UV Completion Research Articles

Complementary LHC searches for UV resonances of the 0νββ decay operators

We investigate the quark-level effective operators related to the neutrinoless double beta (0νββ) decay process and their ultraviolet completions relevant to chiral enhancement effects at the hadronic level. We have classified several kinds of leptoquark models, matching to different standard model effective operators. Assuming weakly coupled new physics, we find the ongoing 0νββ decay experiments are sensitive to new physics scale at around 2–4 TeV, which is in the reach of LHC searches. We discuss the discovery potential of such resonances in the same-sign dilepton channels at the LHC. Therefore, the direct LHC searches and indirect 0νββ decay searches are complementary to each other in testing the UV completions of the effective operators for 0νββ decay. Published by the American Physical Society 2024

UV and IR effects in axion quality control

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent S-type axion dual to a two form Bμν in 4D and a T-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For T-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why T-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For S-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of m/M with m the axion mass and M the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of p-form gauge potentials (for both p = 2 and p = 3) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.

Signatures of primordial energy injection from axion strings

Axion strings are horizon-size topological defects that may be produced in the early Universe. Ultralight axion-like particles may form strings that persist to temperatures below that of big bang nucleosynthesis. Such strings have been considered previously as sources of gravitational waves and cosmic microwave background (CMB) polarization rotation. In this work we show, through analytic arguments and dedicated adaptive mesh refinement cosmological simulations, that axion strings deposit a subdominant fraction of their energy into high-energy Standard Model (SM) final states, for example, by the direct production of heavy radial modes that subsequently decay to SM particles. This high-energy SM radiation is absorbed by the primordial plasma, leading to novel signatures in precision big bang nucleosynthesis, the CMB power spectrum, and gamma-ray surveys. In particular, we show that CMB power spectrum data constrains axion strings with decay constants fa≲1012 GeV, up to model dependence on the ultraviolet completion, for axion masses ma≲10−29 eV; future CMB surveys could find striking evidence of axion strings with lower decay constants. Published by the American Physical Society 2024

(Multi-field) natural inflation and gravitational waves

We provide a detailed study of natural inflation with a periodic non-minimal coupling, which is a well-motivated inflationary model that admits an explicit UV completion. We demonstrate that this construction can satisfy the most recent observational constraints from Planck and the BICEP/Keck collaborations. We also compute the corresponding relic gravitational wave background due to tensor perturbations and show that future space-borne interferometers, such as DECIGO, BBO and ALIA, may be able to detect it. Next, we extend this analysis and establish the validity of these results in a multi-field model featuring an additional R 2 term in the action, which allows us to interpolate between natural and scalaron (a.k.a. Starobinsky) inflation. We investigate the conditions under which the aforementioned future interferometers will have the capability to differentiate between pure natural inflation and natural-scalaron inflation. The latter analysis could open the door to distinguishing between single-field and multi-field inflation through gravitational wave observations in more general contexts.

Axio-Chameleons: a novel string-friendly multi-field screening mechanism

Scalar-tensor theories with the shift symmetries required by light scalars are well-explored modifications to GR. For these, two-derivative scalar self-interactions usually dominate at low energies and interestingly compete with the two-derivative metric interactions of GR itself. Although much effort has been invested in single scalars (on grounds of simplicity) these happen to have no two-derivative interactions, requiring such models to explore higher-derivative interactions (that usually would be less important at low-energies). This suggests multiple-scalar sigma models as well-motivated candidates for finding new phenomena in tests of gravity. We identify a new multi-field screening mechanism appropriate for two light scalar fields (an axion and a Brans-Dicke style dilaton) that relies on their mutual two-derivative interactions. We show how very weak axion-matter couplings can introduce axion gradients that can reduce the apparent coupling of the Brans-Dicke scalar to macroscopic matter sources. We further identify a relaxation mechanism that allows this reduction to be amplified to a suppression by the ratio of the axion gradient's length scale to the source's radius (similar in size to the suppression found in Chameleon models). Unlike some screening mechanisms our proposal is technically natural and works deep within the regime of control of the low-energy EFT. It uses only ingredients that commonly appear in the low-energy limit of string vacua and so is likely to have wider applications to models that admit UV completions. We briefly discuss phenomenological implications and challenges for this scenario, which suggests re-examination of decay loss bounds and the value of equivalence-principle tests for different-sized objects.

Positivity and the electroweak hierarchy

We point out that an unnatural hierarchy between certain higher-dimensional operator coefficients in a low-energy effective field theory (EFT) would automatically imply that the Higgs’ vacuum expectation value is hierarchically smaller than the EFT cutoff, assuming the EFT emerged from a unitary, causal and local UV completion. Future colliders may have the sensitivity to infer such a pattern of coefficients for a little hierarchy with an EFT cutoff up to O(10) TeV. Published by the American Physical Society 2024

Bilocal Field Theory for Composite Scalar Bosons.

We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu-Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, ϕ(r→), in the center-of-mass frame that satisfies a Schrödinger-Klein-Gordon equation with eigenvalues m2. We analyze the "coloron" model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, ∝Nc the number of colors, and is classically critical with gcritical remarkably close to the NJL quantum critical coupling. Negative eigenvalues for m2 lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent.

Cosmology from the vacuum

We argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the Universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. In particular, while inflation may explain the origin of perturbations in the cosmology picture, the perturbations can be deduced from the dual picture without any knowledge of the inflationary potential.

QCD worldsheet axion from the bootstrap

The worldsheet axion plays a crucial role in the dynamics of the Yang-Mills confining flux tubes. According to the lattice measurements, its mass is of order the string tension and its coupling is close to a certain critical value. Using the S-matrix Bootstrap, we construct non-perturbative 2 → 2 branon scattering amplitudes which also feature a weakly coupled axion resonance with these properties. We study the extremal bootstrap amplitudes in detail and show that the axion plays a dominant role in their UV completion in two distinct regimes, in one of which it cannot be considered a parametrically light particle. We conjecture that the actual flux tube amplitudes exhibit a similar behavior.

Soft graviton exchange and the information paradox

We show that there is a remarkable phase in quantum gravity where gravitational scattering amplitudes mediated by virtual gravitons can be calculated explicitly in effective field theory, when the impact parameter b satisfies LPl≪b≲RS, with RS being the Schwarzschild radius. This phase captures collisions with energies satisfying s≫γMPl (with γ∼MPl/MBH) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analog where collisions are trans-Planckian. Hawking’s geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in 2→2 scattering near the horizon, and explicitly calculate the S-matrix nonperturbatively in MPl/MBH. This involves a resummation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase upon this resummation and is agnostic of Planckian physics and any specific ultraviolet completion. In contrast to the flat-space eikonal limit, the black hole eikonal phase captures collisions of extremely low energy near the horizon. Published by the American Physical Society 2024

New lower bounds on scattering amplitudes: non-locality constraints

Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we consider two non-trivial extensions of the previous bound. (i) We generalize the assumption of polynomial boundedness by allowing amplitudes to exponentially grow for some complex momenta and prove a more general lower bound in the hard-scattering regime. (ii) We prove a new lower bound on elastic scattering amplitudes in the Regge regime, in both cases of polynomial and exponential boundedness. A bound on the Regge trajectory for negative momentum transfer squared is also derived. We discuss the relevance of our results for understanding gravitational scattering at the non-perturbative level and for constraining ultraviolet completions. In particular, we use the new bounds as probes of non-locality in black-hole formation, perturbative string theory, classicalization, Galileons, and infinite-derivative field theories, where both the polynomial boundedness and the Cerulus-Martin bound are violated.

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Neutrino Flavor Model Building and the Origins of Flavor and CP Violation

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.

Standard Model in conformal geometry: Local vs gauged scale invariance

We discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a local Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full gauged scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky–Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

Bootstrapping the chiral anomaly at large Nc

The bootstrap approach (demanding consistency conditions to scattering amplitudes) has shown to be quite powerful to tightly constrain gauge theories at large Nc. We extend previous analysis to scattering amplitudes involving pions and external gauge bosons. These amplitudes allow us to access the chiral anomaly and connect low-energy physical quantities to UV properties of the theory. In particular, we are able to obtain an analytic bound on the chiral anomaly coefficient as a function of the pion dipole polarizabilities. This bound can be useful for holographic models whose dual UV completions are not known, and provide a consistency condition to lattice simulations.

UV completions of Chern-Simons gravity

UV completions of Chern-Simons gravity

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Normalization of the vacuum and the ultraviolet completion of Einstein gravity

Second-order-derivative plus fourth-order-derivative gravity is the ultraviolet completion of second-order-derivative quantum Einstein gravity. While it achieves renormalizability through states of negative Dirac norm, the unitarity violation that this would entail can be postponed to Planck energies. As we show in this paper, the theory has a different problem, one that occurs at all energy scales, namely that the Dirac norm of the vacuum of the theory is not finite. To establish this, we present a procedure for determining the norm of the vacuum in any quantum field theory. With the Dirac norm of the vacuum of the second-order-derivative plus fourth-order-derivative theory not being finite, the Feynman rules that are used to establish renormalizability are not valid, as is the assumption that the theory can be used as an effective theory at energies well below the Planck scale. This lack of finiteness is also manifested in the fact that the Lorentzian path integral for the theory is divergent. Because the vacuum Dirac norm is not finite, the Hamiltonian of the theory is not Hermitian. However, it turns out to be [Formula: see text] symmetric. When one continues the theory into the complex plane and uses the [Formula: see text] symmetry inner product, viz. the overlap of the left-eigenstate of the Hamiltonian with its right-eigenstate, one then finds that for the vacuum this norm is both finite and positive, the Feynman rules now are valid, the Lorentzian path integral now is well behaved, and the theory now can serve as a low energy effective theory, one that we show to have a real classical gravity limit. Consequently, the theory can now be offered as a fully consistent, unitary and renormalizable theory of quantum gravity.

Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity

Multi-messenger astronomy provides us with the possibility of discovering phenomenological signatures of quantum-gravity effects. This should be of paramount importance in the pursuit of an elusive quantum theory for the gravitational interactions. Here we discuss feasible explorations within the effective field theory (EFT) treatment of general relativity. By exploring current techniques borrowed from modern amplitude methods, we calculate leading quantum corrections to the classical radiated momentum and spectral waveforms. The lessons drawn from these low-energy results are that phenomenological applications in gravitational-wave physics can be discussed in line with the EFT approach. In turn, we also examine possible phenomenological surveys from the perspective of a UV completion for quantum gravity which employs the metric as the fundamental dynamical variable, namely quadratic gravity. Being more specific, by resorting to the eikonal approximation, we compute the leading-order time delay/advance in the scattering of light by a heavy object and find a possible significant deviation from the standard general-relativity prediction. This allows us to probe causal uncertainty due to quantum fluctuations of the gravitational field as a genuine prediction from Planck-scale physics.

A novel probe of supersymmetry in light of nanohertz gravitational waves

A new era of exploring the early Universe may have begun with the recent strong evidence for the stochastic gravitational wave (GW) background from the data reported by NANOGrav, EPTA (including InPTA data), PPTA, and CPTA. Inspired by this, we propose a new potential source of stochastic GWs in the minimal supersymmetric standard model (MSSM), which could be the theory at a very high energy scale. This source is the “axion” field in the Higgs multiplets when the Higgs field takes a large value along the D-flat direction in the early Universe, for example, during inflation. The axion motion triggers the instability of the standard model U(1) and/or SU(3) gauge fields, producing stochastic GWs during the inflation. This scenario can be seen as a simple UV completion of the commonly studied models where an axion spectator/inflaton is coupled to a hidden U(1) or SU(N) gauge field without matter fields. Thus the nanohertz GWs may be a sign of supersymmetry. Primordial magnetic field production is also argued. In addition, we point out the simple possibility that this axion within the MSSM drives inflation.