We investigate the warm inflationary scenario in Weyl geometric gravity theory, in which the action is constructed by adding matter to the simplest conformally invariant gravitational action in Weyl geometry. The $$\tilde{R}^2$$ theory can be formulated equivalently as a linear theory supplemented by an additional scalar degree of freedom originating from higher-order curvature terms, with the equations of motion obtained via variational methods. We investigate the cosmological implications of the theory by considering the warm inflationary scenario of the early evolution of the Universe, in which radiation, the inflaton field, and the Weyl vector coexist. We consider the widely studied linear dissipation coefficient model along with a quartic potential, and investigate the influence of the Weyl vector term on the dynamics. We performed numerical computations for different coupling models, and we successfully developed a warm inflationary model in which the Universe transitions naturally from an inflationary epoch to a radiation-dominated era. The relevant cosmological observables were calculated and compared with the latest observational constraints from the Atacama Cosmology Telescope (ACT) data.

China

Runhua Huang

Romania

Tiberiu Harko

Shi-Dong Liang

Hong-Hao Zhang

Lei Ming

Warm inflation in Weyl geometric gravity

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.

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)

We explore resonant production of sterile neutrino dark matter via the Shi-Fuller (SF) mechanism, revisiting its cosmological viability in light of recent results demonstrating that lepton-number asymmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>α</mi></msub><mo>≳</mo><mn>1</mn></math> at temperatures <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">T</mi><mo>&gt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> are consistent with big bang nucleosynthesis (BBN). Using a quasiclassical Boltzmann transport calculation of the dark matter production, we compute the nonthermal phase space distributions of sterile neutrinos across a broad range of particle mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>s</mi></msub></math> and mixing angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>sin</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mn>2</mn><mi>θ</mi><mo stretchy="false">)</mo></mrow></math> parameter space. We then evolve the resulting distributions through linear structure formation using CLASS and fit the resulting matter power spectra to thermal warm dark matter (WDM) transfer functions, enabling a direct mapping between SF models and equivalent thermal WDM particle masses <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>th</mi></msub></math>. This allows us to reinterpret existing structure formation limits and Lyman-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math> forest preferences in the context of SF production. We find that lepton asymmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>≳</mo><mn>0.5</mn></math> at high temperatures open significant viable parameter space in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>s</mi></msub><mo>≳</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>sin</mi><mn>2</mn></msup><mo stretchy="false">(</mo><mn>2</mn><mi>θ</mi><mo stretchy="false">)</mo><mo>≲</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>14</mn></mrow></msup></math> regime, compatible with both x-ray constraints from NuSTAR and INTEGRAL/SPI and recent Lyman-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math> inferences of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>th</mi></msub><mo>≈</mo><mn>4.1</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>. Following lepton number evolution below 20 MeV, we also specifically show that this lepton asymmetry parameter space is compatible with BBN and cosmic microwave background constraints. We present updated constraints, a refined <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>th</mi></msub></math> fitting function, and power-law approximations for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> across the parameter space. Our results motivate future x-ray observations targeting the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math> photon regime and testing of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>th</mi></msub><mo>≳</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math> WDM region.

United States

Cannon M. Vogel

Helena García Escudero

Julien Froustey

Kevork N. Abazajian

Return of the lepton number: Sterile neutrino dark matter production and the revival of the Shi-Fuller mechanism

Within the framework of the next-to-minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $ \tau\rightarrow e M^+ M^- $ decays: $ \tau \rightarrow e \pi^+\pi^- $ , $ \tau \rightarrow e \pi^+K^- $ , and $ \tau \rightarrow e K^+K^- $ . Based on the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensitive parameters and LFV sources are non-diagonal elements corresponding to the initial and final leptons. This work can provide a basis for discovering the existence of new physics (NP).

Rong-Zhi Sun

Shu-Min Zhao

Shuang Di

Portugal

Xing-Xing Dong

Study of ${\boldsymbol\tau\rightarrow {\boldsymbol e M^+ M^-}}$ decays in N-B-LSSM * Supported by National Natural Science Foundation of China (NNSFC) (12075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), the Project of the China Scholarship Council (CSC) (202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit (UIDB/00777/2020, UIDP/00777/2020)

In this study, we investigated the neutrino transition magnetic moment in $ U(1)_X $ SSM. $ U(1)_X $ SSM is the $ U(1) $ extension of the Minimal Supersymmetric Standard Model (MSSM), and its local gauge group is extended to $S U(3)_C\times S U(2)_L \times U(1)_Y\times U(1)_X$ . To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to the MSSM, which can explain the results of neutrino oscillation experiments. The neutrino transition magnetic moment is induced by electroweak radiative corrections. By applying the effective Lagrangian method and on-shell scheme, we studied the associated Feynman diagrams and transition magnetic moment of neutrinos in the model. We fit experimental data for neutrino mass variances and mixing angles. Based on the range of data selection, the influences of different sensitive parameters on the results were analyzed. The numerical analysis shows that many parameters, such as $ g_X $ , $ M_2 $ , $ \mu $ , $ \lambda_H $ , and $ g_{YX} $ , have an effect on the neutrino transition magnetic moment. In our numerical results, the order of magnitude of $ \mu_{ij}^M/\mu_B $ is approximately $ 10^{-20} $ $ \sim $ $ 10^{-19} $ .

Long Ruan

Ming-Yue Liu

Xing-Yu Han

Xi Wang

Neutrino transition magnetic moment in $\textit{U}$(1) $\textit{X }$ SSM * Supported by National Natural Science Foundation of China (NNSFC, 12075074), Natural Science Foundation of Hebei Province (A2020201002, A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), Scholarship Council (CSC, 202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit UIDB/00777/2020 and UIDP/00777/2020

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl-type f(Q, T) gravity, in which the non-metricity Q is represented in the standard Weyl form, fully determined by the Weyl vector, while T represents the trace of the matter energy–momentum tensor. The effects of the Weyl geometry and of the extra force induced by the non-metricity–matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the non-metricity–matter coupling, are obtained in the weak-field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl-type f(Q, T) gravity.

Jin-Zhao Yang

Iran

Shahab Shahidi

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type f(Q, T) gravity

Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude, manifesting the gauge invariance of both the expansion basis and coefficients. With the help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.

Bo Feng

Xiao-Di Li

Rijun Huang

Expansion of EYM amplitudes in gauge invariant vector space B.F. is supported by Qiu-Shi Funding and the National Natural Science Foundation of China (NSFC) (11935013, 11575156); R.H. is supported by the National Natural Science Foundation of China (NSFC) (11805102), Natural Science Foundation of Jiangsu Province (BK20180724) and ShuangChuang Talent Program of Jiangsu Province

We consider an f(Q, T) type gravity model in which the scalar non-metricity $$Q_{\alpha \mu \nu }$$ <math><msub><mi>Q</mi><mrow><mi>α</mi><mi>μ</mi><mi>ν</mi></mrow></msub></math> of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $$w_{\mu }$$ <math><msub><mi>w</mi><mi>μ</mi></msub></math> . The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), and we compare the predictions of the theory with the standard $$\Lambda $$ <math><mi>Λ</mi></math> CDM model.

Yixin Xu

Weyl type f(Q, T) gravity, and its cosmological implications

We propose an extension of the symmetric teleparallel gravity, in which the gravitational action L is given by an arbitrary function f of the non-metricity Q and of the trace of the matter-energy-momentum tensor T, so that $$L=f(Q,T)$$ <math><mrow><mi>L</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> . The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry–matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function f(Q, T), corresponding to additive expressions of f(Q, T) of the form $$f(Q,T)=\alpha Q+\beta T$$ <math><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>α</mi><mi>Q</mi><mo>+</mo><mi>β</mi><mi>T</mi></mrow></math> , $$f(Q,T)=\alpha Q^{n+1}+\beta T$$ <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><msup><mi>Q</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>β</mi><mi>T</mi></mrow></math> , and $$f(Q,T)=-\alpha Q-\beta T^2$$ <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mi>α</mi><mi>Q</mi><mo>-</mo><mi>β</mi><msup><mi>T</mi><mn>2</mn></msup></mrow></math> . The Hubble function, the deceleration parameter, and the matter-energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard $$\Lambda $$ <math><mi>Λ</mi></math> CDM model.

Guangjie Li

f(Q, T) gravity

We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy-dependent functions. The Schrödinger equation in the energy-dependent noncommutative algebra is derived for a two-dimensional system for an arbitrary potential. The resulting equation reduces in the small energy limit to the standard quantum mechanical one, while for large energies the effects of the noncommutativity become important. We investigate in detail three cases, in which the noncommutative strengths are determined by an independent energy scale, related to the vacuum quantum fluctuations, by the particle energy, and by a quantum operator representation, respectively. Specifically, in our study we assume an arbitrary power-law energy dependence of the noncommutative strength parameters, and of their algebra. In this case, in the quantum operator representation, the Schrö dinger equation can be formulated mathematically as a fractional differential equation. For all our three models we analyze the quantum evolution of the free particle, and of the harmonic oscillator, respectively. The general solutions of the noncommutative Schrödinger equation as well as the expressions of the energy levels are explicitly obtained.

United Kingdom

Energy-dependent noncommutative quantum mechanics