We analyze the vacuum structure of the Babu-Nandi-Tavartkiladze (BNT) model of neutrino mass generation, in which the Standard Model is extended by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>L</mi></mrow></msub></mrow></math> scalar quadruplet with hypercharge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> and a vectorlike <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub></math> triplet fermion with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo>=</mo><mn>1</mn></math>, generating neutrino masses via an effective dimension-seven operator. We delineate the theoretical constraints on the model, requiring the scalar potential to be bounded from below in all field directions, ensuring perturbative unitarity of scattering amplitudes, and demanding that the electroweak vacuum corresponds to the global minimum of the potential. We find that the electroweak vacuum is not generically guaranteed to be the global minimum: several charge-breaking stationary points may coexist with—and potentially lie below—it in potential depth. For the electroweak-like vacuum with vanishing quadruplet expectation value, the condition of global stability reduces to two simple mass inequalities involving the doubly and triply charged scalars. In contrast, for the general electroweak vacuum with nonzero doublet and quadruplet expectation values—compatible with neutrino-mass generation—no comparably simple analytic condition emerges, and the stability must in general be assessed for specific choices of scalar couplings. In the special case where the interaction responsible for neutrino-mass generation vanishes, both electroweak configurations coexist, and the bounded-from-below conditions ensure a definite ordering between them. In this limit, the mass inequalities alone are sufficient to guarantee that the general electroweak vacuum is the global minimum. In the physically relevant regime, the results provide practical sufficient criteria and a systematic framework for assessing vacuum stability in the BNT model.

Saiyad Ashanujjaman

Siddharth P. Maharathy

Vacuum structure of the Babu-Nandi-Tavartkiladze model of neutrino mass generation

We investigate the in-medium modification and dissociation of heavy quarkonium in a hot QCD medium at finite quark chemical potential and in the weak magnetic-field regime. Starting from the one-loop resummed gluon propagator in the imaginary-time formalism, and incorporating nonperturbative effects through a phenomenological correction to the hard thermal loop description, we compute the real and imaginary parts of the dielectric permittivity. This, in turn, leads to a complex heavy-quark potential: The real part is used to determine binding energies by solving the nonrelativistic Schrödinger equation, while the imaginary part generates thermal decay widths dominated by Landau damping. Within the explored parameter range, the temperature has the greatest control over Debye screening, potential modification, and quarkonium stability, whereas finite density and weak magnetic fields introduce comparatively smaller quantitative changes. As the temperature increases, binding energies decrease and thermal widths grow, giving rise to the expected hierarchy between ground and excited states and a sequential suppression pattern in the dissociation temperatures. Overall, our results indicate that while finite chemical potential and weak magnetic fields can shift quarkonium properties in a measurable way, thermal effects remain the primary driver of dissociation, with direct relevance for heavy-ion collision phenomenology.

Indrani Nilima

Mujeeb Hasan

Mohammad Yousuf Jamal

Salman Ahamad Khan

B.K. Singh

Medium-induced quarkonium dissociation at finite chemical potential and in a weak magnetic field

We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">⟩</mo><mo>/</mo><mo stretchy="false">⟨</mo><mi>x</mi><mo stretchy="false">⟩</mo></mrow></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi><mo>=</mo><mn>6</mn></math>, using the gradient flow in lattice quantum chromodynamics (QCD). As a testing ground, we employ SU(3) isosymmetric gauge configurations generated by the OpenLat initiative with a pseudoscalar mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>411</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our analysis uses four lattice spacings and a nonperturbatively improved action, enabling full control over the continuum extrapolation, and the limit of vanishing flow time, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo stretchy="false">→</mo><mn>0</mn></math>. The flowed ratios exhibit O(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>a</mi><mn>2</mn></msup></math>) scaling across the ensembles, and the continuum-extrapolated results, matched to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> using next-to-next-to-leading order matching coefficients, show only mild residual flow-time dependence. The resulting ratios, computed with a relatively small number of configurations, are consistent with phenomenological expectations for the pion’s valence distribution, with statistical uncertainties that are competitive with modern global fits. These findings demonstrate that the gradient flow provides an efficient and systematically improvable method to access partonic quantities from first principles. Future extensions of this work will target lighter pion masses toward the physical point, and applications to nucleon structure such as the proton PDFs and the gluon and sea-quark distributions.

Anthony Francis

Patrick Fritzsch

Rohith Karur

Jangho Kim

Giovanni Pederiva

Dimitra A. Pefkou

Antonio Rago

Andrea Shindler

André Walker-Loud

Savvas Zafeiropoulos

Moments of parton distribution functions of the pion from lattice QCD using gradient flow

We investigate the consistency between the collinear twist-3 factorization and the transverse-momentum-dependent (TMD) factorization for the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>e</mi><mi>p</mi><mo stretchy="false">→</mo><mi>e</mi><msup><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">↑</mo></mrow></msup><mi>X</mi></mrow></math>. In particular, we focus on the contributions from the twist-3 fragmentation functions (FFs) and the TMD polarizing FF in the region of the hyperon’s intermediate transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>T</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>QCD</mi></msub><mo>≪</mo><msub><mi>P</mi><mi>T</mi></msub><mo>≪</mo><mi>Q</mi></math>, where both frameworks are valid. In this region the polarizing FF can be expressed in terms of the twist-3 FFs including the purely gluonic ones, and the resulting TMD factorization formula in the Ji-Ma-Yuan scheme for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mi>p</mi><mo stretchy="false">→</mo><mi>e</mi><msup><mi mathvariant="normal">Λ</mi><mo stretchy="false">↑</mo></msup><mi>X</mi></math> agrees with the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mi>T</mi></msub></math> limit of the corresponding twist-3 cross section. This matching of the two calculations indicates that the two frameworks describe the same effect in quantum chromodynamics (QCD) and provide complementary frameworks for the process in different kinematic regions.

Riku Ikarashi

Yuji Koike

Shinsuke Yoshida

Matching between collinear twist-3 and TMD fragmentation function contributions to polarized hyperon production in SIDIS

We investigate the phenomenological implications of the bosons associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> subgroup in a simple and realistic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> flavor model. While the Nambu-Goldstone boson of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> factor behaves as a standard QCD axion (an axiflavon) with suppressed flavor-violating couplings, the three degrees of freedom from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> have not been studied before. This work focuses on these states, considering both the case where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>F</mi></msub></math> is a global symmetry, yielding pseudo-Nambu-Goldstone bosons (PNGBs), and the case where it is a gauge symmetry with a potentially small coupling, yielding a triplet of (possibly) light gauge bosons. In both scenarios, these new bosons naturally feature unsuppressed flavor-violating couplings to Standard Model fermions in the mass basis. We derive the resulting predictions for flavor-changing neutral currents and lepton flavor violation, including exotic decays of mesons and leptons. Our analysis shows that processes like <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">→</mo><mi>π</mi><mi>X</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo stretchy="false">→</mo><mi>e</mi><mi>X</mi></math> place the most stringent constraints, probing the flavor symmetry breaking scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>ϕ</mi></msub></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>10</mn></mrow><mrow><mn>11</mn></mrow></msup><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> for light bosons, while heavier states are tested in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> decays, as well as by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mtext>−</mtext><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> mixing and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo stretchy="false">→</mo><mi>e</mi><mi>γ</mi></math>. We demonstrate that low-energy flavor experiments provide a powerful probe of this framework, capable of testing ultrahigh symmetry breaking scales that surpass the limits set by astrophysical observations.

Lorenzo Calibbi

Jiangyi Yi

Phenomenology of non-Abelian gauge and Goldstone bosons in a U(2) flavor model

Over the past two decades, numerous exotic hadron states have been discovered, yet their underlying nature remains unclear. It is widely acknowledged that understanding hadron-hadron interactions is essential to unraveling their properties. Hadron spectroscopy is a powerful tool for this endeavor, providing rich experimental data that can shed light on exotic systems. Recently, the LHCb experiment analyzed the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math> and observed a narrow peak in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> invariant mass spectrum, regarding it as a candidate for a pentaquark. In this work, we extract the coupled-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi><mo>−</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mo>−</mo><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> potential based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> invariant mass spectrum. Our results indicate the existence of a bound state below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> mass threshold, corresponding to the experimentally measured state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math>. Furthermore, we predict the scattering lengths and momentum correlation functions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> channels, which serve as theoretical references for future femtoscopy experiments.

Yi-Bo Shen

Zhi-Wei Liu

Ming-Zhu Liu

Rui-Xiang Shi

Chu-Wen Xiao

Wei-Hong Liang

Li-Sheng Geng

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Λ</mi></math> femtoscopy and the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi mathvariant="normal">Λ</mi></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math>

We present an algorithm to include the correlation between the production and decay planes of gluons in a parton-shower simulation. The technique is based on identifying the charge currents responsible for the creation and annihilation of the vector field. It is applicable in both the hard-collinear and the soft wide-angle region. As a function of the number of particles, the algorithm scales linear in computing time and memory. We demonstrate agreement with fixed-order perturbative calculations in the relevant kinematical limits, and present a new observable that can be used to probe correlations beyond current-current interactions.

Stefan Höche

Mareen Hoppe

Daniel Reichelt

Simple algorithm for polarized parton evolution

We investigate the static scaling behavior of the chiral condensate near the two-flavor critical point within the framework of the soft-wall AdS/QCD. The scaling functions are extracted from the chiral order parameters and are found to precisely match those obtained through mean-field calculations. Additionally, it is also checked that the scaling functions are independent of the specific construction of the holographic model. Furthermore, we develop the formalism for calculating the chiral susceptibility and demonstrate that the pseudocritical temperatures obey the scaling law for moderate quark masses. It is shown that the temperature scaling could be comparable with those obtained from Dyson-Schwinger equations and lattice simulations. While the soft-wall AdS/QCD framework predicts mean-field critical exponents that are universal, the critical coefficients and the crossover dynamics are model dependent and provide quantitative constraints for phenomenological model building. These findings could help improve the effectiveness of the soft-wall AdS/QCD.

Zhongzheng Zhang

Danning Li

Lang Yu

Zhibin Li

Xinyang Wang

Scaling functions in the soft-wall AdS/QCD models

We investigate abelian Chern-Simons gauge theory on a strip geometry with two spatial boundaries. In the presence of boundaries, gauge invariance is broken by boundary conditions, leading to physical edge excitations. By deriving the most general local boundary conditions consistent with power counting in the sense of Symanzik, we show that the bulk equations of motion determine the boundary degrees of freedom through a broken gauge Ward identity, yielding boundary Kac-Moody current algebras with opposite central charges on the two edges. The corresponding two-dimensional boundary actions are of Tomonaga-Luttinger type and describe chiral bosons propagating in opposite directions along the two boundaries. A consistency condition, interpreted as a holographic-like bulk-boundary matching, relates the Chern-Simons coupling constant and the boundary parameters to the physical edge velocities. Within this framework, the equality and opposite sign of the two velocities in a symmetric setup follow directly from the boundary structure rather than from model-dependent assumptions about confining potentials, and the velocities are independent of the strip width. Our analysis provides a fully field-theoretic realization of bulk-boundary correspondence in Chern-Simons theory with two boundaries, with direct applications to edge physics in quantum Hall systems and related topological/hydrodynamic settings.

Erica Bertolini

Michael Doyle

Nicola Maggiore

Conor Murphy

Carlotta Piras

Edge modes in Chern-Simons theory on a strip

The correct identification of charged hadrons plays a crucial role in flavor-physics measurements. The final detector configurations at the proposed Future Circular Collider are yet to be determined and this study aims to contribute to this discussion by benchmarking the particle-identification (PID) performance of the proposed CLD and IDEA detectors using fully simulated events. At present, neither detector proposal includes dedicated PID systems, relying instead on information from the tracking subsystems. We estimate the expected level of contamination due to misidentified charged hadrons for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-flavor tagging, rare <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi></math> transitions, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-jet tagging. The PID information provided by silicon trackers, namely time-of-flight and energy-deposit measurements, leads to significant background suppression with high signal efficiency for the low-momentum hadrons considered for same-side <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-flavor tagging. In order to improve the contamination in rare decays where momenta are in the medium range, only good timing resolution of 30 ps and below can yield an improvement of one order of magnitude below the level achieved by kinematic criteria alone. Light-quark jet-flavor tagging requires identification of particles with very large momentum, which is not possible using only time-of-flight or energy-deposit information in silicon. Access to the number of clusters in a drift-chamber setup, as proposed for the IDEA detector, however, results in strong background suppression in every case. This suppression can be further improved in some scenarios by time-of-flight resolution of 30–50 ps or better. The PID quality generally exhibits only a small dependence on the cluster-counting efficiency. Whether dedicated PID detectors could further enhance flavor-physics sensitivity should be the subject of future study.

Anja Beck

Eluned Smith

Flavor-physics benchmarks for tracker-based particle identification at the FCC-ee