Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using fermions that are appropriately charged under some Maxwell or Yang-Mills field defined on the internal manifold. A well known example in the physics literature is $$ {\mathbbm{CP}}^2 $$ , which has four real dimensions and is the coset SU(3)/U(2). In this paper we focus on a five-dimensional coset space, namely the Wu manifold SU(3)/SO(3) , where SO(3) is maximal in SU(3). Intriguingly, the Wu manifold does not admit a spin structure or spin structure, it does admit a spin structure. We provide a physical interpretation of the spin structure by considering spinors that are coupled to an SO(3) Yang-Mills field defined on the Wu manifold, but which carry half-integer “isospin,” thereby canceling the minus sign in the holonomy for uncharged spinors that provides the original obstruction to an ordinary spin structure. We also construct a gauge-covariantly constant spinor in the Wu manifold, and we show how this can be employed in order to construct spin spinor harmonics from scalar harmonics. We provide a very explicit construction of all the scalar and spin harmonics. In a follow-up paper, we shall employ the results we obtain here in order to discuss dimensional reductions and consistent reductions on the Wu manifold.

United States

Cameron Gibson

Okan Günel

Gabriel Larios

C. Pope

Spin $\textit{h}$ structure, scalar and charged spinor eigenfunctions on the SU(3)/SO(3) Wu manifold

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

China

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

In a talk at an IHEP-Beijing symposium celebrating the 50th anniversary of the discovery of the <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math>, I reminisced about some of the interesting phenomena that were observed in <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> decays in the BES, BESII, and BESIII detectors during the 35 year long BES experimental program. The three order of magnitude increase in the <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> event samples and the improved detector capabilities that occurred during this time led to a persistent series of interesting discoveries and new insights. As more <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> events were collected, the scientific interest in them increased and the breadth of physics topics that are addressed by them expanded. In addition, I speculated on what might happen if, in the next few decades, the magnitude of <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> data samples and the detector capabilities continued to increase at similar paces. In particular, I emphasize the possibilities of searches for <math altimg='si111.svg'><mi mathvariant='script'>C</mi></math> <math altimg='si112.svg'><mi mathvariant='script'>P</mi></math> violation in strange hyperon decays and testing the <math altimg='si111.svg'><mi mathvariant='script'>C</mi></math> <math altimg='si112.svg'><mi mathvariant='script'>P</mi></math> <math altimg='si113.svg'><mi mathvariant='script'>T</mi></math> theorem with strangeness-tagged neutral kaon decays.

South Korea

Stephen Lars Olsen

You never have enough <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> events - The case for a <math altimg='si3.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi></mrow></math> factory

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

Multiple pulsar timing array (PTA) collaborations, including the European PTA in partnership with the Indian PTA, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes PTA, and the Chinese PTA have recently reported strong evidence for a signal at nanohertz, potentially the first detection of the stochastic gravitational-wave background (SGWB). We investigate whether the NANOGrav signal is consistent with the SGWB predicted by string cosmology models. By performing Bayesian parameter estimation on the NANOGrav 15-year data set, we constrain the key parameters of a string cosmology model: the frequency $$f_s$$ and the fractional energy density $$\Omega _\textrm{gw}^{s}$$ of gravitational waves at the end of the dilaton-driven stage, and the Hubble parameter $$H_r$$ at the end of the string phase. Our analysis yields constraints of $$f_s = 1.2^{+0.6}_{-\,0.6}\times 10^{-8} \textrm{Hz}$$ and $$\Omega _\textrm{gw}^{s} = 2.9^{+5.4}_{-2.3}\times 10^{-8}$$ , consistent with theoretical predictions from string cosmology. However, the current NANOGrav data is not sensitive to the $$H_r$$ parameter. We also compare the string cosmology model to a simple power-law model using Bayesian model selection, finding a Bayes factor of 2.2 in favor of the string cosmology model. Future pulsar timing array observations with improved sensitivity and extended frequency coverage will enable tighter constraints on string cosmology parameters.

Qin Tan

You Wu

Lang Liu

Constraining string cosmology with the gravitational-wave background using the NANOGrav 15-year data set

We investigate the Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>&#965;</mi></mrow><mrow><mi>&#965;</mi></mrow></msubsup></math>. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital <italic>&#8467;</italic>-excitations, for all radial quantum numbers <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>&#8805;</mo><mn>0</mn></math>. Our procedure is shown to be quite handy, in the sense that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

Türkiye

Omar Mustafa

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

For the Laplacian of an n-Riemannian manifold X, the Weyl law states that the k-th eigenvalue is asymptotically proportional to (k/V)2/n , where V is the volume of X. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification on X behaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion on X is ergodic, for large k the eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volume V, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we call weighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only for p = 6, 7, 8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory.

G. Luca

Italy

Nicolò Ponti

United Kingdom

Andrea Mondino

Alessandro Tomasiello

Can you hear the Planck mass?

Machine learning-based jet classifiers are able to achieve impressive tagging performance in a variety of applications in high-energy and nuclear physics. However, it remains unclear in many cases which aspects of jets give rise to this discriminating power, and whether jet observables that are tractable in perturbative QCD such as those obeying infrared-collinear (IRC) safety serve as sufficient inputs. In this article, we introduce a new classifier, Jet Flow Networks (JFNs), in an effort to address the question of whether IRC unsafe information provides additional discriminating power in jet classification. JFNs are permutation-invariant neural networks (deep sets) that take as input the kinematic information of reconstructed subjets. The subjet radius and a cut on the subjet’s transverse momenta serve as tunable hyperparameters enabling a controllable sensitivity to soft emissions and nonperturbative effects. We demonstrate the performance of JFNs for quark vs. gluon and Z vs. QCD jet tagging. For small subjet radii and transverse momentum cuts, the performance of JFNs is equivalent to the IRC-unsafe Particle Flow Networks (PFNs), demonstrating that infrared-collinear unsafe information is not necessary to achieve strong discrimination for both cases. As the subjet radius is increased, the performance of the JFNs remains essentially unchanged until physical thresholds that we identify are crossed. For relatively large subjet radii, we show that the JFNs may offer an increased model independence with a modest tradeoff in performance compared to classifiers that use the full particle information of the jet. These results shed new light on how machines learn patterns in high-energy physics data.

Dimitrios Athanasakos

Andrew Larkoski

James Mulligan

Mateusz Płoskoń

Felix Ringer

Is infrared-collinear safe information all you need for jet classification?

We consider Klein–Gordon (KG) particles in a global monopole (GM) spacetime within Eddington-inspired Born–Infeld gravity (EiBI-gravity) and in a Wu–Yang magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime settings. We propose a textbook power series expansion for the KG radial wave function that allows us to retrieve the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some conditionally exact, closed form, energy levels (through some parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar potential. We report the effects of the Eddington parameter  $$\kappa $$  <math> <mi>κ</mi> </math>  , GM-parameter  $$\alpha $$  <math> <mi>α</mi> </math>  , WYMM strength  $$\sigma $$  <math> <mi>σ</mi> </math>  , KG-oscillators’ frequency  $$\Omega $$  <math> <mi>Ω</mi> </math>  , and the coupling parameters of the Coulomb plus linear Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators at hand. Such effects are studied over a vast range of the radial quantum number  $$n_r\ge 0$$  <math> <mrow> <msub> <mi>n</mi> <mi>r</mi> </msub> <mo>≥</mo> <mn>0</mn> </mrow> </math>   and include energy levels clustering at  $$\kappa&gt;&gt;1$$  <math> <mrow> <mi>κ</mi> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme EiBI-gravity), and at  $$|\sigma |&gt;&gt;1$$  <math> <mrow> <mo>|</mo> <mi>σ</mi> <mo>|</mo> <mo>&gt;</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math>   (i.e., extreme WYMM strength).

Brazil

A. Soares

C. Pereira

R. Vitória

On the Klein–Gordon oscillators in Eddington-inspired Born-Infeld gravity global monopole spacetime and a Wu–Yang magnetic monopole

The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well-known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark models and quantum chromodynamics (QCD) for a large number of colors provide predictions, but some recent phenomenological analyses even suggest an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible; the weak semileptonic decay of the Omega baryon to a spin <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.

Sweden

Magnus Bertilsson

Stefan Leupold

Goldberger-Treiman relation and Wu-type experiment in the decuplet sector