Loop Level Research Articles

A renormalizable left-right symmetric model with low scale seesaw mechanisms

We propose a low scale renormalizable left-right symmetric theory that successfully explains the observed SM fermion mass hierarchy, the tiny values for the light active neutrino masses and is consistent with the lepton and baryon asymmetries of the Universe, the muon and electron anomalous magnetic moments as well as with the constraints arising from the meson oscillations. In the proposed model the top and exotic quarks obtain masses at tree level, whereas the masses of the bottom, charm and strange quarks, tau and muon leptons are generated from a tree level Universal Seesaw mechanism, thanks to their mixings with the charged exotic vector like fermions. The masses for the first generation SM charged fermions arise from a radiative seesaw mechanism at one loop level, mediated by charged vector like fermions and electrically neutral scalars. The light active neutrino masses are produced from a one-loop level inverse seesaw mechanism mediated by electrically neutral scalar singlets and right handed Majorana neutrinos. Our model is also consistent with the experimental constraints arising from the Higgs diphoton decay rate as well as with the constraints arising from charged lepton flavor violation. We also discuss the Z′ and heavy scalar production at a proton-proton collider.

Homotopy Transfer and Effective Field Theory I: Tree‐level

AbstractWe use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are integrated out, as first explored by Sen in the context of closed string field theory. We treat ‐algebras both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. These are then shown to govern the integrating out of degrees of freedom at tree level, while the generalization to loop level will be explored in a sequel to this paper.

Singlet fermion dark matter and Dirac neutrinos from Peccei-Quinn symmetry

The Peccei-Quinn (PQ) mechanism not only acts as an explanation for the absence of strong CP violation but also can play a main role in the solution to other open questions in particle physics and cosmology. Here we consider a model that identifies the PQ symmetry as a common thread in the solution to the strong CP problem, the generation of radiative Dirac neutrino masses and the origin of a multicomponent dark sector. Specifically, scotogenic neutrino masses arise at one loop level with the lightest fermionic mediator field acting as the second dark matter (DM) candidate thanks to the residual $Z_2$ symmetry resulting from the PQ symmetry breaking. We perform a phenomenological analysis addressing the constraints coming from the direct searches of DM, neutrino oscillation data and charged lepton flavor violating (LFV) processes. We find that the model can be partially probed in future facilities searching for WIMPs and axions, and accommodates rates for rare leptonic decays that are within the expected sensitivity of upcoming LFV experiments.

Perturbatively exact w1+\u221e asymptotic symmetry of quantum self-dual gravity

The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a w1+∞ asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the w1+∞ algebra persists in quantum self-dual gravity without corrections.

Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes

We analyze the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the KK gravitational Goldstone bosons in the compactified 5d general relativity (GR). Using a general R ξ gauge fixing, we study the geometric Higgs mechanism for the massive spin-2 KK gravitons. We newly propose and prove a gravitational equivalence theorem (GRET) to connect the scattering amplitudes of longitudinal KK gravitons to that of the KK gravitational Goldstone bosons, which formulates the geometric gravitational Higgs mechanism at the scattering S - matrix level. We demonstrate that the GRET provides a general energy cancellation mechanism guaranteeing the N -point longitudinal KK graviton scattering amplitudes to have their leading energy dependence cancelled down by a large power factor of E 2 N N ≥ 4 up to any loop level. We propose an improved double-copy approach to construct the massive KK graviton (Goldstone) amplitudes from the KK gauge boson (Goldstone) amplitudes. With these, we establish a new correspondence between the two types of energy cancellations in the four-point longitudinal KK amplitudes at tree level: E 4 ⟶ E 0 in the KK gauge theory and E 10 ⟶ E 2 in the KK GR theory.

From dS to AdS and back

We describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields.

An instrumentation framework for performance analysis of Halide schedules

This work extends Halide with a profiling API to measure events supported by the target processor during the application runtime. We demonstrate how developers can use this extension to profile application loop levels, functions’ producer and consumer relations, and threads on parallel regions. We also show that the extension is library agnostic, hence developers can choose the profiling library that best suits their environment. As a case study we measure data traffic, number of flops and clock-cycles per instruction on x86 processors, and discuss how the reported results can be used to detail the performance aspects and improve Halide schedules.

Implementing spectra response function approaches for fast calculation of power spectra and bispectra

Perturbation theory of large-scale structures of the Universe at next-to-leading order and next-to-next-to-leading order provides us with predictions of cosmological statistics at subpercent level in the mildly nonlinear regime. Its use to infer cosmological parameters from spectroscopic surveys, however, is hampered by the computational cost of making predictions for a large number of parameters. In order to reduce the running time of the codes, we present a fast scheme in the context of the regularized perturbation theory approach and applied it to power spectra at 2-loop level and bispectra at 1-loop level, including the impact of binning. This method utilizes a Taylor expansion of the power spectrum as a functional of the linear power spectrum around fiducial points at which costly direct evaluation of perturbative diagrams is performed and tabulated. The computation of the predicted spectra for arbitrary cosmological parameters then requires only one-dimensional integrals that can be done within a few minutes. It makes this method suitable for Markov chain Monte-Carlo analyses for cosmological parameter inference.

Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator

Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature.

Extracting Einstein from the loop-level double-copy

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.

Amplituhedron-like geometries

We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

Conflicting interactions in multiple closed-loop controlled critical care Treatments: A hemorrhage resuscitation-intravenous propofol sedation case study

Closed-loop automation of critical care therapy has the potential to reduce the workload of clinical personnel while maintaining the quality of care. In the real-world clinical arena, critically ill patients receive multiple medical treatments. However, existing body of work has predominantly focused on closed-loop automation of isolated individual treatments. How these individual treatment loops interact with each other has not been investigated. The goal of this work is to garner insights on the safety of critical care therapy and potential deleterious conflicts therein when multiple isolated and individually closed-loop controlled medical treatments act upon a patient, using a case study of hemorrhage resuscitation and intravenous propofol sedation. For this purpose, a physiological model of a critically ill patient was developed and experimentally validated to describe the collective cardiovascular and pharmacological effects of these treatments. Then, isolated and individually closed-loop controlled hemorrhage resuscitation and intravenous propofol sedation treatments were simultaneously applied to the physiological model and their interactive behavior was investigated. The results showed that (i) the influence of one treatment on the other must be taken into account in selecting treatment set point to maintain the safety of overall therapy, and that (ii) information sharing between control loops may enhance the efficacy and robustness of individual treatment loops. In sum, it was concluded that hemorrhage resuscitation and intravenous propofol sedation treatments may benefit from coordination both at the set point and the loop levels. The conclusion may generalize to a wide spectrum of multiple closed-loop controlled medical treatments.

Phenomenology of a fake Inert Doublet Model

We introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly off-shell degrees of freedom: the fakeons. To demonstrate the approach and exemplify its reach, we re-analyze the phenomenology of the Inert Doublet Model under the assumption that the second doublet is a fakeon. Remarkably, the fake doublet avoids the most stringent Z-pole constraints regardless of the chosen mass scale, thereby allowing for the presence of new effects well below the electroweak scale. Furthermore, the absence of on-shell propagation prevents fakeons from inducing missing energy signatures in collider experiments. The distinguishing features of the model appear at the loop level, where fakeons modify the Higgs boson h → γγ decay width and the Higgs trilinear coupling. The running of Standard Model parameters proceeds as in the usual Inert Doublet Model case. Therefore, the fake doublet can also ensure the stability of the Standard Model vacuum. Our work shows that fakeons are a valid alternative to the usual tools of particle physics model building, with the potential to shape a new paradigm, where the significance of the existing experimental constraints towards new physics must necessarily be reconsidered.

Double Copy from Homotopy Algebras

AbstractWe show that the BRST Lagrangian double copy construction of supergravity as the ‘square’ of Yang–Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double‐copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.

Dark matter candidates in a type-II radiative neutrino mass model

We explore the connection between Dark Matter and neutrinos in a model inspired by radiative Type-II seessaw and scotogenic scenarios. In our model, we introduce new electroweakly charged states (scalars and a vector-like fermion) and impose a discrete ℤ2 symmetry. Neutrino masses are generated at the loop level and the lightest ℤ2-odd neutral particle is stable and it can play the role of a Dark Matter candidate. We perform a numerical analysis of the model showing that neutrino masses and flavour structure can be reproduced in addition to the correct dark matter density, with viable DM masses from 700 GeV to 30 TeV. We explore direct and indirect detection signatures and show interesting detection prospects by CTA, Darwin and KM3Net and highlight the complementarity between these observables.

Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-Mills Theory.

We show that the double copy of gauge theory amplitudes to N=0 supergravity amplitudes extends from tree level to loop level. We first explain that color-kinematics duality is a condition for the Becchi-Rouet-Stora-Tyutin operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory. We then apply this argument to Yang-Mills theory, where color-kinematics duality is known to be satisfied on shell at the tree level. Finally, we show that the latter restriction can only lead to terms that can be absorbed in a sequence of field redefinitions, rendering the double copied action equivalent to N=0 supergravity.

Controlled fermion mixing and FCNCs in a \u2206(27) 3+1 Higgs Doublet Model

We propose a 3+1 Higgs Doublet Model based on the ∆(27) family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved {Z}_2^{(1)} discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates. The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations. For the scenario of normal neutrino mass hierarchy, the model predicts an effective Majorana neutrino mass parameter in the range 3 meV ≲ mββ ≲ 18 meV, which is within the declared range of sensitivity of modern experiments. The model predicts Flavour Changing Neutral Currents which constrain the model, for instance, μ→e nuclear conversion processes and Kaon mixing are found to be within the reach of the forthcoming experiments.

Excited lepton triplet contribution to electroweak observables at one loop level

In this paper, we present the one-loop radiative corrections to the electroweak precision observable Delta rho coming from the I_W=1 multiplet excited leptons. We have calculated the couplings of the exotic lepton triplet to the vector bosons and ordinary leptons using the effective Lagrangian approach. These couplings are then used to estimate the excited lepton triplet contribution to the Delta rho parameter. The mass degenerate excited lepton contribution to Delta rho is small and can be neglected. However, if the excited leptons are non-degenerate, their contribution can be large which can result in more stringent constraints on the excited fermion parameter space compared to the constraints from present experimental searches and perturbative unitarity condition.

(g \u2212 2)\u03bc versus K \u2192 \u03c0 + Emiss induced by the (B \u2212 L)23 boson

To address the long-standing (g − 2)μ anomaly via a light boson, in ref. [1] we proposed to extend the standard model (SM) by the local (B − L)23, under which only the second and third generations of fermions are charged. It predicts an invisible Z′ with mass mathcal{O}(100) MeV, and moreover it has flavor-changing neutral current (FCNC) couplings to the up-type quarks at tree level. Such a Z′, via KL→ π0 + Z′(→ voverline{v} ) at loop level, may be a natural candidate to account for the recent KOTO anomaly. In this article, we investigate this possibility, to find that Z′ can readily do this job if it is no longer responsible for the (g − 2)μ anomaly. We further find that both anomalies can be explained with moderate tuning of the CP violation, but may contradict the B meson decays.

Contributions to ZZV^* (V=gamma ,Z,Z') couplings from CP violating flavor changing couplings

The one-loop contributions to the trilinear neutral gauge boson couplings ZZV^* (V=gamma ,Z,Z'), parametrized in terms of one CP-conserving f_5^{V} and one CP-violating f_4^{V} form factors, are calculated in models with CP-violating flavor changing neutral current couplings mediated by the Z gauge boson and an extra neutral gauge boson Z'. Analytical results are presented in terms of Passarino-Veltman scalar functions. Constraints on the vector and axial couplings of the Z gauge boson left| g_{{VZ}}^{tu}right| < 0.0096 and left| g_{{VZ}}^{tc}right| <0.011 are obtained from the current experimental data on the trightarrow Z q decays. It is found that in the case of the ZZgamma ^* vertex the only non-vanishing form factor is f_5^{gamma }, which can be of the order of 10^{-3}, whereas for the ZZZ^* vertex both form factors f_5^{Z} and f_4^{Z} are non-vanishing and can be of the order of 10^{-6} and 10^{-5}, respectively. Our estimates for f_5^{gamma } and f_5^{Z} are smaller than those predicted by the standard model, where f_4^{Z} is absent up to the one loop level. We also estimate the ZZ{Z'}^{*} form factors arising from both diagonal and non-diagonal Z' couplings within a few extension models. It is found that in the diagonal case f_{5}^{Z'} is the only non-vanishing form factor and its real and imaginary parts can be of the order of 10^{-1}–10^{-2} and 10^{-2}–10^{-3}, respectively, with the dominant contributions arising from the light quarks and leptons. In the non-diagonal case f_{5}^{Z^prime } can be of the order of 10^{-4}, whereas f_4^{Z'} can reach values as large as 10^{-7}–10^{-8}, with the largest contributions arising from the Z'tq couplings.