France

Ingo Schienbein

Germany

United Kingdom

Florian Staub

Tom Steudtner

Kseniia Svirina

Erratum to “Revisiting RGEs for general gauge theories” [Nucl. Phys. B 939 (2019) 1–48]

Several ideas exist on how the stringent mass limits from LHC on new colored particles can be avoided. One idea are the so-called “stealth” scenarios in which missing transversal energy (<math><msub><mi>E</mi><mi>T</mi></msub></math>) is avoided due a peculiar mass configuration. It is usually assumed that the cascade decay of the dominantly produced colored particle finishes in a two-body decay, where this mass configuration leads to a very small amount of <math><msub><mi>E</mi><mi>T</mi></msub></math>. We discuss here the potential impact of other decay channels, either loop-induced or via off-shell mediators. It is shown that those channels already become important even for moderate branching ratios of 10%. Larger branching ratios, in particular, into a photon can completely wash out all benefits of the stealth setup. We discuss this in a model-independent form, but also at the simplest supersymmetry stealth scenario which can be realized in the next-to-minimal supersymmetric standard model.

South Africa

Jong Soo Kim

Manuel E. Krauss

Víctor Martín Lozano

Illuminating stealth scenarios at the LHC

We consider a low-energy effective theory of the next-to-minimal supersymmetric Standard Model by decoupling all scalar states except one Higgs doublet and the complex gauge singlet. The mass spectrum of the resulting singlet extended Standard Model is calculated from two different perspectives: (i) using a matching of the scalar sectors at next-to-leading order and (ii) using the simplified-model approach of calculating the masses in the effective theory at fixed order at the weak scale ignoring any connection to the full theory. Significant deviations between the two methods are found not only in the scalar sector, but also properties of the additional fermions can be very different. Thus, only a small part of the parameter space of the simplified model can be embedded in a well-motivated supersymmetry framework.

Martin Gabelmann

M. Margarete Mühlleitner

Singlet extended standard model in the context of split supersymmetry

There are nowadays strong experimental constraints on supersymmetric theories from the Higgs measurements as well as from the null results in Sparticle searches. However, even the parameter spaces which are in agreement with experimental data can be further constrained by using theoretical considerations. Here, we discuss for the MSSM and NMSSM the impact of perturbative unitarity as well as of the stability of the one-loop effective potential. We find in the case of the MSSM, that vacuum stability is always the stronger constraint. On the other side, the situation is more diverse in the NMSSM and one should always check both kind of constraints.

Theoretical constraints on supersymmetric models: Perturbative unitarity vs. vacuum stability

We study the predictions of generic ultraviolet completions of two-Higgs doublet models. We assume that at the matching scale between the two-Higgs doublet model and an ultraviolet complete theory – which can be anywhere between the TeV and the Planck scale – arbitrary but perturbative values for the quartic couplings are present. We evaluate the couplings down from the matching scale to the weak scale and study the predictions for the scalar mass spectrum. In particular, we show the importance of radiative corrections which are essential for both an accurate Higgs mass calculation as well as determining the stability of the electroweak vacuum. We study the relation between the mass splitting of the heavy Higgs states and the size of the quartic couplings at the matching scale, finding that only a small class of models exhibit sizeable mass splittings between the heavy scalars at the weak scale. Moreover, we find a clear correlation between the maximal size of the couplings and the considered matching scale.

Manuel Krauss

Toby Opferkuch

The ultraviolet landscape of two-Higgs doublet models

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the β-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings. There are two sources for these discrepancies. Firstly, the known expressions for the scalar couplings assume a diagonal wave-function renormalisation which is not appropriate for models with mixing in the scalar sector. Secondly, the dimensionful parameters have been derived in the literature using a dummy field method which we critically re-examine, obtaining revised expressions for the β-function of the fermion mass. We perform an independent cross-check using well-tested supersymmetric RGEs which confirms our results. The numerical impact of the changes in the β-function for the fermion mass terms is illustrated using a toy model with a heavy vector-like fermion pair coupled to a scalar gauge singlet. Unsurprisingly, the correction to the running of the fermion mass becomes sizeable for large Yukawa couplings of the order of <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>. Furthermore, we demonstrate the importance of the correction to the β-functions of the scalar quartic couplings using a general type-III Two-Higgs-Doublet-Model. All the corrected expressions have been implemented in updated versions of the Mathematica package SARAH and the Python package PyR@TE.

Revisiting RGEs for general gauge theories

Two-Higgs-Doublet-Models (THDMs) are among the simplest extensions of the standard model and are intensively studied in the literature. Using on-shell parameters such as the masses of the additional scalars as input, corresponds often to large quartic couplings in the underlying Lagrangian. Therefore, it is important to check if these couplings are for instance in agreement with perturbative unitarity. The common approach for doing this check is to consider the two-particle scattering matrix of scalars in the large centre-of-mass energy limit where only point interactions contribute. We show that this is not always a valid approximation: the full calculation including all tree-level contributions at finite energy can lead to much more stringent constraints. We show how the allowed regions in the parameter space are affected. In particular, the light Higgs window with a second Higgs below 125 GeV completely closes for large values of the <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> breaking parameter <math><msub><mrow><mi>M</mi></mrow><mrow><mn>12</mn></mrow></msub></math>. We also compare against the loop corrected constraints, which use also the large <math><msqrt><mrow><mi>s</mi></mrow></msqrt></math> approximation, and find that (effective) cubic couplings are often more important than radiative corrections.

Mark D. Goodsell

Improved unitarity constraints in Two-Higgs-Doublet-Models

We present an update of the Mathematica package SARAH to calculate unitarity constraints in BSM models. The new functions can perform an analytical and numerical calculation of the two-particle scattering matrix of (uncoloured) scalars. We do not make use of the simplifying assumption of a very large scattering energy, but include all contributions which could become important at small energies above the weak scale. This allows us to constrain trilinear scalar couplings. However, it can also modify (weakening or strengthening) the constraints on quartic couplings, which we show via the example of a singlet extended Standard Model.

Mark Goodsell

Unitarity constraints on general scalar couplings with SARAH

Triplet extensions are attractive alternatives to the standard model (SM) of particle physics. While models with only one triplet are highly constrained by electroweak precision observables, this is not necessarily the case once several triplets are present as in the Georgi-Machacek model. As in all other BSM models, the parameter space of triplet extensions is constrained by the condition that perturbative unitarity is not violated. For this purpose, limits on the eigenvalues of the scalar <math><mn>2</mn><mo>→</mo><mn>2</mn></math> scattering matrix are set. It is very common in the BSM literature that the scattering matrix is calculated under one crucial assumption: the scattering energy <math><mi>s</mi></math> is so large that only point interactions involving quartic couplings provide non-negligible contributions. However, it is not given that this approximation is always valid—in fact, diagrams involving propagators can play an important role. We discuss the examples of (i) the SM model extended by a real triplet, (ii) the <math><mi>Y</mi><mo>=</mo><mn>1</mn></math> triplet extension of the SM, and (iii) the Georgi-Machacek model, how the tree-level unitarity constraints are affected once the large <math><mi>s</mi></math> approximation is given up. For all models we find that the impact of (effective) cubic couplings can be crucial.

Unitarity constraints in triplet extensions beyond the large <math><mi>s</mi></math> limit

Phenomenological studies performed for non-supersymmetric extensions of the Standard Model usually use tree-level parameters as input to define the scalar sector of the model. This implicitly assumes that a full on-shell calculation of the scalar sector is possible – and meaningful. However, this doesn’t have to be the case as we show explicitly at the example of the Georgi-Machacek model. This model comes with an appealing custodial symmetry to explain the smallness of the ρ parameter. However, the model cannot be renormalised on-shell without breaking the custodial symmetry. Moreover, we find that it can often happen that the radiative corrections are so large that any consideration based on a perturbative expansion appears to be meaningless: counter-terms to quartic couplings can become much larger than 4π and/or two-loop mass corrections can become larger than the one-loop ones. Therefore, conditions are necessary to single out parameter regions which cannot be treated perturbatively. We propose and discuss different sets of such perturbativity conditions and show their impact on the parameter space of the Georgi-Machacek model. Moreover, the proposed conditions are general enough that they can be applied to other models as well. We also point out that the vacuum stability constraints in the Georgi-Machacek model, which have so far only been applied at the tree level, receive crucial radiative corrections. We show that large regions of the parameter space which feature a stable electroweak vacuum at the loop level would have been – wrongly – ruled out by the tree-level conditions.