefly, and for further details about the chargino field renormalization and the renormalization of other sectors we refer the reader to refs. [14,15,19,44].…”

“…We can then determine the necessary conditions to obtain the absolute values |M 1 |, |M 2 | and |µ|, depending on which three physical masses are chosen to be on-shell. As we have two external charginos, and in order to easily extend our setup to the case ofχ + 1χ − 2 production, we assume the NCC scheme with χ [14][15][16]19], such that i = 1 and i = 1 and 2. Note that in choosing the scheme, it is desirable that the on-shell particles should contain significant bino, wino and higgsino components, in order that the M 1 , M 2 and µ parameters are accessible.…”