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

Türkiye

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

Japan

France

Slava Rychkov

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

In this letter, we present an explicit rephasing transformation that maps an arbitrary mixing matrix <italic>U</italic> to the PDG standard parameterization <inline-formula><tex-math id='TM0002' notation='LaTeX'>$U^{0} = {\rm diag} (e^{ - i \arg U_{e1}}, e^{i \arg [ {U_{e2} U_{\tau 3} \over \det U}]} , e^{i \arg [ {U_{e2} U_{\mu 3} \over \det U}]})$</tex-math></inline-formula> <inline-formula><tex-math id='TM0003' notation='LaTeX'>$U {\rm diag} (1 , e^{- i \arg [{U_{e2} \over U_{e1}}]}, e^{- i \arg [ {U_{e2} U_{\mu 3} U_{\tau 3} \over \det U}] })$</tex-math></inline-formula>. With this procedure, which has remained largely conceptual for more than four decades, six independent phases of the mixing matrix are expressed systematically in terms of the arguments. We also apply this framework to the fermion diagonalization matrices <inline-formula><tex-math id='TM0004' notation='LaTeX'>$U^{\nu ,e}$</tex-math></inline-formula> under the approximation <inline-formula><tex-math id='TM0005' notation='LaTeX'>$U^{\nu ,e}_{13}=0$</tex-math></inline-formula>. By partially employing the inversion formula, we factorize all CP phases through the explicit rephasing, thereby revealing the entire CP structure of the mixing matrix. The observable Dirac phase depends only on two relative phases between the fermion sectors and is determined by fermion-specific invariants.

Masaki J S Yang

Explicit Rephasing Transformation to PDG Parameterization and Simplified Expression of the Dirac CP Phase by Fermion-Specific Invariants

The gauge theory bootstrap computes the strongly coupled pion dynamics by considering the most general scattering matrix, form factors, and spectral densities and matching them with perturbative QCD at high energy and with weakly coupled pions at low energy. In this work, we show that further constraints on the spectral densities significantly reduce the possible solutions to a small set of qualitatively similar ones. Quantitatively, the precise solution is controlled by the asymptotic value of the form factors and Shifman–Vainshtein–Zakharov sum rules. We also introduce an iterative procedure that, starting from a generic feasible point, converges to a unique solution parameterized by the UV input. For the converged solution we compute the masses and widths of resonances that appear, scattering lengths and effective ranges of partial waves, and low-energy coefficients in the effective action. Additionally, we use these results to discuss the thermodynamics of a pion gas including pair correlations of pions with the same and opposite charge.

Yifei He

United States

Martin Kruczenski

The Gauge Theory Bootstrap: Predicting Pion Dynamics from QCD

In particle accelerators, broad characterization of the 6D beam phase space is crucial but difficult to obtain with conventional beam diagnostics. We develop a two-stage convolutional neural network that reconstructs the 6D phase space from only 16 transverse <inline-formula><tex-math id='TM0001' notation='LaTeX'>$x\text{-}y$</tex-math></inline-formula> screen images taken at a place with dispersion by different phase-space rotation angles. The model is trained with simulation data for the KEK-Accelerator Test Facility (ATF) injector with ASTRA. The real-space images in the chicane orbit at the KEK-ATF injector were acquired by varying the RF phase of the RF electron gun and the solenoid magnetic field. From these data, we reconstructed a pseudo-6D phase-space distribution at the cathode surface, expressed through 15 2D distributions covering all pairwise coordinate combinations. The time width and spatial spread of the electron beam at the cathode showed values consistent with the measured values at KEK-ATF. Compared to existing 6D beam imaging measurement techniques such as tomography, it significantly reduces measurement time and necessary computational resources, enabling the provision of a more practical 6D phase-space measurement method.

S Mukherjee

M Kuriki

Z J Liptak

H Hayano

M Kurata

N Terunuma

T Okugi

Y Yamamoto

Two-Stage Convolutional Neural Network for Pseudo-6D Phase-Space Reconstruction

Antiprotonic atoms have served as a pivotal tool for investigating the properties of baryon–baryon interactions, including their spin dependence. Examining the spin–orbit splittings induced by their strong interactions also could help clarify the nature of the <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\bar{p}$</tex-math></inline-formula>&#8211;nucleus interactions and their fraction mediated by scalar and vector mesons. Although the strong spin&#8211;orbit splittings for a certain nucleus have been observed experimentally, thorough theoretical investigations have not yet been conducted. In this study, theoretical calculations based on the Dirac equation are systematically performed for nuclei along several isotone &#8220;chains.&#8221; As a result, it is found that the magnitude of the strong spin&#8211;orbit splittings exhibits a significant dependence not only on the corresponding level shifts and widths almost linearly, but also on whether the optical potential enters as a vector or scalar potential. These results are expected to provide deeper insights into <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\bar{p}$</tex-math></inline-formula>&#8211;nucleus interactions, and by extension baryon&#8211;baryon interactions, as well as into the properties of the mesons that mediate them.

Kenta Yoshimura

Shunsuke Yasunaga

Daisuke Jido

Hiroyuki Fujioka

Isotone Chain Study of <italic>p&#773;</italic>&#8211;Atom Spectroscopy and Strong Spin&#8211;Orbit Splittings

By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge- or Becchi-Rouet-Stora-Tyutin (BRST)-invariant nonperturbative ansatz of the one-particle irreducible (1PI) Wilson action in quantum electrodynamics. The gauge invariance of the Wilson action is <italic>exactly</italic> preserved under the RG flow. We explicitly solve the GFERG equation in the leading and partially next-to-leading orders of the large- <inline-formula><tex-math id='TM0001' notation='LaTeX'>$N_f$</tex-math></inline-formula> approximation, where <inline-formula><tex-math id='TM0002' notation='LaTeX'>$N_f$</tex-math></inline-formula> is the number of flavors. We obtain gauge-invariant critical exponents and the gauge-invariant 1PI Wilson action at an infrared fixed point for&#160; <inline-formula><tex-math id='TM0003' notation='LaTeX'>$D\lt 4$</tex-math></inline-formula>, where <italic>D</italic> is the space-time dimension.

Sorato Nagao

Hiroshi Suzuki

Gauge-Invariant Nonperturbative Wilson Action in Quantum Electrodynamics

We discuss the cancellation of the ultraviolet cutoff scale <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\Lambda _{\rm cut}$</tex-math></inline-formula> in the calculation of the expectation value of the 5D energy&#8211;momentum tensor <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\left\langle T_{MN} \right\rangle$</tex-math></inline-formula> ( <inline-formula><tex-math id='TM0003' notation='LaTeX'>$M,N=0,1,\cdots ,4$</tex-math></inline-formula>). Since 5D fields feel the background geometry differently depending on their spins, the bosonic and the fermionic contributions to the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\Lambda _{\rm cut}$</tex-math></inline-formula>-dependent part <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\left\langle T_{MN} \right\rangle ^{\rm UV}$</tex-math></inline-formula> may have different profiles in the extra dimension. In that case, there is no chance for them to be canceled by each other. We consider arbitrary numbers of scalar and spinor fields with arbitrary bulk masses, calculate <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\left\langle T_{MN} \right\rangle$</tex-math></inline-formula> using the 5D propagators, and clarify the dependence of <inline-formula><tex-math id='TM0007' notation='LaTeX'>$\left\langle T_{MN} \right\rangle ^{\rm UV}$</tex-math></inline-formula> on the extra-dimensional coordinate <italic>y</italic> for a general background geometry of the extra dimension. We find that if the geometry is neither flat nor (a slice of) anti-de Sitter (AdS) space, it is impossible to cancel <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\left\langle T_{MN} \right\rangle ^{\rm UV}$</tex-math></inline-formula> between the bosonic and the fermionic contributions. This may suggest that the flat (or AdS) space is energetically favored over the other geometries, and thus the dynamics forces the compact space to be flat (or AdS).

Yutaka Sakamura

Quantum Vacuum Energy and Geometry of the Extra Dimension

In this paper, we propose a hybrid quantum machine learning framework to improve the sensitivity of double Higgs boson searches in the <inline-formula><tex-math id='TM0001' notation='LaTeX'>$HH \rightarrow b\bar{b}\gamma \gamma$</tex-math></inline-formula> final state at <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\sqrt{s} = 13.6~\text{TeV}$</tex-math></inline-formula>. The proposed model combines parameterized quantum circuits with a classical neural network meta-model, enabling event-level features to be embedded in a quantum feature space while maintaining the optimization stability of classical learning. In our benchmark setup, the hybrid model outperforms the pure quantum implementation and improves over the XGBoost baseline while performing similarly to the graph neural network baseline, achieving an expected 95%&#160;CL upper limit on the nonresonant double Higgs boson production cross section&#160;of <inline-formula><tex-math id='TM0003' notation='LaTeX'>$1.9\times \sigma _{\text{SM}}$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0004' notation='LaTeX'>$2.1\times \sigma _{\text{SM}}$</tex-math></inline-formula> under background normalization uncertainties of 10% and 50%, respectively. In addition, expected constraints on the Higgs boson self-coupling <inline-formula><tex-math id='TM0005' notation='LaTeX'>$\kappa _{\lambda }$</tex-math></inline-formula> and quartic vector-boson&#8211;Higgs coupling <inline-formula><tex-math id='TM0006' notation='LaTeX'>$\kappa _{2V}$</tex-math></inline-formula> are improved relative to the pure quantum model and competitive with the classical baselines considered in this work.

Morocco

Marwan Ait Haddou

not found

Mohamed Belfkir

Salah Eddine Elharrauss

From Qubits to Couplings: A Hybrid Quantum Machine Learning Framework for LHC Physics

A dark matter axion with mass <inline-formula><tex-math id='TM0002' notation='LaTeX'>$m_a$</tex-math></inline-formula> induces an oscillating electric field in a cylindrical sample placed under a magnetic field <inline-formula><tex-math id='TM0003' notation='LaTeX'>$B_0$</tex-math></inline-formula> parallel to the cylinder axis. When the cylinder is made of a highly electrically conductive material, the induced oscillating current flows only at the surface. In contrast, if the cylinder is composed of a material with small conductivity, e.g. <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\sigma = 10^{-3}\text{ eV}$</tex-math></inline-formula>, the electric current flows inside the bulk of the cylinder. Within the QCD axion model, the current <italic>I</italic> is estimated as <inline-formula><tex-math id='TM0006' notation='LaTeX'>$I(\sigma =10^{-3}\text{ eV})\simeq 2.8\times 10^{-14}\text{ A }g_{\gamma }\left(\frac{R}{6\text{ cm}}\right)^2 \left(\frac{\sigma }{10^{-3}\text{ eV}}\right)\left(\frac{B_0}{15\text{ T}}\right)\left(\frac{10}{\epsilon }\right) \left(\frac{\rho _a}{0.3\text{ GeVcm}^{-3}}\right)^{1/2}$</tex-math></inline-formula> for <inline-formula><tex-math id='TM0007' notation='LaTeX'>$m_a=10^{-4}$</tex-math></inline-formula>&#8201;eV, with radius <italic>R</italic>, permittivity <inline-formula><tex-math id='TM0009' notation='LaTeX'>$\epsilon = 10$</tex-math></inline-formula> of the cylinder, and axion energy density <inline-formula><tex-math id='TM0010' notation='LaTeX'>$\rho _a$</tex-math></inline-formula>, where <inline-formula><tex-math id='TM0011' notation='LaTeX'>$g_{\gamma }$</tex-math></inline-formula> is a model-dependent parameter; <inline-formula><tex-math id='TM0012' notation='LaTeX'>$g_{\gamma }(\text{KSVZ}) = -0.96$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0013' notation='LaTeX'>$g_{\gamma }(\text{DFSZ}) = 0.37$</tex-math></inline-formula>. Because the current is proportional to <inline-formula><tex-math id='TM0014' notation='LaTeX'>$R^2$</tex-math></inline-formula>, using a large sample with <inline-formula><tex-math id='TM0015' notation='LaTeX'>$R=80$</tex-math></inline-formula>&#8201;cm, we have a large signal-to-noise ratio ( <inline-formula><tex-math id='TM0016' notation='LaTeX'>$&gt;1$</tex-math></inline-formula>) even at temperature <inline-formula><tex-math id='TM0017' notation='LaTeX'>$T=4$</tex-math></inline-formula>&#8201;K, <inline-formula><tex-math id='TM0018' notation='LaTeX'>$\frac{I(\sigma =10^{-3}\text{ eV})}{I_n({\sigma =10^{-3}\text{ eV})}}\times \sqrt{\frac{\delta \omega \delta t_{ob}}{2\pi }} \simeq 1.1g_{\gamma }\left(\frac{4\text{ K}}{T}\right)^{1/2}\left(\frac{L}{100\text{ cm}}\right)^{1/2}\left(\frac{R}{80\text{ cm}}\right) \left(\frac{B_0}{7\text{ T}}\right)\left(\frac{\rho _a}{0.3\text{ GeVcm}}^{-3}\right)^{1/2} \left(\frac{\delta t_{ob}}{10^3\, \mathrm{s}}\right)^{1/2}$</tex-math></inline-formula> for <inline-formula><tex-math id='TM0019' notation='LaTeX'>$m_a=10^{-4}\text{ eV}$</tex-math></inline-formula> with <inline-formula><tex-math id='TM0020' notation='LaTeX'>$\epsilon =10$</tex-math></inline-formula> and <inline-formula><tex-math id='TM0021' notation='LaTeX'>$\sigma =\epsilon m_a$</tex-math></inline-formula>, where thermal noise is <inline-formula><tex-math id='TM0022' notation='LaTeX'>$I_n=\sqrt{\frac{2T\delta \omega }{\pi R_c}}$</tex-math></inline-formula> with <inline-formula><tex-math id='TM0023' notation='LaTeX'>$\delta \omega =10^{-6}m_a$</tex-math></inline-formula> and resistance <inline-formula><tex-math id='TM0024' notation='LaTeX'>$R_c=\frac{L}{\sigma \pi R^2}$</tex-math></inline-formula> for the cylinder with length <italic>L</italic>. Although a superconducting solenoid sufficiently large to accommodate such a sample is required, the detection of dark matter axions in our proposal may be feasible in the mass range <inline-formula><tex-math id='TM0026' notation='LaTeX'>$m_a =10^{-4}\!-\!10^{-3}\text{ eV}$</tex-math></inline-formula>.

Aiichi Iwazaki

A Method of Axion Detection with Mass 10 <sup>&#8722;4</sup>&#8211;10 <sup>&#8722;3</sup> eV Using a Cylindrical Sample with Low Electrical Conductivity