arXiv subjects

Wojciech Broniowski

Publications and source records attributed to Wojciech Broniowski.

At least 19 recordsLinked to original sources

arXiv2026

Wounded parton scaling of multiplicities in ultra-relativistic light- and heavy-ion collisions

Multiplicities of charged particles produced in O+O, Ne+Ne, Xe+Xe, and Pb+Pb collisions at $\sqrt{s_{NN}} \sim 5$~TeV are studied in a uniform way within a wounded parton Glauber framework with overlaid negative binomial fluctuations. In this model, the nucleon's inelastic interaction is modeled via its constituent partons, whose number is a parameter, with best description obtained with four partons per nucleon. We fit directly the experimental multiplicity distributions (histograms), using {\it the same model parameters} for each reaction. The fit is performed in the c=1--80 $\%$ centrality range. Avoiding the most peripheral events makes the method insensitive to the normalization issues caused by the difficulty in separating the Coulomb interactions, whereas the most central collisions may involve a different particle production mechanism. We find a proper model description of multiplicity distributions across all the studied systems for $c \lesssim 1\%$.

nucl-th↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2026

Magnetic susceptibility of a hot hadronic medium and quark degrees of freedom near the QCD cross-over point

The lattice QCD results for the temperature-dependent magnetic susceptibility of the medium below the cross-over temperature are not possible to reconcile with the widely used Hadron Resonance Gas model, also amended with the physical magnetic moments of hadrons or the pion--vector-meson loops. As noticed earlier, one observes a substantially too strong diamagnetism at temperatures in the range above $\approx 120$~MeV compared to the lattice. This hints at a presence of quarks significantly below the QCD cross-over temperature, which are needed as a source of paramagnetism. However, the pions must be retained to describe the diamagnetism data at low temperatures. Therefore, we consider here a quark-meson approach, where the temperature-dependent quark masses are fixed in a model-free way using the baryon-baryon and baryon-strangeness susceptibilities from the lattice at zero magnetic field. The constituent quarks possess anomalous magnetic moments estimated from the octet baryon magnetic moments. The vacuum quark-loop and meson-loop contributions are duly incorporated. We show that in such a framework, one can describe the magnetic susceptibility up to the cross-over point. The qualitative conclusion is that the QCD degrees of freedom must extend far below the cross-over temperature, down to $\approx 120$~MeV.

hep-ph↗

arXiv2025

Magnetic properties of the hadron resonance gas with physical magnetic moments

We study magnetic properties of the Hadron Resonance Gas in the presence of a strong ($0 \le B \le 0.15~{\rm GeV}^2$) uniform magnetic field, using physical values of the magnetic moments of hadrons, i.e., including their anomalous parts. The values of these moments are taken from experiment, or when unavailable, from theoretical estimates. We evaluate the conserved charge susceptibilities, finding the expected sizable effects of the anomalous magnetic moments, in particular of the octet baryons, such as the proton and neutron, where they are exceptionally large. We also study in detail the large effects of the magnetic moments of the $Δ(1232)$ states, for which various theoretical estimates and experimental values differ significantly. We compare our model results with the lattice QCD data and find reasonable agreement within the model uncertainty.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

arXiv2022

Baryonic form factors of the pion and kaon in a chiral quark model

The baryonic form factor of charged pions is studied in detail in the Nambu--Jona-Lasinio model with constituent quarks, where the spontaneously broken chiral symmetry is the key dynamical ingredient guaranteeing the would-be Goldstone boson nature of the pseudoscalar mesons octet. In general, this form factor arises when the isospin symmetry is broken, which is the case if the $u$ and $d$ quark masses are split, as in the real world, or if the electromagnetic effects were taken into account. We obtain estimates for this basic property of the pion resulting from the quark mass splitting for a range of model parameters, and importantly, for different pion masses, going up to the values used in lattice QCD. We find very stable model results, with the mean square radius of $π^+$ in the range $(0.05-0.07~{\rm fm})^2$. From charge conjugation, the baryonic form factor of $π^+$ and $π^-$ are equal and opposite. We also obtain the transverse-coordinate, relativistically invariant baryonic density of the charged pion. In $π^+$, the inner region carries a negative, and the outside -- a positive baryon number density, both cancelling to zero, as obviously the pion carries no net baryon charge. We also carry out an analogous analysis for the kaon, where the effect is much larger due to the sizable $s$ and $u/d$ quark mass splitting. We discuss the prospects of lattice QCD measurements of the baryonic form factors of charged pions and kaons.

hep-ph↗

arXiv2021

Baryonic content of the pion

The baryon form factor of charged pions arises since isospin symmetry is broken with unequal up and down quark masses, $m_d>m_u$, as well as electromagnetic effects. We obtain estimates for this basic property in two phenomenological ways: from simple constituent quark models, as well as from fitting the $e^+e^- \to π^+ π^-$ data. All our methods yield the result that the baryon mean square radius, extracted from the slope of the form factor, is positive for $π^+$, hence a picture where the outer region has a net baryon, and the inner region a net antibaryon density, both compensating each other such that the total baryon number is zero. For $π^-$ the effect is equal and opposite. We estimate the corresponding mean squared baryon radius as $\langle r^2 \rangle_B^{π^{+}} = (0.03-0.04~{\rm fm})^2$.

hep-ph↗

arXiv2020

Vector-axial vector lattice cross section and valence parton distribution in the pion from a chiral quark model

Within a chiral quark model, we evaluate the good cross section in the Euclidean space in the vector - axial vector channel, proposed recently by Ma and Qiu as means to extract the so far elusive parton distribution functions of the pion from lattice QCD. Our results are remarkably simple at the quark model scale and agree well, after the necessary QCD evolution, with with the most recent lattice calculations at the scale $μ\sim 2$ GeV for various values of the lattice pion mass. Comparisons are made as functions of the Ioffe time variable. We also comment on the information on the lowest moments in the momentum fraction $x$, generically extractable from such analyses, as well as on the inaccessibility of the $x \to 1$ limit from the present data.

hep-ph↗