With the discovery of nonzero <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\theta _{13}$</tex-math></inline-formula> and a near-maximal value of the Dirac CP phase as reflected from the measurements of the T2K and NO <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\nu$</tex-math></inline-formula>A experiments, the significance of <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry becomes more prominent. In this work, we study the renormalization group (RG) running effects on neutrino parameters as a perturbation to <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry. Assuming the symmetry to be exact at the seesaw scale, we account the deviations of the parameters at the electroweak scale due to RG running. We solve numerically a set of 19 one-loop RG equations in total, including those of neutrino mixing parameters, mass eigenvalues, and gauge and Yukawa couplings, using a top-down approach. We aim to examine the consistency of the low-energy solutions at the EW scale with the observational data. Working in the Minimal Supersymmetric Standard Model framework, we choose three benchmark values at <inline-formula><tex-math id='TM0006' notation='LaTeX'>$1\ \text{TeV},\ 7\ \text{TeV}$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0007' notation='LaTeX'>$14\ \text{TeV}$</tex-math></inline-formula> for the supersymmetry breaking scale intermediate between the seesaw scale and EW scale. This requires a two-step running procedure to solve the RG equations and it also allows us to study the impact of variation of the supersymmetry breaking scale on the running effects. Our numerical results indicate that the deviations from <inline-formula><tex-math id='TM0008' notation='LaTeX'>$\mu \text{-} \tau$</tex-math></inline-formula> reflection symmetry induced by RG running remain compatible with the current <inline-formula><tex-math id='TM0009' notation='LaTeX'>$3\sigma$</tex-math></inline-formula> global oscillation data.

India

Chandan Kumar Borah

Chandan Duarah

Perturbations to <italic>&#956;-&#964;</italic> Reflection Symmetry Due to Renormalization Group Running Effects

We investigate the static electromagnetic properties of three charm–strange molecular tetraquark candidates with quantum numbers <inline-formula><tex-math id='TM0002' notation='LaTeX'>$J^{P}=1^{+}$</tex-math></inline-formula>, namely the <inline-formula><tex-math id='TM0003' notation='LaTeX'>$D\bar{K}^{\ast }$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0004' notation='LaTeX'>$D^{\ast }\bar{K}$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0005' notation='LaTeX'>$D^{\ast }\bar{K}^{\ast }$</tex-math></inline-formula> systems. The analysis is carried out within the framework of quantum chromodynamics (QCD) light-cone sum rules, using interpolating currents constructed from color-singlet meson bilinears to reflect their molecular configurations. Both perturbative and nonperturbative photon contributions are included, and numerical predictions for the magnetic and electric quadrupole moments are obtained. The magnetic moments are found to lie in the range of 1&#8211;3 nuclear magnetons, with the largest value associated with the&#160; <inline-formula><tex-math id='TM0006' notation='LaTeX'>$D^{*}\bar{K}$</tex-math></inline-formula> configuration. The quadrupole moments are an order of magnitude smaller, of order <inline-formula><tex-math id='TM0007' notation='LaTeX'>$10^{-3}\, \mathrm{fm}^{2}$</tex-math></inline-formula>, indicating only weak deviations from spherical charge distributions. A flavor decomposition shows that the magnetic response is dominated by the light quarks, whereas the charm-quark contribution is strongly suppressed, a feature naturally expected for loosely bound hadronic molecules. The present analysis extends QCD light-cone sum-rule studies of exotic hadrons by providing a systematic determination of the electromagnetic moments of the <inline-formula><tex-math id='TM0008' notation='LaTeX'>$D^{(\ast )}\bar{K}^{(\ast )}$</tex-math></inline-formula> molecular systems. These results provide quantitative benchmarks and identify several qualitative fingerprints&#8212;most notably the vanishing electromagnetic moments of the neutral <inline-formula><tex-math id='TM0009' notation='LaTeX'>$D\bar{K}^{*}$</tex-math></inline-formula>, the strong charm-quark suppression, and the smallness of the quadrupole deformations&#8212;that, taken together, distinguish the molecular scenario from compact diquark&#8211;antidiquark interpretations and may offer useful guidance for future experimental studies of charm&#8211;strange exotic states.

Türkiye

Ulaş Özdem

Structural Dissection of Hadronic Molecules: The <italic>D</italic> (*)&#8201; <italic>K&#773;</italic> (*) Family under QCD Light-Cone Sum Rules

We investigate the magnetic moments of strange hidden-bottom pentaquark states within the constituent quark model, considering both molecular and compact configurations. The system with quark content <inline-formula><tex-math id='TM0001' notation='LaTeX'>$qqqb\bar{b}$</tex-math></inline-formula> ( <inline-formula><tex-math id='TM0002' notation='LaTeX'>$q=u,d,s$</tex-math></inline-formula>) is analyzed in three configurations: a baryon&#8211;meson molecular form <inline-formula><tex-math id='TM0003' notation='LaTeX'>$(\bar{b} q_1)(b q_2 q_3)$</tex-math></inline-formula>, a diquark&#8211;diquark&#8211;antiquark structure <inline-formula><tex-math id='TM0004' notation='LaTeX'>$(b q_1)(q_2 q_3)\bar{b}$</tex-math></inline-formula>, and a diquark&#8211;triquark configuration <inline-formula><tex-math id='TM0005' notation='LaTeX'>$(b q_1)(\bar{b} q_2 q_3)$</tex-math></inline-formula>. Negative-parity states with <inline-formula><tex-math id='TM0006' notation='LaTeX'>$J^P = 1/2^-$</tex-math></inline-formula>, <inline-formula><tex-math id='TM0007' notation='LaTeX'>$3/2^-$</tex-math></inline-formula>, and <inline-formula><tex-math id='TM0008' notation='LaTeX'>$5/2^-$</tex-math></inline-formula> are studied for strangeness <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\mathcal {S}=-1,-2,-3$</tex-math></inline-formula>. For the dominant spin couplings, the two compact configurations yield identical or numerically very close magnetic moments. This indicates that the magnetic properties are governed primarily by the global spin&#8211;flavor structure and heavy-quark suppression effects rather than by the specific clustering of quarks. A systematic suppression with increasing strangeness and a clear spin hierarchy are observed across all configurations. Due to the large bottom-quark mass, heavy-quark contributions are strongly suppressed, and the magnetic moments are dominated by light-strange spin correlations. These results provide useful theoretical benchmarks for future experimental and lattice studies of exotic multiquark states.

Pallavi Gupta

Vikash Kumar Garg

Magnetic Moments of Strange Hidden-Bottom Pentaquarks and the Role of Spin–Flavor Correlations

An analysis of the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$B_s\rightarrow \phi \ell ^+ \ell ^-$</tex-math></inline-formula> rare decay within the covariant confined quark model (CCQM) is performed in this paper. The&#160; <inline-formula><tex-math id='TM0003' notation='LaTeX'>$B_s\rightarrow \phi$</tex-math></inline-formula> transition form factors are calculated and then used to compute the branching fractions and angular observables in various <inline-formula><tex-math id='TM0004' notation='LaTeX'>$q^2$</tex-math></inline-formula> bins, including the forward&#8211;backward asymmetry <inline-formula><tex-math id='TM0005' notation='LaTeX'>$A_{FB}$</tex-math></inline-formula>, the longitudinal polarization <inline-formula><tex-math id='TM0006' notation='LaTeX'>$F_L$</tex-math></inline-formula>, and the optimized observables <inline-formula><tex-math id='TM0007' notation='LaTeX'>$A_i$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0008' notation='LaTeX'>$S_i$</tex-math></inline-formula>. Angular observables and branchings were calculated for the bins that were presented by the LHCb collaboration. Generally, CCQM predictions are consistent with data from the LHCb collaboration within the error bars. However, the largest discrepancy is observed in the forward&#8211;backward asymmetry of <inline-formula><tex-math id='TM0009' notation='LaTeX'>$A_{FB}$</tex-math></inline-formula> for the bin [6,8] GeV <inline-formula><tex-math id='TM0010' notation='LaTeX'>$^2$</tex-math></inline-formula> owing to the reverse signs. Discrepancies are also observed in the observed values of <inline-formula><tex-math id='TM0011' notation='LaTeX'>$A_{FB}$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0012' notation='LaTeX'>$A_5$</tex-math></inline-formula> for the bins [11,12.5] and [15,18.9] GeV <inline-formula><tex-math id='TM0013' notation='LaTeX'>$^2$</tex-math></inline-formula>.

Kazakhstan

Russia

Aidos Issadykov

Angular Observables and Branching Ratio for <italic>Bs</italic>&#8594; &#966; &#8467; + &#8467; &#8722; Decay

We investigate a Standard Model (SM) extension containing <italic>n</italic> degenerate down-type isosinglet vector-like quarks (VLQs) with masses <inline-formula><tex-math id='TM0002' notation='LaTeX'>$M_{\mathcal {D}}$</tex-math></inline-formula> and Yukawa couplings <inline-formula><tex-math id='TM0003' notation='LaTeX'>$y_{\mathcal {D}}$</tex-math></inline-formula>, supplemented by a single right-handed neutrino (RHN), aiming to simultaneously address neutrino mass generation, electroweak vacuum stability, and Higgs inflation. The VLQs play the dominant role in stabilizing the Higgs potential through their impact on the renormalization-group (RG) evolution, while the RHN generates light neutrino masses via a Type-I seesaw mechanism and smooths the high-scale running of the Higgs quartic coupling in the inflationary regime. We perform a two-loop SM RG equation analysis supplemented by the one-loop contributions of the VLQs and the RHN, with proper matching across their mass thresholds. Using these RG trajectories, we identify the regions in <inline-formula><tex-math id='TM0004' notation='LaTeX'>$(n,\, y_{\mathcal {D}},\, M_{\mathcal {D}})$</tex-math></inline-formula> that stabilize the Higgs potential up to the Planck scale while satisfying experimental constraints. Employing the RG-improved Higgs potential in the metric formulation of non-minimal Higgs inflation, we compute the inflationary observables <inline-formula><tex-math id='TM0005' notation='LaTeX'>$n_s$</tex-math></inline-formula> and <italic>r</italic>. The SM+( <italic>n</italic>)VLQ+RHN framework yields predictions consistent with the latest Planck-LB-BK18 and ACT-LB-BK18 data, while simultaneously ensuring electroweak vacuum stability and phenomenologically viable neutrino masses within well-defined regions of parameter space. For comparison, we also investigate the SM+( <italic>n</italic>)VLQ limit and present its vacuum stability and Higgs inflation predictions as a reference to quantify the stabilizing role of the VLQ sector.

Canan Karahan

Neutrino Mass, Vacuum Stability, and Higgs Inflation with Vector-Like Quarks and a Single Right-Handed Neutrino

The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank–Shor–Steane (CSS) codes. In this work, we extend this framework to construct a broad class of logical gates for general CSS codes, including the <italic>S</italic>, Hadamard, <italic>T</italic>, and (multi)controlled- <italic>Z</italic> gates, under the condition where fault-tolerance or circuit-depth optimality is not necessarily imposed. We show that these logical gates can be expressed as exponentials of polynomial functions of the electric and magnetic gauge fields, which allows us to derive explicit decompositions into physical gates. We further prove that their logical action depends only on the (co)homology classes of the corresponding logical qubits, establishing consistency as logical operations. Our results provide a systematic method for formulating logical gates for general CSS codes, offering new insights into the interplay between quantum error correction, algebraic topology, and quantum field theory.

Japan

Junichi Haruna

Note on Logical Gates by Gauge Field Formalism of Quantum Error Correction

In this work, the dynamics of quark–antiquark pair systems is investigated by modeling them as general time-dependent 3D oscillators perturbed by a Coulomb potential. Solving this model enables the prediction of key mesonic properties such as the probability density, energy spectra, and quadrature uncertainties, offering theoretical insights into the confinement of quarks via gluon-mediated strong interactions. To tackle the mathematical difficulty raised by the time dependence of parameters in the system, special mathematical techniques, such as the invariant operator method, unitary transformation method, and the Nikiforov–Uvarov functional analysis are used. The wave functions of the system, derived using these mathematical techniques, are expressed analytically in terms of the Gauss hypergeometric function whose mathematical properties are well characterized. Our results provide the quantum-mechanical framework of quark–antiquark systems that are essential for exploring the nonperturbative aspects of quantum chromodynamics. In addition, the underlying mathematical structure may serve as a foundation for addressing broader challenges in particle physics, including the origin of mass and its connection to the Higgs mechanism.

South Korea

Jeong Ryeol Choi

Algeria

Salim Medjber

Salah Menouar

Ramazan Sever

Time-Dependent 3D Oscillator with Coulomb Interaction: An Alternative Approach for Analyzing Quark–Antiquark Systems

In our earlier work, we revisited the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$d=2+\epsilon$</tex-math></inline-formula> expansion in the <inline-formula><tex-math id='TM0003' notation='LaTeX'>$O(N)$</tex-math></inline-formula> nonlinear sigma model (NLSM), emphasizing the existence of a protected operator, which is a closed form with <inline-formula><tex-math id='TM0004' notation='LaTeX'>$N-1$</tex-math></inline-formula> indices. The scaling dimension of this operator stays exactly equal to <inline-formula><tex-math id='TM0005' notation='LaTeX'>$N-1$</tex-math></inline-formula>, independently of <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\epsilon$</tex-math></inline-formula>. Its existence is problematic for the identification of the NLSM fixed point in <inline-formula><tex-math id='TM0007' notation='LaTeX'>$d=2+\epsilon$</tex-math></inline-formula> with the Wilson&#8211;Fisher fixed point family obtained by analytically continuing from near <inline-formula><tex-math id='TM0008' notation='LaTeX'>$d=4$</tex-math></inline-formula>, which does not possess such a protected operator. Multiplet recombination is one scenario discussed in our earlier work, which could allow the connection of the two families continuously (although not analytically). In this scenario, the protected dimension is lifted at some critical value of&#160; <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\epsilon$</tex-math></inline-formula>, thanks to the short conformal multiplet of scaling dimension <inline-formula><tex-math id='TM0010' notation='LaTeX'>$N-1$</tex-math></inline-formula> eating a long conformal multiplet of higher scaling dimension. In this follow-up work, we assess this scenario for the cases <inline-formula><tex-math id='TM0011' notation='LaTeX'>$N=3$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0012' notation='LaTeX'>$N=4$</tex-math></inline-formula>. We identify the lowest candidates for the long multiplet that could be eaten, and compute their one-loop anomalous dimensions. We find that, at one loop, the scaling dimensions of these candidates grow with <inline-formula><tex-math id='TM0013' notation='LaTeX'>$\epsilon$</tex-math></inline-formula>, while they should decrease to&#160; <italic>N</italic> for recombination to occur. We conclude that multiplet recombination is unlikely.

Italy

Fabiana De Cesare

France

Slava Rychkov

Disturbing News about the <italic>d</italic>&#160;=&#160;2&#160;+&#160; <italic>&#1013;</italic> Expansion: II. Assessing the Recombination Scenario

We study properties of vertex (operator) algebras associated with 3D H-twisted <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\mathcal {N}=4$</tex-math></inline-formula> supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by Becchi&#8211;Rouet&#8211;Stora&#8211;Tyutin (BRST) cohomologies of currents with symplectic bosons, complex fermions, and bc-ghosts. We point out that VOAs for 3D <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\mathcal {N}=4$</tex-math></inline-formula> Abelian gauge theories are fermionic extensions of VOAs associated with toric hyper-K&#228;hler varieties. From this relation, it follows that the VOA associated with the 3D mirror of <italic>N</italic>-flavor <inline-formula><tex-math id='TM0006' notation='LaTeX'>$U(1)$</tex-math></inline-formula> SQED is a fermionic extension of a <italic>W</italic>-algebra <inline-formula><tex-math id='TM0008' notation='LaTeX'>$W^{-N+1}(\mathfrak {sl}_N, f_{\text{sub}})$</tex-math></inline-formula>. For <italic>N</italic>&#160;=&#160;3, we explicitly compute the operator product expansion of elements in the BRST cohomology and find a new algebra that is a fermionic extension of a Bershadsky&#8211;Polyakov algebra <inline-formula><tex-math id='TM0010' notation='LaTeX'>$W^{-2}(\mathfrak {sl}_3, f_{\text{sub}})$</tex-math></inline-formula>. We also suggest an expression for the vacuum character of the fermionic extension of <inline-formula><tex-math id='TM0011' notation='LaTeX'>$W^{-N+1}(\mathfrak {sl}_N, f_{\text{sub}})$</tex-math></inline-formula> predicted by 3D <inline-formula><tex-math id='TM0012' notation='LaTeX'>$\mathcal {N}=4$</tex-math></inline-formula> mirror symmetry.

Yutaka Yoshida

Fermionic Extensions of <italic>W</italic>-Algebras via 3D <italic>&#119977;</italic>&#160;=&#160;4 Gauge Theories with a Boundary

Large-volume neutrino experiments are ideal for testing boosted dark matter (DM) scenarios. We propose, for the first time, an approach to utilize knockout neutrons from DM interaction with a nucleus, whereas previous studies have focused on recoiling free protons. This method is especially crucial for water Čerenkov detectors, where the high proton Čerenkov threshold ( <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\sim$</tex-math></inline-formula>1 GeV) suppresses signal acceptance. The knockout neutrons produce <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\gamma$</tex-math></inline-formula> rays when captured by the medium, which are detectable in coincidence with oxygen de-excitation&#160; <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\gamma$</tex-math></inline-formula> rays. Recently, Super-Kamiokande (SK) was doped with gadolinium (SK-Gd) to enhance neutron detection efficiency. Using SK-Gd as a target experiment, we demonstrate that this method increases sensitivity to boosted-DM models by an order of magnitude compared to free proton&#8211;based analysis, and it allows exploration of a wider range of light DM models previously inaccessible with proton-based analysis. We also present the projected sensitivity for the upcoming Hyper-Kamiokande detector.