arXiv subjects

Dario Melle

Publications and source records attributed to Dario Melle.

14 recordsLinked to original sources

arXiv2026

The Gravitational Form Factor of the Pion in Perturbative QCD with a Dilaton Interaction

We investigate the pion gravitational form factors (GFFs) at intermediate and large momentum transfer within the framework of QCD factorization. Our analysis centers on the non-Abelian $TJJ$ correlator, which couples the local QCD energy-momentum tensor to two external gluon fields and explicitly encodes the perturbative effects of the trace anomaly. We demonstrate how this quantum anomaly induces a scalar, dilaton-like contribution to the hard-scattering kernel. To ensure field-theoretic consistency, a careful separation of the quark and gluon sectors is performed, accounting for the modifications introduced by gauge-fixing terms and Slavnov-Taylor identities on the off-shell gluonic structure. To obtain realistic phenomenological predictions and regulate soft-gluon endpoint divergences in the hard kernel, we implement the Sudakov resummation framework coupled with a Gaussian model for the pion's transverse-momentum-dependent wave function. We show that the resulting anomaly-induced corrections significantly modify the behavior of the pion GFFs at large momentum transfer, leaving a unique imprint on the trace sector and the $D$-term.

hep-ph↗

arXiv2026

The Pion Gravitational Form Factors and the Trace Anomaly in QCD Factorization

We study the pion gravitational form factor in QCD factorization, focusing on the trace-anomaly component generated by the non-Abelian $TJJ$ vertex. The calculation combines a Sudakov-resummation-improved pion hard kernel with the anomaly form factor suggested by momentum-space conformal field theory and by the perturbative dilaton sum rule. Comparison with lattice QCD data shows a refined projection hierarchy: the isolated anomaly cancels in the form factor $A_\pi(Q^2)$, while the full $TJJ$ insertion lowers the leading-order curve at small momentum transfer squared $Q^2$; the anomaly is important in $D_\pi(Q^2)$, and it gives the dominant $TJJ$ contribution to the trace form factor.

hep-ph↗

arXiv2026

Anomaly-mediated Scalar Gravitational Interactions and the Coupling of Conformal Sectors

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of $2\to2$ scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons $(TTT)$ and Abelian gauge currents $(TJJ)$, through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated $4$-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated $2\to2$ graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

hep-th↗

arXiv2026

Dilaton Sum Rules of Gravitational Form Factors in QCD at Order $α_s$

We formulate a partonic description of hadronic gravitational form factors within QCD, focusing on the three-point function of the energy-momentum tensor and two gluon currents. Despite the lack of exact conformal symmetry in QCD, the correlator may be organized around the conformal limit through momentum-space CFT methods, suitably adjusted for gauge-fixing effects. This yields a tensor decomposition into spin-2, spin-1, and spin-0 sectors, with the spin-0 contribution governed by the conformal anomaly. The corresponding anomaly form factor satisfies a mass-independent dispersive sum rule and allows a dilaton-like interpretation. In the light-cone limit, this term and an additional traceless structure become dominant, indicating an effective anomaly-mediated description relevant to hadronic gravitational form factors.

hep-ph↗

arXiv2026

Heavy Quark Decays in the Bilepton Model

Given the current absence of new physics signals at the LHC, it is increasingly important to investigate alternative scenarios beyond those commonly explored. In this work, we study a variant of the 331 model that predicts the existence of vector bileptons with electric charge and lepton number +/-2, as well as TeV-scale exotic quarks carrying charges +/- 5/3 and +/- 4/3. Specifically, we focus on the primary production of heavy quarks with charge +/- 5/3, which decay into a bottom quark and a bilepton, followed by the bilepton's decay into same-sign muon pairs. As a case study, we select a benchmark point that complies with current experimental exclusion limits and theoretical expectations for the bilepton mass. Our analysis shows that the resulting signal stands out clearly from Standard Model backgrounds and could be observed at a future 100 TeV hadron collider such as FCC-hh. In contrast, the LHC, even in its high-luminosity phase, lacks the sensitivity required to detect this signal.

hep-ph↗

arXiv2025

A Dilaton Sum Rule for the Conformal Anomaly Form Factor in QCD at Order $α_s$

We present an off-shell dispersive analysis of the graviton-gluon-gluon ($TJJ$) vertex, extending previous investigations carried out in both QED and QCD. Within the framework of a non-Abelian gauge theory, we extract the conformal anomaly form factor from the trace component of the correlator and demonstrate that it satisfies a one-loop sum rule, valid under the most general kinematic conditions. Analogously to the chiral and chiral-gravitational cases, a spectral flow emerges in which the exchanged intermediate state becomes localized at zero invariant mass along the graviton line as the quark mass approaches zero. The total integral of the spectral density precisely reproduces the anomaly. We examine how the behaviour of these spectral densities evolves as the system approaches the conformal limit with on-shell gluons. The perturbative analysis reveals that such sum rules are fundamental dynamical features of anomaly-induced interactions. In particular, the appearance or absence of associated dilaton poles is closely tied to whether the sum rule is saturated by a pole contribution or by a dispersive continuum. In the conformal, on-shell limit, the particle-pole interaction yields a nonlocal S-matrix element entirely supported on the light-cone.

hep-ph↗

arXiv2025

Topological Sum Rules and Spectral Flows of Chiral and Gravitational Axion-like Interactions

We examine the structure of off-shell effective actions arising from chiral and gravitational anomalies, focusing on the $JJJ_A$ (axial-vector/vector/vector) and $J_A TT $ (axial-vector/stress-energy tensors) correlators, relevant in the analysis of anomaly-driven interactions in perturbation theory. Our approach relies on conformal field theory in momentum space, extended to chiral anomalies. The analysis centers on the presence of both particle poles and anomaly poles within these interactions, characterizing their behavior both in the conformal and non conformal limits. Through explicit computations, we show that universal sum rules in the longitudinal sector regulate these interactions for all kinematic conditions, extending previous analysis, and we discuss the resulting spectral flow, an area law of the absorptive part of the anomaly form factors as one moves away from or returns to the conformal point. These features are absent in the local effective action of anomaly interactions, commonly used in the description of axion-like particles. The spectral densities in both cases are shown to be self-similar. Our results further show that anomaly poles correspond to true particle poles only in the conformal limit, when the interaction describes a massless S-matrix process supported on a null-surface. Under these conditions, they can be effectively described by two kinetically mixed pseudoscalar fields propagating on the light-cone. These studies find application in polarized deeply inelastic scattering, axion-like dark matter and analogue systems such as topological materials.

hep-ph↗

arXiv2025

Gravitational Form Factors and the QCD Dilaton at Large Momentum Transfer

We investigate the hard scatterings of hadronic matrix elements corresponding to hadronic gravitational form factors (GFFs) of the pion and proton using QCD factorization, applying conformal field theory (CFT) tools. These GFFs are key to understanding quark and gluon angular momentum via their connection to DVCS moments. The core object is the non-Abelian $ TJJ $ 3-point function, which shows an anomaly-induced dilaton exchange in the $ t $-channel. We analyze quark, ghost, and gauge-fixing effects through a CFT-based decomposition and propose a parameterization useful for future DVCS studies at the Electron-Ion Collider. The dilaton interaction is interpolated by a conformal anomaly form factor, defined in the nonconformal case, which is constrained by a (dilaton) sum rule.

hep-ph↗

arXiv2025

The Gravitational Form Factors of Hadrons from CFT in Momentum Space and the Dilaton in Perturbative QCD

We analyze the hard scattering amplitude of the gravitational form factors (GFFs) of hadrons at one-loop, in relation to their conformal field theory (CFT) description, within the framework of QCD factorization for hard exclusive processes at large momentum transfers. These form factors play an essential role in studying the quark and gluon angular momentum of the hadrons due to their relation to the Mellin moments of the Deeply Virtual Compton Scattering (DVCS) invariant amplitudes. Our analysis is performed using a diffeomorphism invariant approach, applying the formalism of the gravitational effective action and conformal symmetry in momentum space for the discussion of the quark and gluon contributions. The interpolating correlator in the hard scattering of any GFF is the non-Abelian $TJJ$ (stress-energy/gluon/gluon) 3-point function at $O(α_s^2)$, revealing an effective dilaton interaction in the $t$-channel due to the trace anomaly, in the form of a massless anomaly pole in the QCD hard scattering. We investigate the role of quarks, gauge-fixing and ghost contributions in the reconstruction of the hard scattering amplitude mediated by this interaction, performed in terms of its transverse traceless, longitudinal, and trace decomposition, as identified from CFT in momentum space (CFT$_p$). We present a convenient parameterization of the hard scattering amplitude relevant for future experimental investigations of the DVCS/GFF amplitudes at the Electron-Ion Collider at BNL.

hep-ph↗

arXiv2025

The 33311 Left-Right Bilepton Model

We discuss extension of the electroweak gauge group to $SU(3)_L \times SU(3)_R \times U(1)_{XL} \times U(1)_{XR}$. This adds new leptons to the familiar 331-model. The explanation for three light quark-lepton families remains but new particles are introduced which have no TeV scale upper limit on their masses.

hep-ph↗

arXiv2024

The Gravitational Form Factor of the Pion and Proton and the Conformal Anomaly

We analyze the hard scattering amplitude of gravitational form factors (GFFs) of hadrons within QCD factorization at large momentum transfers, focusing on their conformal field theory (CFT) description. These form factors are key to studying quark and gluon angular momentum in hadrons, connected to Mellin moments of Deeply Virtual Compton Scattering (DVCS). The analysis uses diffeomorphism invariance and conformal symmetry in momentum space. A non-Abelian $TJJ$ 3-point function at $O(α_s^2)$ reveals a dilaton interaction in the $t$-channel. We present a parameterization relevant for future DVCS/GFF experiments at the Electron-Ion Collider.

hep-ph↗

arXiv2024

Conformal Backreaction, Chiral and Conformal Anomalies in the Early Universe

The backreaction of a conformal matter sector and its associated conformal anomaly on gravity can be systematically studied using the formalism of the anomaly effective action. This action, defined precisely in flat spacetime within ordinary quantum field theory, can be analyzed perturbatively in terms of external graviton insertions. The expansion coefficients correspond to correlation functions of the stress-energy tensor, which are renormalized through two key counterterms: the square of the Weyl tensor $(C^2)$ and the Gauss-Bonnet term $(E)$. Anomalous conformal Ward identities impose hierarchical constraints on this expansion, revealing that the anomaly's contribution arises from bilinear mixings of the form $R \Box^{-1} E$ and $R \Box^{-1} C^2$, supplemented by local Weyl-invariant terms. These mixings reflect the non-local structure of the anomaly. The precise form of the effective action, however, may vary depending on the regularization scheme used, with potential differences manifesting through additional Weyl-invariant terms. These actions encapsulate the breaking of Weyl invariance in the early universe, with implications that are particularly relevant during the inflationary epoch. For chiral and gravitational anomalies, we demonstrate that the corresponding effective actions exhibit similar structures, influencing the evolution of chiral asymmetries in the early universe plasma.

astro-ph.CO↗

arXiv2024

The $SU(3)_C\times SU(3)_L\times U(1)_X$ (331) Model:Addressing the Fermion Families Problem within Horizontal Anomalies Cancellation

One of the most important and unanswered problems in particle physics is the origin of the three generations of quarks and leptons. The standard Model does not provide any hint regarding its sequential charge assignments, which remain a fundamental mystery of Nature. One possible solution of the puzzle is to look for charge assignments, in a given gauge theory, that are inter-generational, by employing the cancellation of the gravitational and gauge anomalies horizontally. The 331 model, based on an $SU(3)_C\times SU(3)_L \times U(1)_X$ does it in an economic way, and defines a possible extension of the Standard Model, where the number of families has to be necessarily three. We review the model in Frampton's formulation, that predicts the existence of bileptons. Another characteristics of the model is to unify the $SU(3)_C\times SU(2)_L \times U(1)_X$ into the 331 symmetry at a scale which is in the TeV range, and can be tested at the LHC. Expressions of the scalar mass eigenstates and of the renormalization group equations of the model are also presented.

hep-ph↗

arXiv2024

Axion-like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

We discuss fundamental aspects of chiral anomaly-driven interactions in conformal field theory (CFT) in four spacetime dimensions. They find application in very general contexts, from early universe plasma to topological condensed matter. We outline the key shared characteristics of these interactions, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman-Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by an excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, we demonstrate how conformal Ward identities (CWIs) in momentum space allow us to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern-Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial-vector channel satisfies mass-independent sum rules related to the anomaly in any chiral interaction. The detection of an axion-like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analogue of a similar one in ordinary axion physics, in the presence of an axion-like condensate, that we rederive using axion electrodynamics.

hep-ph↗