arXiv subjects

Enrique Ruiz Arriola

Publications and source records attributed to Enrique Ruiz Arriola.

At least 19 recordsLinked to original sources

arXiv2026

The axial-vector nucleon form factor in the meson dominance picture: the role triangle singularities from a dispersive view

The nucleon axial form factor is analyzed in terms of a dispersion relation comprising chiral perturbation theory (ChPT) and perturbative QCD (pQCD) in the low- and high-momentum regimes respectively, which implies a set of superconvergence sum rules for the $A \to N \bar N$ spectral function. In the timelike region below the $N \bar N$ production threshold we include the $a_1$ and $a_1'$ resonances, with finite-width effects modeled through $ρπ$ and $σπ$ intermediate states. Above the $N \bar N$ threshold, we model an infinite tower of radially excited $1^{++}$ resonances with a non-integer power fall-off, eventually matching pQCD. In this setup, we find that both the ChPT and pQCD contributions are tiny. In turn, the dominant $ρπ$ triangle provides the leading deviations from axial meson dominance. Our calculation is not a fit; it contains parameters with a priori uncertainties estimates. The axial radius is predicted to be $r_A^2 =(0.28-0.33)~\textrm{fm}^2 = ( 0.47-0.57~\textrm{fm})^2$ in agreement with recent lattice QCD results but inconsistent with the MINER$ν$A determination. A simple semiempirical formula is provided accounting for the main physical effects.

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arXiv2026

Hadronic form factors in QCD and the incompleteness problem in the time-like region

Hadronic form factors fulfill dispersion relations and superconvergence sum rules for their spectral density as genuine imprints of QCD. We show several instances where these conditions are flagrantly violated due to the lack of information in the region above the largest known resonance mass and below the onset of perturbative QCD. We propose to use radial Regge trajectories to fill this gap and examine the consequences of such a minimal spectral hadronic ansatz. We illustrate the results with the pion charge form factor.

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arXiv2026

Particle seismology: mechanical and gravitational properties from parton-hadron duality

The internal structure of hadrons is characterized by form factors which correspond to matrix elements of currents. Among those, the stress-energy-momentum tensor is a universally conserved quantity providing the gravitational form factors, from which mechanical properties may be derived via the response to the space-time fluctuations. They have received much attention because of their role as moments of the Generalized Parton Distributions, where the stress-energy-momentum tensor couples to two photons, and more recently, due to the explicit lattice QCD determination for the pion and nucleon. In these lectures we attempt a pedagogical review of the topic from a purely hadronic point of view, based on the notion of dispersion relations, meson dominance, and parton-hadron duality. We show that despite the overwhelming simplicity of the approach, a rather successful description of the lattice QCD data is achieved.

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arXiv2026

Pseudoscalar meson dominance, the pion-nucleon coupling constant and the Goldberger-Treiman discrepancy

We analyze the matrix elements of the pseudoscalar density with pion-quantum numbers $I^G J^{PC}= 1^- 0^{-+}$ in the nucleon in terms of dispersion relations, PCAC and pQCD asymptotic sum rules for the pseudoscalar form factor. We show that the corresponding spectral density must have at least one zero. A model based on ChPT at low energies, resonances at intermediate energies, Regge power-like behaviour at high energies and pQCD at asymptotically high energies, allows to deduce the pion-nucleon coupling constant and the Goldberger-Treiman discrepancy $Δ_{\rm GT} = 1 -\frac{m_N g_A}{F_πg_{πNN}}$, yielding the results for the charged channel \[g_{π^+ pn} = 13.14(^{+6}_{-4})(7)_{\rm IB}, \quad Δ_{\rm GT} = 1.26(^{+51}_{-34})(50)_{\rm IB}\ , \] to be compared with the most precise determinations, $g_{π^+ np} = 13.25(5)$ (and hence $Δ_{\rm GT}=2.1(4) \%$), from $np, pp$ scattering analysis of the Granada-2013 database and $g_{π^+pn}=13.11(10)$, $Δ_{\rm GT}=1.0(7)\%$ from the GMO sum rule. Our work supports the concept of pseudoscalar dominance in the nucleon structure suggested by Dominguez long ago. The minimal resonance saturation of the pseudoscalar form factor of the nucleon with the lowest isovector-pseudoscalar mesons compatible with analyticity, pQCD short distance constraints and chiral symmetry leads to an extended PCAC in the large-$N_c$ limit, and effectively depends on the $π(1300)$ excited pion state. Our results are compatible, though more accurate, than recent lattice QCD studies and are consistent with almost flat strong pion-nucleon-nucleon vertices.

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arXiv2025

Gravitational form factors and mechanical properties of the nucleon in a meson dominance approach

We analyze the gravitational form factors and mechanical properties of the nucleon, focusing on both some general issues as well as on modeling with meson dominance. We show that the lattice QCD results for the nucleon gravitational form factors at $m_π=170$~MeV, available for space-like momentum transfer squared up to 2GeV, are explained in a natural way within the meson dominance approach. We carry out the proper Raman spin decomposition of the energy-momentum tensor and in each spin channel use a minimum number of resonances consistent with the perturbative QCD short-distance constraints. These constraints are related to the super-convergence sum rules, following from the asymptotic perturbative QCD fall-off of the form factors. The value of the nucleon $D$-term following from the fits is -3.0(4). Next, we obtain the two-dimensional transverse gravitational densities of the nucleon in the transverse coordinate $b$. With the super-convergence sum rules, we derive new sum rules for these densities at the origin and for their derivatives, involving logarithmic weighting in the corresponding spectral density integrals. From analysis of the threshold behavior in the time-like region and the properties of the $ππ\to N\bar{N}$ reaction, we infer the behavior of the transverse densities at asymptotically large coordinates. We also carry out the meson dominance analysis of the two- and three-dimensional mechanical properties of the nucleon (the pressure and stress) and explore their connection to the spectral densities via dispersion relations.

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arXiv2025

Pion transverse charge density from $e^+$$e^-$ annihilation data and logarithmic dispersion relations

The transverse charge density of the pion is extracted from a dispersive analysis of the $e^+e^- \rightarrow π^+π^-$ exclusive annihilation data. A logarithmic dispersion relation is used to compute the unknown phase of the timelike pion form factor from the modulus obtained from the annihilation cross section. The method is model-independent and permits quantitative uncertainty estimates. The density is obtained with few-percent accuracy down to $b \sim 0.1$ fm; at smaller distances it depends qualitatively on the assumed high-energy behavior of the timelike form factor. Implications for pion structure and the relevance of pQCD asymptotics are discussed.

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arXiv2025

Transverse densities of the energy-momentum tensor and the gravitational form factors the pion

We present general features of the transverse densities of the stress-energy-momentum tensor $Θ^{μν}$ in the pion. We show positivity of the transverse density of $Θ^{++}$ (analogous to the positivity of the transverse density of the electromagnetic current $J^+$) and discuss its consequences in conjunction with analyticity and quark-hadron duality, as well as the connection to $ππ$ scattering at low energies. Our analysis takes into account the perturbative QCD effects, dominating at high momenta (or low transverse coordinate $b$), the effects of Chiral Perturbation Theory, dominating at low momenta (high $b$), and meson dominance in the intermediate region. We incorporate constraints form analyticity, leading to sum rules for the spectral densities of the corresponding form factors, which {\em i.a.} are relevant for the high-momentum (or the low-$b$) asymptotics. With the obtained high- and low-$b$ behavior, we deduce that the scalar (trace-anomaly) gravitational transverse density $Θ^μ_μ(b)$ must change sign, unlike the case of the positive definite $J^+(b)$ or $Θ^{++}(b)$. We also discuss the transverse pressure in the pion, which is positive and singular at low $b$, and negative at high $b$, in harmony with the stability criterion. The results for the form factors for space-like momenta are compared to the recent lattice QCD data.

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arXiv2024

Scalar and tensor meson dominance and gravitational form factors of the pion

We analyze the recent MIT lattice data for the gravitational form factors (GFFs) of the pion which extend up to $Q^2= 2~{\rm GeV}^2$ for $m_π=170$~MeV~\cite{Hackett:2023nkr}. We show that simple monopole fits comply with the old idea of meson dominance. We use Chiral Perturbation theory ($χ$PT) to next-to-leading order (NLO) to transform the MIT data to the physical world with $m_π=140~$MeV and find that the spin-0 GFF is effectively saturated with the $f_0(600)$ and the spin-2 with the $f_2(1270)$, with monopole masses $m_σ= 630(60)$~MeV and $m_{f_2}= 1270(40)$~MeV. We determine in passing the chiral low energy constants (LECs) from the MIT lattice data alone \[ 10^3 \cdot L_{11} (m_ρ^2)=1.06(15) \, , \qquad 10^3 \cdot L_{12} (m_ρ^2)= -2.2(1) \, , \qquad 10^3 \cdot L_{13} (m_ρ^2) = -0.7(1.1). \] which agree in sign and order of magnitude % to be compared with the original estimates by Donoghue and Leutwyler. The corresponding D-term (druck) has the value $ D(0) = -0.95(3) $. We also analyze the sum rules based on perturbative QCD (pQCD) that imply that the corresponding spectral functions are not positive definite. We show that these sum rules are strongly violated in a variety of $ππ-K \bar K$ coupled channel Omnès-Muskhelishvili calculations. This is not mended by the inclusion of the pQCD tail, suggesting the need for an extra negative spectral strength. Using a simple model implementing all sum rules, we find the expected onset of pQCD at very high momenta.

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arXiv2024

The electromagnetic pion form factor and its phase

In this work, we employ a dispersion relation that allows to recover the electromagnetic form factor of the pion from its modulus along the unitarity cut. Unlike the standard dispersive approach, this method extends in a straightforward manner above the inelastic region, allowing us to obtain the form factor's phase, as well as its real and imaginary parts. As applications, we extract the $P$-wave $ππ$ phase shift, the octet form factor, derive bounds in the spacelike region, and offer insights into the onset of perturbative QCD.

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arXiv2024

Gravitational form factors of the pion and meson dominance

We show that the recent MIT lattice QCD data for the pion's gravitational form factors are, in the covered momentum transfer range, fully consistent with the meson dominance principle. In particular, the $2^{++}$ component can be accurately saturated with the $f_2(1270)$ meson, whereas the $0^{++}$ component with the $σ$ meson. To incorporate the large width of the $σ$, we use the dispersion relation with the spectral density obtained from analyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation Theory and are found to be small between the lattice and the physical point. We also discuss the implications of the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral densities of the gravitational form factors, and argue that these densities cannot be of definite sign.

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arXiv2024

The phase of the electromagnetic form factor of the pion

We employ a dispersion relation that allows to recover the phase of the electromagnetic form factor of the pion from its absolute value above threshold. Compared to alternative approaches building on the phase, this approach builds on experimental input directly accessible at colliders. Employing the precise datasets from the $e^+e^-\toπ^+π^-$ reaction, we obtain the phase of the electromagnetic form factor up to $2.5$~GeV, well beyond standard dispersive approaches. In addition, we separate the isovector and isoscalar components, that allows to extract the $P$-wave $ππ$ phase shift. We also provide relevant results, including the radius of the form factor and bounds in the spacelike region. Last, but not least, the study assess potential systematic uncertainties from the interpolation method and potential zeros of the form factor.

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arXiv2024

Vacuum correlations of the stress-energy-momentum tensor with constituent quarks

The two point correlation function of the stress-energy-momentum tensor describes the propagation of a space-time "micro-earthquake" in the vacuum. In the framework of the path integral formulation of field theory in curved space-time, we derive the Ward-Takashi identity for two-point Green's function of the stress-energy-momentum tensor for a general case of a non-conformal theory. The identity constrains the longitudinal part of the correlator, with the vacuum expectation value of the stress-energy-momentum, non-zero in a non-conformal theory. The obtained formula is demonstrated on the free massive Dirac fermion theory, treated at the one-loop level. This example befits a class of phenomenological chiral quarks models which have been used successfully in numerous applications in the soft non-perturbative regime of strong interactions. We discuss the constraints following from the Ward-Takahashi identity for the correlation functions in these models. We also show how the temporal representation of the two-point correlators, which is an object amenable to lattice QCD, displays an expected exponential fall-off.

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arXiv2023

Off-shellness in generalized parton distributions and form factors of the pion

We study the effects of off-shellness in the generalized parton distributions of the pion. On general grounds, these distributions exhibit a richer structure than in the on-shell case due to absence of the crossing symmetry. In particular, their moments involve additional terms odd in the skewness parameter, associated with new form factors. We bring up relations between the off-shell charge and gravitational form factors, as well as the pion form factor, and discuss their derivations based on the Ward-Takahashi identities. We illustrate the features at the (leading-$N_c$) one-quark-loop level with the help of the spectral quark model of the pion, constructed to embed the vector meson dominance. Simple analytic expressions for the form factors and the distributions follow. Thus obtained off-shell generalized parton distributions are evolved from the quark model scale to higher scales with the LO DGLAP equations. We evaluate the corresponding Compton amplitudes which enter the cross-section for the electroproduction of the pion off the proton (the Sullivan process). It is found in our model that the effects of off-shellness in the generalized parton distribution are substantial, however, they can be largely canceled by the corresponding off-shell corrections to the pion propagator. In particular, this is the case of the Compton form factors entering the deeply virtual Compton scattering amplitude. As a result, we expect small off-shellness effects in electroproduction reactions, such as the Sullivan process.

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arXiv2023

Wigner and Husimi partonic distributions of the pion in a chiral quark model

Generalized transverse momentum distributions (GTMDs), the Wigner, and the Husimi distributions of quarks in the pion are evaluated in a chiral quark model at the one-loop-level. Analytic expressions are obtained for GTMDs, allowing for a qualitative discussion of their features, whereas the Wigner and the Husimi distribution are obtained with numerical integration of simple formulas. We explain the features of the Wigner distributions, in particular their non-positivity. In our model, the Husimi distributions, which are interpreted as coarse-grained Wigner distributions, are not mathematically positive-definite, but the magnitude of their negative values is tiny and occurs at large transverse momenta and impact parameters. Hence, as expected, coarse-graining leads to better behaved functions from the point of view of the probabilistic interpretation.

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arXiv2023

Pseudoscalar meson dominance and nucleon structure

Pseudoscalar meson dominance has implications for nucleon structure which follow from an Extended Partial Conservation of the Axial Current (EPCAC). The minimal resonance saturation of the nucleon pseudoscalar form factor of the lowest pseudoscalar and isovector mesons compatible with pQCD short distance constraints and chiral symmetry. Using PDG tabulated pseudoscalarisovector masses and widths we obtain $g_{πNN} = 13.21(^{+0.11}_{-0.06})$, to be compared with the most precise determinations from $np, pp$ scattering, $g_{π^+ np} = 13.25(5)$ from the Granada-2013 database. Equivalently a Goldberger-Treiman discrepancy $Δ_{\rm GT} = 1.8^{+0.9}_{-0.4}\%$ is found. Our results are consistent with almost flat strong pion-nucleon-nucleon vertices.

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arXiv2023

Off-shell generalized parton distributions of the pion

We analyze off-shell effects in the generalized parton distributions (GPDs) of the pion in the context of the Sullivan electroproduction process, as well as the corresponding half-off-shell electromagnetic and gravitational form factors. We illustrate our general results within a chiral quark model, where the off-shell effects show up at a significant level, indicating their contribution to uncertainties in the extraction of the GPDs from the future experimental data.

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arXiv2023

Off-shell generalized parton distributions and form factors of the pion

Off-shell effects in generalized parton distributions (GPDs) of the pion, appearing, e.g., in the Sullivan process, are considered. Due to the lack of crossing symmetry, the moments of GPDs involve also odd powers of the skewness (longitudinal momentum transfer) parameter, which results in emergence of new off-shell form factors. With current-algebra techniques, we derive exact relations between the four off-shell gravitational form factors of the pion, in analogy to the electromagnetic case. Our results place stringent constraints on the off-shell GPDs of the pion. We provide an explicit realization in terms of a chiral quark model, where we show that the off-shell effects in GPDs are potentially significant in modeling physical processes and should not be neglected.

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arXiv2022

Generalized quasi, Ioffe-time, and pseudo quark distributions of the pion in the Nambu--Jona-Lasinio model

We analyze the generalized quasi, Ioffe-time, and pseudo distributions of the valence quarks in the pion at the quark model scale. We use the framework of the Nambu-Jona-Lasinio model and investigate the basic question of how fast the pion has to move to effectively reach the infinite momentum limit, where the approach can provide the information on the generalized parton distribution functions. We consider both the vector distributions and the transversity distributions, related to the spin densities. With the developed analytic expressions, we conclude that to effectively approach the infinite momentum limit, one roughly needs the pion momenta of the order of $\sim 3$GeV. We also explore polynomiality of the quasi distributions and study the generalized quasi form factors. The issue of separability of the transverse and longitudinal dynamics in the model is studied with the help of the generalized Ioffe-time distributions, with the conclusion that the breaking is not substantial, unless the momentum transfer $t$ is large. We also provide an estimate of the range of the Ioffe-time values needed to obtain the generalized parton distributions with a reasonable accuracy. Our model results, which are analytic or semi-analytic, provide a valuable insight into the theoretical formalism and illustrate the intricate features of the investigated distributions.

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