We investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

China

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

We study the ODE/IM correspondence between two-dimensional <math><mi>W</mi><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub></math>/<math><mi>W</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msub></math>-type conformal field theories and the higher-order ordinary differential equations (ODEs) obtained from the affine Toda field theories associated with <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math>-type affine Lie algebras. We calculate the period integrals of the WKB solution to the ODE along the Pochhammer contour, where the WKB expansions correspond to the classical conserved currents of the Drinfeld-Sokolov integrable hierarchies. We also compute the integrals of motion for <math><mi>W</mi><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub></math>(<math><mi>W</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>r</mi></mrow></msub></math>) algebras on a cylinder. Their eigenvalues on the vacuum state are confirmed to agree with the period integrals up to the sixth order. These results generalize the ODE/IM correspondence to higher-order ODEs and can be used to predict higher-order integrals of motion.

Japan

Katsushi Ito

Mingshuo Zhu

Integrals of motion in conformal field theory with -symmetry and the ODE/IM correspondence

We show that dark matter axions or axionlike particles (ALP) induce spontaneously alternating electric currents in conductors along the external magnetic fields due to the (medium) axial anomaly, realizing the chiral magnetic effects (CME). We propose a new experiment to measure this current to detect the dark matter axions or ALP. These induced currents are the electron medium effects, directly proportional to the axion or ALP coupling to electrons, which depends on their microscopic physics. In the experimental setup, one measures the sum of the electric current due to CME and the vacuum current due to the anomalous axion-photon coupling. The CME current is, in general, subdominant by a factor of the Fermi velocity of electrons, compared to latter, unless the axion or ALP coupling to electrons is much bigger than its coupling to photons to compensate the Fermi velocity suppression. However, we find that repurposing the currently operating and planned axion haloscopes may have good sensitivity to probe the CME current.

South Korea

Deog Ki Hong

Sang Hui Im

Kwang Sik Jeong

Dong-han Yeom

Detecting axion dark matter with chiral magnetic effects

We study two dimensional systems with extended conformal symmetry generated by the   <math> <mi>W</mi> </math>  $$ \mathcal{W} $$  3 algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We compute the eigenvalues of the quantum Boussinesq charges in both the vacuum and first excited states of the higher spin module through the ODE/IM correspondence. By studying the higher spin conformal field theory on the torus, we also calculate thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. By combining these results, we show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module.

India

Sujay Ashok

Sanhita Parihar

Tanmoy Sengupta

Adarsh Sudhakar

Italy

Roberto Tateo

Integrable structure of higher spin CFT and the ODE/IM correspondence

We estimate the impact of asymmetry measurements of Deeply Virtual Compton Scattering (DVCS) with transversely polarized proton beam taken at a future Electron Ion Collider in China (EicC) on the extraction of Compton Form Factors (CFFs). The CFFs extracted from an analysis based on artificial neural-network approach are reweighted by means of pseudo-data generated in the expected kinematic region of EicC. We find a remarkable improvement in the extraction of CFF  $$Im {\mathcal E}$$  <math> <mrow> <mi>I</mi> <mi>m</mi> <mi>E</mi> </mrow> </math>  , especially at the range of parton momentum fraction  $$x \sim $$  <math> <mrow> <mi>x</mi> <mo>∼</mo> </mrow> </math>   0.01, thus hinting for a future experimental probe of the parton orbital angular momentum. This work casts a glance at a practical implementation of Bayesian reweighting method on CFFs’ impact study.

Xu Cao

Jinlong Zhang

Accessing compton form factors at the electron ion collider in China: an impact study on  $${\textbf {Im}} {\mathcal E}$$  <math> <mrow> <mi>Im</mi> <mi>E</mi> </mrow> </math>

The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \textrm{T}\overline{\textrm{T}} $$  perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \textrm{T}\overline{\textrm{T}} $$ . Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.

Fabrizio Aramini

Nicolò Brizio

Stefano Negro

Deforming the ODE/IM correspondence with   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \textrm{T}\overline{\textrm{T}} $$

We study the linear differential system associated with the supersymmetric affine Toda field equations for affine Lie superalgebras, which has a purely odd simple root system. For an affine Lie algebra, the linear problem modified by conformal transformation leads to an ordinary differential equation (ODE) that provides the functional relations in the integrable models. This is known as the ODE/IM correspondence. For the affine Lie superalgebras, the linear equations modified by a superconformal transformation are shown to reduce to a couple of ODEs for each bosonic subalgebra. In particular, for <math><mi>o</mi><mi>s</mi><mi>p</mi><msup><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msup></math>, the corresponding ODE becomes the second-order ODE with squared potential, which is related to the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> supersymmetric minimal model via the ODE/IM correspondence. We also find ODEs for classical affine Lie superalgebras with purely odd simple root systems.

ODE/IM correspondence and supersymmetric affine Toda field equations

We show that an axionlike particle (ALP) naturally implements spontaneous electroweak baryogenesis through a cosmic evolution strongly tied to the electroweak phase transition (EWPT) if it feebly couples to the Higgs field while giving a small contribution to the Higgs boson mass. The observed baryon asymmetry can be generated successfully if the ALP couples strongly enough to the electroweak anomaly. Also interesting is that the ALP contributes to dark matter, and its coupling to a hidden gauge sector makes the relic abundance insensitive to the cosmic history before the EWPT. The ALP explains both the baryon asymmetry and dark matter in a wide range of the couplings owing to the friction induced by the hidden gauge sector. To be compatible with cosmological and astrophysical observations, the ALP should have a mass in the range between about 0.01 and 30 eV, and is further required to be photophobic if its coupling to the electroweak anomaly is strong, constraining the field content and charge assignment of the UV completion.

Yeseong Lee

Electroweak baryogenesis by axionlike dark matter

Implications of supersymmetrizing the clockwork axions are studied. Supersymmetry ensures that the saxions and axinos have the same pattern of the coupling hierarchy as the clockwork axions. If we assume supersymmetry breaking is universal over the clockwork sites, the coupling structure is preserved, while the mass orderings of the saxions and axinos can differ depending on the supersymmetry breaking scale. While the massive saxions and axions quickly decay, the lightest axino can be stable and, thus, a dark matter candidate. The relic abundance of the axino dark matter from thermal production is mostly determined by decays of the heavier axinos in the normal mass ordering. This exponentially enhances the thermal yield compared to the conventional axino scenarios. Some cosmological issues are discussed.

Kyu Jung Bae

Supersymmetric clockwork axion model and axino dark matter