Non-renormalizable Operators Research Articles

Electroweak multiplet dark matter at future lepton colliders

An electroweak multiplet stable due to a new global symmetry is a simple and well-motivated candidate for thermal dark matter. We study how direct searches at a future linear collider, such as the proposed CLIC, can constrain scalar and fermion triplets, quintets and septets, as well as a fermion doublet. The phenomenology is highly sensitive to charged state lifetimes and thus the mass splitting between the members of the multiplet. We include both radiative corrections and the effect of non-renormalisable operators on this splitting. In order to explore the full range of charged state lifetimes, we consider signals including long-lived charged particles, disappearing tracks, and monophotons. By combining the different searches we find discovery and exclusion contours in the mass-lifetime plane. In particular, when the mass splitting is generated purely through radiative corrections, we can exclude the pure-Higgsino doublet below 310 GeV, the pure-wino triplet below 775 GeV, and the minimal dark matter fermion quintet below 1025 GeV. The scenario where the thermal relic abundance of a Higgsino accounts for the whole dark matter of the Universe can be excluded if the mass splitting between the charged and neutral states is less than 230 MeV. Finally, we discuss possible improvements to these limits by using associated hard leptons to idenify the soft visible decay products of the charged members of the dark matter multiplet.

Proton decay and light sterile neutrinos

Within the standard model, non-renormalizable operators at dimension six (d = 6) violate baryon and lepton number by one unit and thus lead to proton decay. Here, we point out that the proton decay mode with a charged pion and missing energy can be a characteristic signature of d = 6 operators containing a light sterile neutrino, if it is not accompanied by the standard π0e+ final state. We discuss this effect first at the level of effective operators and then provide a concrete model with new physics at the TeV scale, in which the lightness of the active neutrinos and the stability of the proton are related.

Cosmological bounds on non-Abelian dark forces

Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the Standard Model through non-renormalizable operators. These operators will transfer energy between the dark and visible sectors, and they allow some or all of the dark glueballs to decay. In this work we investigate the cosmological evolution and decays of dark glueballs in the presence of connector operators to the Standard Model. Dark glueball decays can modify cosmological and astrophysical observables, and we use these considerations to put very strong limits on the existence of pure non-Abelian dark forces. On the other hand, if one or more of the dark glueballs are stable, we find that they can potentially make up the dark matter of the universe.

Feynman rules for the Standard Model Effective Field Theory in R\u03be-gauges

We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, commonly referred to as “Warsaw basis”. We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear Rξ-gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this mass basis we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available Mathematica code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.

Stability and UV completion of the Standard Model

The knowledge of the electroweak vacuum stability condition is of the greatest importance for our understanding of beyond Standard Model physics. It is widely believed that new physics that lives at very high-energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher-order operators. Here we consider for the first time new physics at extremely high-energy scales (say close to the Planck scale) in terms of renormalizable operators, in other words we consider a sort of toy UV completion of the Standard Model, and definitely show that its presence can be crucial in determining the vacuum stability condition. This result has important phenomenological consequences, as it provides useful guidance in studying beyond Standard Model theories. Moreover, it suggests that very popular speculations based on the so-called “criticality” of the Standard Model do not appear to be well founded.

Non-renormalizable operators for solar neutrino mass generation in Split SuSy with bilinear R-parity violation

The Minimal Supersymmetric Extension of the Standard Model (MSSM) is able to explain the current data from neutrino physics. Unfortunately Split Supersymmetry as low energy approximation of this theory fails to generate a solar square mass difference, including after the addition of bilinear R-Parity Violation. In this work, it is shown how one can derive an effective low energy theory from the MSSM in the spirit of Split Supersymmetry, which has the potential of explaining the neutrino phenomenology. This is achieved by going beyond leading order in the process of integrating out heavy scalars from the original theory, which results in non-renormalizable operators in the effective low energy theory. It is found that in particular a d=8 operator is crucial for the generation of the neutrino mass differences.

Gauge fixing and renormalization scale independence of tunneling rate in Abelian Higgs model and in the standard model

We explicitly show perturbative gauge fixing independence of the tunneling rate to a stable radiatively induced vacuum in the abelian Higgs model. We work with a class of $R_\xi$ gauges in the presence of both dimensionless and dimensionful gauge fixing parameters. We show that Nielsen identities survive the inclusion of higher order oparators and compute the tunnelling rate to the vacua modified by the nonrenormalisable operators in a gauge invariant manner. We also discuss implications of this method for the complete Standard Model.

Dissecting jets and missing energy searches using n-body extended simplified models

Simplified Models are a useful way to characterize new physics scenarios for the LHC. Particle decays are often represented using non-renormalizable operators that involve the minimal number of fields required by symmetries. Generalizing to a wider class of decay operators allows one to model a variety of final states. This approach, which we dub the $n$-body extension of Simplified Models, provides a unifying treatment of the signal phase space resulting from a variety of signals. In this paper, we present the first application of this framework in the context of multijet plus missing energy searches. The main result of this work is a global performance study with the goal of identifying which set of observables yields the best discriminating power against the largest Standard Model backgrounds for a wide range of signal jet multiplicities. Our analysis compares combinations of one, two and three variables, placing emphasis on the enhanced sensitivity gain resulting from non-trivial correlations. Utilizing boosted decision trees, we compare and classify the performance of missing energy, energy scale and energy structure observables. We demonstrate that including an observable from each of these three classes is required to achieve optimal performance. This work additionally serves to establish the utility of $n$-body extended Simplified Models as a diagnostic for unpacking the relative merits of different search strategies, thereby motivating their application to new physics signatures beyond jets and missing energy.

Direct generation of a Majorana mass for the neutron from exotic instantons

We discuss a new mechanism in which non-perturbative quantum gravity effects directly generate a Majorana mass for the neutron. In particular, in string theory, exotic instantons can generate an effective six quark operator by calculable mixed disk amplitudes. In a low string scale scenario, with $M_{S}\simeq 10\div 10^{5}\, \rm TeV$, a neutron-antineutron oscillation can be reached in the next generation of experiments. we argue that protons and neutralinos are not destabilized and that dangerous FCNCs are not generated. We show an example of quiver theories, locally free by tadpoles and anomalies, reproducing MSSM plus a Majorana neutron and a Majorana neutrino. These models naturally provide a viable baryogenesis mechanism by resonant RH neutrino decays, as well as a stable WIMP-like dark matter. We also discuss how LHC data will provide useful inputs for our model, in the immediate future, testing several different regions of the parameter space. Such a mechanism represents a simple and calculable counter-example to the Wilsonian UV completion of effective non-renormalizable operators.

Dark matter and global symmetries

General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. {Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have $O(1)$ couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile}, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.

CP violation tests of alignment models at LHCII

We analyse the low-energy phenomenology of alignment models both model-independently and within supersymmetric (SUSY) scenarios focusing on their CP violation tests at LHCII. Assuming that New Physics (NP) contributes to K-Kbar and D-Dbar mixings only through non-renormalizable operators involving SU(2)_L quark-doublets, we derive model-independent correlations among CP violating observables of the two systems. Due to universality of CP violation in Delta F=1 processes the bound on CP violation in Kaon mixing generically leads to an upper bound on the size of CP violation in D mixing. Interestingly, this bound is similar in magnitude to the current sensitivity reached by the LHCb experiment which is starting now to probe the natural predictions of alignment models. Within SUSY, we perform an exact analytical computation of the full set of contributions for the D-Dbar mixing amplitude. We point out that chargino effects are comparable and often dominant with respect to gluino contributions making their inclusion in phenomenological analyses essential. As a byproduct, we clarify the limit of applicability of the commonly used mass insertion approximation in scenarios with quasi-degenerate and split squarks.

Dark matter at the LHC: Effective field theories and gauge invariance

Effective field theory (EFT) formulations of dark matter interactions have proven to be a convenient and popular way to quantify LHC bounds on dark matter. However, some of the non-renormalizable EFT operators considered do not respect the gauge symmetries of the Standard Model. We carefully discuss under what circumstances such operators can arise, and outline potential issues in their interpretation and application.

Integrating in the Higgs portal to fermion dark matter

Fermion dark matter (DM) interacting with the standard model through a Higgs portal requires non-renormalizable operators, signaling the presence of new mediator states at the electroweak scale. Collider signatures that involve the mediators are a powerful tool to experimentally probe the Higgs portal interactions, providing complementary information to strong constraints set by direct DM detection searches. Indirect detection experiments are less sensitive to this scenario. We investigate the collider reach for the mediators using three minimal renormalizable models as examples, and requiring the fermion DM to be a thermal relic. The Large Hadron Collider in its high-energy, high-luminosity phase can probe most scenarios if DM is lighter than about 200 GeV. Beyond this scale, future high-energy experiments such as an electron-positron collider or a 100-TeV proton-proton collider, combined with future direct detection experiments, are indispensable to conclusively test these models.

Axion like particles and the inverse seesaw mechanism

Light pseudoscalars known as axion like particles (ALPs) may be behind physical phenomena like the Universe transparency to ultra-energetic photons, the soft $\gamma$-ray excess from the Coma cluster, and the 3.5 keV line. We explore the connection of these particles with the inverse seesaw (ISS) mechanism for neutrino mass generation. We propose a very restrictive setting where the scalar field hosting the ALP is also responsible for generating the ISS mass scales through its vacuum expectation value on gravity induced nonrenormalizable operators. A discrete gauge symmetry protects the theory from the appearance of overly strong gravitational effects and discrete anomaly cancellation imposes strong constraints on the order of the group. The anomalous U$(1)$ symmetry leading to the ALP is an extended lepton number and the protective discrete symmetry can be always chosen as a subgroup of a combination of the lepton number and the baryon number.

On the strong coupling scale in Higgs G-inflation

Higgs G-inflation is an inflation model that takes advantage of a Galileon-like derivative coupling. It is a non-renormalizable operator and is strongly coupled at high energy scales. Perturbative analysis does not have a predictive power any longer there. In general, when the Lagrangian is expanded around the vacuum, the strong coupling scale is identified as the mass scale that appears in non-renormalizable operators. In inflationary models, however, the identification of the strong coupling scale is subtle, since the structures of the kinetic term as well as the interaction itself can be modified by the background inflationary dynamics. Therefore, the strong coupling scale depends on the background. In this letter, we evaluate the strong coupling scale of the fluctuations around the background in the Higgs G-inflation including the Nambu–Goldstone modes associated with the symmetry breaking. We find that the system is sufficiently weakly coupled when the scales which we now observe exit the horizon during inflation and the observational predictions with the semiclassical treatment are valid. However, we also find that the inflaton field value at which the strong coupling scale and the Hubble scale meet is less than the Planck scale. Therefore, we cannot describe the model from the Planck scale, or the chaotic initial condition.

UltraViolet freeze-in

If dark matter is thermally decoupled from the visible sector, the observed relic density can potentially be obtained via freeze-in production of dark matter. Typically in such models it is assumed that the dark matter is connected to the thermal bath through feeble renormalisable interactions. Here, rather, we consider the case in which the hidden and visible sectors are coupled only via non-renormalisable operators. This is arguably a more generic realisation of the dark matter freeze-in scenario, as it does not require the introduction of diminutive renormalisable couplings. We examine general aspects of freeze-in via non-renormalisable operators in a number of toy models and present several motivated implementations in the context of Beyond the Standard Model (BSM) physics. Specifically, we study models related to the Peccei-Quinn mechanism and Z ′ portals.

Searching for traces of Planck-scale physics with high energy neutrinos

High energy cosmic neutrino observations provide a sensitive test of Lorentz invariance violation, which may be a consequence of quantum gravity theories. We consider a class of non-renormalizable, Lorentz invariance violating operators that arise in an effective field theory description of Lorentz invariance violation in the neutrino sector inspired by Planck-scale physics and quantum gravity models. We assume a conservative generic scenario for the redshift distribution of extragalactic neutrino sources and employ Monte Carlo techniques to describe superluminal neutrino propagation, treating kinematically allowed energy losses of superluminal neutrinos caused by both vacuum pair emission and neutrino splitting. We consider EFTs with both non-renormalizable CPT-odd and non-renormalizable CPT-even operator dominance. We then compare the spectra derived using our Monte Carlo calculations in both cases with the spectrum observed by IceCube in order to determine the implications of our results regarding Planck-scale physics. We find that if the drop off in the neutrino flux above ~2 PeV is caused by Planck scale physics, rather than by a limiting energy in the source emission, a potentially significant pileup effect would be produced just below the drop off energy in the case of CPT-even operator dominance. However, such a clear drop off effect would not be observed if the CPT-odd, CPT-violating term dominates.

Large tensor-to-scalar ratio and running of the scalar spectral index with instep inflation

If a sizeable tensor-to-scalar ratio $\ensuremath{\sim}0.1$ turns out to be detected and a negative running of the scalar spectral index $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ is significantly required by the data, the vast majority of single field models of inflation will be ruled out. We show that a flat tree-level effective potential, lifted by radiative corrections and by the imprints of a high energy scale (in the form of nonrenormalizable operators) can explain those features and produce enough inflation in the slow-roll regime.

Renormalizing an initial state

The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.

Majorana neutrinos ineγcolliders from an effective Lagrangian approach

We study the production of heavy Majorana neutrinos ($N$) in ${e}^{\ensuremath{-}}\ensuremath{\gamma}$ colliders. We consider the tree-level process ${e}^{\ensuremath{-}}\ensuremath{\gamma}\ensuremath{\rightarrow}{W}^{\ensuremath{-}}N$, which allows for lepton number violation via the decay $N\ensuremath{\rightarrow}{l}^{+}2j$. We follow the approach of an effective theory, where we consider all possible gauge invariant and nonrenormalizable operators of lowest dimension, which determine the interactions of the Majorana neutrino with the standard particles. We study the total cross section for different masses of the Majorana neutrino and different center-of-mass energies. We give an estimate for the range of the Majorana neutrino masses which may be detected in a ${e}^{\ensuremath{-}}\ensuremath{\gamma}$ collider.