arXiv subjects

Juan Carlos Vasquez

Publications and source records attributed to Juan Carlos Vasquez.

At least 19 recordsLinked to original sources

arXiv2026

Minimal Proper-time in Quantum Field Theory

We propose a generalization of quantum field theory within Schrodinger's functional representation, inspired by Nambu's proper-time formulation of quantum mechanics. The key motivation for this generalization is to incorporate a fundamental, Lorentz-invariant minimum scale, which in this formulation is played by a minimal proper time $τ_{\min}$. The introduction of $τ_{\min}$ leads to several significant effects at very high energies: it modifies the Heisenberg uncertainty principle, induces a controlled violation of unitarity, and suppresses high-energy modes. This minimal scale renders the theory asymptotically safe through a mechanism akin to dimensional reduction, while reproducing all the standard results at low energies, where quantum field theory emerges. Remarkably, the same framework can accommodate a deterministic regime at energies approaching the Planck scale. These features suggest that a minimal proper-time formulation renders the quantum field theory an effective but finite theory, superseded at trans-Planckian energies.

hep-th↗

arXiv2025

Dissecting Lepton Number Violating Interactions in the Left-Right Symmetric Model: $0νββ$ decay, Møller scattering, and collider searches

In the context of the left-right symmetric model, we study the interplay of neutrinoless double beta ($0νββ$) decay, parity-violating Møller scattering, and high-energy colliders, resulting from the Yukawa interaction of the right-handed doubly-charged scalar to electrons, which could evade the severe constraints from charged lepton flavor violation. The $0νββ$ decay amplitude receives additional contributions from right-handed sterile neutrinos. The half-life, calculated in the effective field theory (EFT) framework, allows for an improved description of the contributions involving non-zero mixing between left- and right-handed $W$ bosons and those arising from exchanging a light right-handed neutrino. We find that the relative sensitivities between the low-energy (or high-precision) and high-energy experiments are affected by the left-right mixing. On the other hand, our results show how the interplay of collider and low-energy searches provides a manner to explore regions that are inaccessible to $0νββ$ decay experiments.

hep-ph↗

arXiv2025

Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness

Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working within canonical quantization, we demonstrate how to properly quantize fields in such a multifractal spacetime. Our analysis reveals that a non-differentiable nature of spacetime is not merely compatible with quantum field theory but significantly enhances its mathematical foundation. Most notably, this approach ensures perturbative UV finiteness and improved behavior of the series expansion and enables rigorous construction of the S-matrix in the interaction picture by breaking vacuum translational invariance. The multifractal structure tames dominant, large-order divergence sources in the perturbative series and resolves the Landau pole problem through asymptotic safety, substantially improving the theory's behavior in the deep ultraviolet regime. Our formulation preserves all established predictions of standard quantum field theory at low energies while offering novel physical behaviors at high energy scales.

hep-th↗

arXiv2025

Hadron Collider Signatures of Lepton Number Violation in the Type II Seesaw Model

We examine the prospect of observing genuine lepton number violating (LNV) signals at hadron colliders in the context of the Type II seesaw mechanism. The model features smoking gun signals involving same-sign di-leptons and jets that may be the primary observable channel in certain regions of the parameter space. The flavour composition of final-state charged leptons in the minimal model is related to the origin of neutrino masses and is correlated with other rare processes, such as neutrinoless double beta decay. We review existing collider limits and provide sensitivity estimates from LNV signals at upcoming runs of the LHC, for zero and non-zero mass splittings between the scalar triplet components.

hep-ph↗

arXiv2024

Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series

We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel-Padé approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel-Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed.

math-ph↗

arXiv2024

Gluon Mass Generation from Renormalons and Resurgence

We establish a link between the concepts of infrared renormalons, infrared fixed point, and dynamical nonperturbative mass generation of gluons in pure Yang-Mills theories. By utilizing recent results in the resurgent analysis of renormalons through non-linear ordinary differential equations, we develop a new description for the gluon propagator, thereby realizing the Schwinger mechanism. Specifically, this approach leads to a nonperturbative, dynamic mass generation for Yang-Mills gauge bosons in the deep infrared region, a phenomenon closely associated with color confinement. Furthermore, we present arguments about the limit of applicability of the Borel-Ecalle resummation of the renormalons by comparing it with the Kallen-Lehman representation of the gluon propagator.

hep-th↗

arXiv2024

Resurgence and self-completion in renormalized gauge theories

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well-defined at any energy, thus with no Landau pole. We illustrate the point within the case of QED. This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

hep-th↗

arXiv2023

A consistent quantum field theory from dimensional reduction

We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an effective mass energy associated with the dimensional reduction scale. We quantize the theory within canonical formalism. We then show that it can be made finite in perturbation theory, free of renormalon ambiguities, and with better analytic behavior for infinitesimal coupling constant compared to standard quantum field theory. The new approach reproduces the known results at low energies. One key feature of this class of models is that the coupling constant always reaches a fixed point in the ultraviolet region, making the models ultra-violet complete.

hep-th↗

arXiv2022

Light Sterile Neutrinos, Left-Right Symmetry, and $0νββ$ Decay

We investigate neutrinoless double beta ($0νββ$) decay rates in minimal left-right symmetric models in presence of relatively light right-handed neutrinos. By use of an effective field theory approach, we systematically include all contributions in the model as well as the dependence of the decay amplitude on the masses of right-handed neutrinos. In type-I and type-II seesaw scenarios, we analyze the impact of right-handed neutrinos heavier than about 10 MeV, showing that this effect can lead to a detection of $0νββ$ decay in the next-generation experiments even for the normal hierarchy and a relatively large right-handed scale set by the mass of hypothetical right-handed gauge bosons. Finally, we comment on a possible connection between light right-handed neutrinos and the strong CP problem.

hep-ph↗

arXiv2022

The QCD Adler function and the muon $g-2$ anomaly from renormalons

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon's anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon's anomalous magnetic moment and the experimental value obtained by the most recent muon g-2 collaboration. The latter shows that the Adler function's new representation can also be consistent with recent lattice determinations.

hep-ph↗

arXiv2022

Lepton Number Violation: from $0νββ$ Decay to Long-Lived Particle Searches

We study the complementary tests of lepton number violation in $0νββ$-decay experiments, long-lived particle (LLP) searches at the LHC main detectors ATLAS/CMS, and a proposed far detector MATHUSLA. In the context of a simplified model with a scalar doublet $S$ and a Majorana fermion $F$, we show that while the $0νββ$-decay experiments can probe a larger portion of parameter space, the LLP searches can uniquely probe the region of smaller couplings and masses if $S$ is at TeV scale while $F$ is at or below the electroweak scale. We also investigate constraints on the parameter space from the existing searches that are insensitive to lepton number violation.

hep-ph↗

arXiv2022

Unravelling the left-right mixing using $0νββ$ decay and collider probes

In the context of the minimal left-right symmetric model, we study the interplay between current and future neutrinoless double beta ($0νββ$) decay experiments, long-lived particle searches at the LHC main detectors ATLAS/CMS, and the proposed far detector MATHUSLA. The heavy Majorana neutrino can be produced in association with an electron from the decay of $W$ boson for a non-zero left-right mixing and subsequently decays into another electron with the same charge and jets. Owing to the suppression of large right-handed charged gauge boson $W_R$ mass, the heavy neutrinos could be long-lived. We show that long-lived particle (LLP) searches for heavy Majorana neutrinos in the same-sign dilepton channel at the LHC can be used to extend $W_R$ boson mass reach relative to the reach of the Keung-Senjanovic (KS) process. Finally, we show that sensitivities of LLP searches at the high-luminosity LHC with main detectors ATLAS/CMS are competitive with those of future $0νββ$ decay searches.

hep-ph↗

arXiv2021

On Haag's theorem and renormalization ambiguities

We revisit the implications of Haag's theorem in the light of the renormalization group. There is still some lack of discussion in the literature about the possible impact of the theorem on the standard (as opposite of axiomatic) quantum field theory, and we try to shed light in this direction. Our discussion then deals with the interplay between Haag's theorem and renormalization. While we clarify how perturbative renormalization (for the sub-class of interactions that are renormalizable) marginalizes the its impact when the coupling is formally small, we argue that a non-perturbative and non-ambiguous renormalization cannot be built if there is any reference to the interaction picture with free fields. In other words, Haag's theorem should be regarded as a no-go theorem for the existence of a non-ambiguous analytic continuation from perturbative to non-perturbative QFT.

hep-th↗

arXiv2021

Resurgence of the QCD Adler function

We study the QCD Adler function in the energy region $\approx 0.7-2.5$ GeV, in which the non-perturbative effects become dominant. Our analysis is a renormalon-based evaluation using transseries within the resurgence of the Renormalization-Group-Equation and does not require the Operator-Product-Expansion.

hep-ph↗

arXiv2020

Left-right symmetry and electric dipole moments. A global analysis

We perform a global fit using results of searches for electric dipole moments (EDM) of diamagnetic systems within the context of the minimal left-right symmetric model. In this way, we disentangle the new "left-right" electroweak and $\barθ$ contributions that cannot be separated using a single EDM system. Although the fit is done for a specific model, the approach can be applied to any particle physics model. Finally, we revisit the constraint on the $D$ coefficient in $β$-decay and find that current EDM bounds do not preclude observation of this T-violating effect in a possible next generation $β$-decay experiment.

hep-ph↗

arXiv2020

Non-Wilsonian ultraviolet completion via transseries

We study some of the implications for the perturbative renormalization program when augmented with the Borel-Ecalle resummation. We show the emergence of a new kind of non-perturbative fixed point for the scalar $ϕ^4$ model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cut-off, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel-Laplace resummation of the renormalons in non-asymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

hep-th↗

arXiv2020

Left-right symmetry and leading contributions to neutrinoless double beta decay

We study the impact of the mixing (LR mixing) between the standard model $W$ boson and its hypothetical, heavier right-handed parter $W_R$ on the neutrinoless double beta decay ($0νββ$-decay) rate. Our study is done in the minimal left-right symmetric model assuming type-II dominance scenario with charge conjugation as the left-right symmetry. We then show that the $0νββ$-decay rate may be dominated by the contribution proportional to this LR mixing, which at the hadronic level induces the leading-order contribution to the interaction between two pions and two charged leptons. The resulting long-range pion exchange contribution can significantly enhance the decay rate compared to previously considered short-range contributions. Finally, we find that even if future cosmological experiments rule out the inverted hierarchy for neutrino masses, there are still good prospects for a positive signal in the next generation of $0νββ$-decay experiments.

hep-ph↗

arXiv2020

Resurgence of the Renormalization Group Equation

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

hep-th↗