External leg corrections as an origin of large logarithms

Abstract

The appearance of large logarithmic corrections is a well-known phenomenon in the presence of widely separated mass scales. In this work, we point out the existence of large Sudakov-like logarithmic contributions related to external-leg corrections of heavy scalar particles which cannot be resummed straightforwardly using renormalisation group equations. Based on a toy model, we discuss in detail how these corrections appear in theories containing at least one light and one heavy particle that couple to each other with a potentially large trilinear coupling. We show how the occurrence of the large logarithms is related to infrared singularities. In addition to a discussion at the one-loop level, we also explicitly derive the two-loop corrections containing the large logarithms. We point out in this context the importance of choosing an on-shell-like renormalisation scheme. As exemplary applications, we present results for the two-loop external-leg corrections for the decay of a gluino into a scalar top quark and a top quark in the Minimal Supersymmetric extension of the Standard Model as well as for a heavy Higgs boson decay into two tau leptons in the singlet-extended Two-Higgs-Doublet Model.

MUonE, muon $g-2$ and electroweak precision constraints within 2HDMs

“…As T is independent of the Yukawa structure of the 2HDM, it is the same for each Type we discuss here; the difference between the results of the four Types will come purely through the different parameter constraints found from the global fits (Table III). Some studies of m W in 2HDMs consider T in the exact alignment limit [40,47,48], however here we do not constrain ourselves to this. Instead we take the constraints on cos(β − α) at 2σ from the global fit to each Type and vary within these.…”

“…4, both the orange and blue data are calculated using 1-loop expressions for the T parameter in the 2HDM. There are however 2-loop calculations for the 2HDM contributions to m W calculated [92,93] and used [40] in literature, remaining in the alignment limit. We use the package THDM EWPOS 1 to compare the 1-and 1+2-loop calculations for m W in 2HDM.…”

“…If such a deviation from the Standard Model is confirmed, this can open the door for a plethora of New Physics (NP) models which could explain this anomaly. Previously [39] it was expected that any 2HDM would only ever have much smaller corrections to m W than the deviation found in [37], however revived analyses of flavour conserving 2HDMs with a softly broken Z 2 symmetry claim larger contributions can arise, which could bridge this gap [40][41][42][43][44][45][46][47][48][49]. It is therefore worthwhile to comment, in passing, on the corrections to the Wboson mass within the 2HDM using the context of our fits from other sectors to inform the parameter regions used, resulting in ranges of values which m W could take from a particular 2HDM realisation.…”

External-leg corrections as an origin of large logarithms

“…We refer the reader to Ref. [6] for our definitions and conventions for these two models, as well as for our analytical results. First, in the MSSM, we investigate the decay of a gluino into a top quark and a stop quark (either leftor right-handed).…”

“…In Ref. [6], we pointed out the existence of a new type of large Sudakov-like logarithmic contributions, arising in external-leg corrections of heavy scalars and that can be enhanced by sizeable trilinear couplings. We carried out a detailed analysis of the origin and possible magnitude of these terms, which we summarise in these proceedings.…”