We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, $ a_{\mu} $ . Utilizing a coupled non-perturbative framework combining Schwinger-Dyson and Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing $ a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13} $ , $ a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = $ $ -(2.02 \pm 0.10) \times 10 ^{-13} $ . Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to $ a_{\mu} $ .

Spain

Mexico

Angel S. Miramontes

K. Raya

A. Bashir

P. Roig

G. Paredes-Torres

Radially excited pion: electromagnetic form factor and the box contribution to the muon's $\textit{g}$-2 * A. S. Miramontes acknowledges $\textit{Consejo Nacional de Ciencia, Humanidades y Tecnología}$ (CONAHCyT), Mexico, for the financial support received through the program '$\textit{Postdoctorados Nacionales por México}$', additionally, has been partially funded by the 'PROMETEO' programme of the 'Generalitat Valenciana' grant CIPROM/2022/66, and by the Spanish 'Agencia Estatal de Investigación', MCIN/AEI/10.13039/501100011033, through the grants PID2020-113334GB-I00 and PID2023-151418NB-I00. A. Bashir thanks $\textit{Coordinación de la Investigación Científica}$ of the $\textit{Universidad Michoacana de San Nicolás de Hidalgo}$ Grant No. 4.10., CONAHCyT grant CBF2023-2024-3544 and $\textit{Ayudas Beatriz Galindo}$, Spain. P. Roig acknowledges Conahcyt (México) funding through project CBF2023-2024-3226 as well as Spanish support during his sabbatical year through projects MCIN/AEI/10.13039/501100011033, grant PID2020-114473GB-I00, and Generalitat Valenciana grant PROMETEO/2021/071. G. Paredes-Torres acknowledges CONAHCyT, Mexico, for the financial support provided to him through the program '$\textit{Beca de Posgrado en México}$'. The work of A. Bashir and K. Raya is supported by Spanish Ministry of Science and Innovation (MICINN grant no. PID2022-140440NB-C22) and Junta de Andalucía (grant P18-FR-5057)

We systematically analyze the impact of dilatonic dynamics on Skyrme spheres, crystals, and branes. The effects of the dilatonic model parameters, encompassing different underlying near-conformal dynamics, on the macroscopic properties of skyrmions such as their mass and radius are discussed. For spheres and crystals we identify special values of the ratio of the decay constants for which the second order differential equations reduce to a solvable first order system. Additionally, in the case of the crystals, the dilaton presence spatially separates the baryon and isospin charge distributions. For branes, we show how the dilaton smooths out their configurations. Our results are expected to have wide implications from the study of near-conformal dynamics stemming from QCD-like theories to phenomenological investigations of nuclear matter in extreme regimes.

Japan

Jahmall Bersini

Italy

Denmark

Alessandra D’Alise

Francesco Sannino

Belgium

Matías Torres

Dilatonic dynamics of baryonic crystals, branes, and spheres

We construct topological soliton solutions describing baryonic tubes and layers with modulation in the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> non-linear sigma model coupled with ω-mesons in <math><mn>3</mn><mo>+</mo><mn>1</mn></math> dimensions. Using appropriate Ansäntze for the pionic matter field and the ω-mesons vector potential, the complete set of seven coupled partial differential equations can be solved analytically. These solutions represent modulated tubes and layers at finite volume with arbitrary baryon number, where the modulation of the solitons in one direction is determined by one of the three degrees of freedom of the pionic field, satisfying the equation of a two-dimensional free massless chiral scalar field. As expected, the inclusion of the ω-mesons to the non-linear sigma model allows to reduce the repulsion energy between baryons, which leads to a flattening of the tubes and layers in one direction, forming a kind of “nuclear linguine phase”. Also, we show that this construction can be carried out even when higher order terms in the large <math><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> expansion are included -in particular the Skyrme term- without spoiling the integrability of the field equations.

Chile

Gonzalo Barriga

Aldo Vera

Exact modulated hadronic tubes and layers at finite volume in a cloud of And Mesons

We determine the impact of the <math><mi>θ</mi></math> angle and axion physics on the near conformal dynamics of the large-charge baryon sector of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> gauge theories with <math><msub><mi>N</mi><mi>f</mi></msub></math> fermions in the fundamental representation. We employ an effective approach featuring Goldstone and dilaton degrees of freedom augmented by the topological terms in the theory. We investigate how different dilaton potentials, including the ones for which a systematic counting scheme can be established, affect the results. Via state-operator correspondence we compute the corrections to the would-be conformal dimensions of the lowest large-charge operators as a function of the <math><mi>θ</mi></math> term and dilaton potential.

Croatia

CERN

Charging the conformal window at nonzero <math><mi>θ</mi></math> angle

We analyze the impact of the θ-angle and axion dynamics for two-color (in fact any Sp(2N )) QCD at nonzero baryon charge and as a function of the number of matter fields on the vacuum properties, the pattern of chiral symmetry breaking as well as the spectrum of the theory. We show that the vacuum acquires a rich structure when the underlying CP violating topological operator is added to the theory. We discover novel phases and analyse the order of their transitions characterizing the dynamics of the odd and even number of flavours. We further determine the critical chemical potential as function of the θ angle separating the normal from the superfluid phase of the theory. Our results will guide numerical simulations and novel tests of the model’s dynamics. The results are also expected to better inform phenomenological applications of the model ranging from composite Higgs physics to strongly interacting massive dark matter models featuring number changing interactions. In the companion work [1] we repurpose and upgrade the approach to determine the impact of the θ-angle and axion physics on non-perturbative near conformal dynamics related to the fixed baryon charge sector.

The θ-angle and axion physics of two-color QCD at fixed baryon charge

In this work we analize how the inclusion of extra mesonic degrees of freedom affect the finite density solitons crystals of the Skyrme model. In particular, the first analytic examples of hadronic crystals at finite baryon density in both the Skyrme ω-mesons model as well as for the Skyrme ρ-mesons theory are constructed. These configurations have arbitrary topological charge and describe crystals of baryonic tubes surrounded by a cloud of vector-mesons. In the ω-mesons case, it is possible to reduce consistently the complete set of seven coupled non-linear field equations to just two integrable differential equations; one ODE for the Skyrmion profile and one PDE for the ω-mesons field. This analytical construction allows to show explicitly how the inclusion of ω-mesons in the Skyrme model reduces the repulsive interaction energy between baryons. In the Skyrme ρ-mesons case, it is possible to construct analytical solutions using a meron-type ansatz and fixing one of the couplings of the ρ-mesons action in terms of the others. We show that, quite remarkably, the values obtained for the coupling constants by requiring the consistency of our ansatz are very close to the values used in the literature to reduce nuclei binding energies of the Skyrme model without vector-mesons. Moreover, our analytical results are in qualitative agreement with the available results on the nuclear spaghetti phase.

Fabrizio Canfora

Marcela Lagos

On the robustness of solitons crystals in the Skyrme model

We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are O(N) and QED 3. We show that in d = 3 − ϵ dimensions the contribution to the O(N) fixed charge Q conformal dimensions obtained in the double scaling limit of large charge and vanishing ϵ is non-Borel summable, doubly factorial divergent, and with order   <math> <msqrt> <mi>Q</mi> </msqrt> </math>  $$ \sqrt{Q} $$  optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large Q and N of ref. [1]. In d = 4 − ϵ dimensions the story changes since in the same large Q and small E regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the O(N) large charge sector for negative ϵ. Although the QED 3 model shares the same large charge behaviour of the O(N) model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order Q optimal truncation order.

Oleg Antipin

The analytic structure of the fixed charge expansion

We show that the (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional gauged nonlinear sigma model minimally coupled to a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge field possesses analytic solutions representing gauged solitons at finite baryon density whose electromagnetic field is a force-free plasma. These gauged solitons manifest a crystalline structure and generate in a very natural way persistent currents able to support force-free plasma electromagnetic fields. The trajectories of charged test particles moving within these configurations can be characterized. Quite surprisingly, despite the nonintegrable nature of the theory, some of the perturbations of these gauged solitons allow one to identify a proper resurgent parameter. In particular, the perturbations of the solitons profile are related to the Lamé operator. On the other hand, the electromagnetic perturbations on the configurations satisfy a two-dimensional effective Schrödinger equation, where the soliton’s background interacts with the electromagnetic perturbations through an effective two-dimensional periodic potential. We studied numerically the band energy spectrum for different values of the free parameters of the theory and we found that band gaps are modulated by the potential strength. Finally we compare our crystal solutions with those of the (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Gross-Neveu model.