We investigate the production and detection of gravitational waves (GWs) within the framework of gravitational quantum field theory (GQFT). In this theory, GWs exhibit five propagating modes: one scalar, two vector, and two tensor modes. Unlike general relativity, the gravitational field equations in GQFT involve both symmetric and antisymmetric tensors, governed by their respective energy-momentum tensors, both of which can act as sources for GW radiation. By solving the linearized gravitational equations, we derive general analytic expressions for the different GW degrees of freedom. Our analysis reveals that the symmetric energy-momentum tensor generates scalar and tensor GWs through the trace and traceless parts of the quadrupole moment, respectively. In contrast, the antisymmetric stress tensor induces scalar and vector GWs with enhanced coupling strengths. We examine two illustrative examples: a black hole binary with a slightly elliptical orbit, which produces scalar GWs, and a neutron star binary where one component has a net spin aligned with its velocity, leading to vector GW emission. Finally, we study the detectability of these GW polarizations by analyzing their signatures in GW detectors. Our findings indicate that current observatories can detect both scalar and tensor modes, while a newly designed detector would be required to probe vector GWs.

China

Yuan-Kun Gao

Da Huang

Yue-Liang Wu

Gravitational wave generation and detection in gravitational quantum field theory

Sterile neutrino is a promising dark matter (DM) candidate. However, the parameter space of this scenario has almost been ruled out by the X-ray observation results whenever the sterile neutrino is solely produced by the Dodelson–Widrow (DW) mechanism in the early Universe. In this letter, we propose an extension to the minimal sterile neutrino DM model by introducing the pseudo-Dirac sterile neutrino, which implies the existence of two nearly degenerate Majorana states $${\hat{N}}_{1,2}^{\phantom{a}}$$ , and a permutation symmetry. The heavy state $${\hat{N}}_1$$ is produced via the DW mechanism, and the light state $${\hat{N}}_2$$ , which serves as the DM, is produced from the decay of $${\hat{N}}_1$$ in the early Universe. The X-ray constraint is avoided by the permutation symmetry, which forbids the two-body decay of the DM into active neutrinos and photons. A promising signal of this scenario is the effective number of neutrino species, which will be precisely measured in future experiments, such as CMB stage IV. We further study the impact of this model on the cosmological parameters. The Markov Chain Monte Carlo analysis for the Planck + BAO + R19 data gives $$H_0=69.2_{-0.59}^{+0.58}$$ , which may relieve the Hubble tension.

Wei Chao

Siyu Jiang

Yue Wang

United States

Zhu-Yao Wang

Ren-Peng Zhou

Yu-feng Zhou

Pseudo-Dirac sterile neutrino dark matter

In light of the recently discovered W-boson mass anomaly by the CDF Collaboration, we discuss two distinct mechanisms that could possibly explain this anomaly through the introduction of high-dimensional <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math> scalar multiplets. The first mechanism is the tree-level W-boson mass correction induced by the vacuum expectation values of one or more <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math> scalar multiplets with odd dimensions of <math><mi>n</mi><mo>≥</mo><mn>3</mn></math> and zero hypercharge of <math><mi>Y</mi><mo>=</mo><mn>0</mn></math> in order to avoid the strong constraint from measurements of the Z-boson mass. The second mechanism is to consider the one-loop level W-boson mass correction from a complex multiplet. In particular, we focus on the case with an additional scalar octuplet with <math><mi>Y</mi><mo>=</mo><mn>7</mn><mo>/</mo><mn>2</mn></math>. As a result, we find that both mechanisms can explain the W-boson mass anomaly without violating any other theoretical or experimental constraints.

Jiajun Wu

Chao-Qiang Geng

-boson Mass Anomaly From High-dimensional Scalar Multiplets

Motivated by the long-standing discrepancy between the Standard Model prediction and the experimental measurement of the muon magnetic dipole moment, we have recently proposed to interpret this muon  $$g-2$$  <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>   anomaly in terms of the loop effect induced by a new massive spin-2 field G. In the present paper, we investigate the unitarity bounds on this scenario. We calculate the s-wave projected amplitudes for two-body elastic scatterings of charged leptons and photons mediated by G at high energies for all possible initial and final helicity states. By imposing the condition of the perturbative unitarity, we obtain the analytic constraints on the charged-lepton-G and photon-G couplings. We then apply our results to constrain the parameter space relevant to the explanation of the muon  $$g-2$$  <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>   anomaly.

Unitarity bounds on the massive spin-2 particle explanation of muon  $$g-2$$  <math> <mrow> <mi>g</mi> <mo>-</mo> <mn>2</mn> </mrow> </math>   anomaly

It is widely believed that extensions of the minimal Higgs sector is one of the promising directions for resolving many puzzles beyond the Standard Model (SM). In this work, we study the unitarity bounds on the models by extending the two-Higgs-doublet model with an additional real or complex Higgs triplet scalar. By noting that the SM gauge symmetries SU(2) L  × U(1) Y  are recovered at high energies, we can classify the two-body scattering states by decomposing the direct product of two scalar multiplets into their direct sum of irreducible representations of electroweak gauge groups. In such state bases, the s-wave amplitudes of two-body scalar scatterings can be written in the form of block-diagonalized scattering matrices. Then the application of the perturbative unitarity conditions on the eigenvalues of scattering matrices leads to the analytic constraints on the model parameters. Finally, we numerically investigate the complex triplet scalar extension of the two-Higgs-doublet model, finding that the perturbative unitarity places useful stringent bounds on the model parameter space.

Bo-Qiang Lu

Unitarity bounds on extensions of Higgs sector

We explain the W-boson mass anomaly by introducing an   $S U(2)_L$   scalar multiplet with general isospin and hypercharge {in the case without its vacuum expectation value}. It is shown that the dominant contribution from the scalar multiplet to the W-boson mass arises at the one-loop level, which can be expressed in terms of the electroweak (EW) oblique parameters T and S at leading order. We first rederive the general formulae of T and S induced by a scalar multiplet of EW charges, confirming the results in literature. We then study several specific examples of great phenomenological interest by applying these general expressions. As a result, it is found that the model with a scalar multiplet in an   $S U(2)_L$   real representation with   $S U(2)_L$   cannot generate the required   $S U(2)_L$   correction because it leads to vanishing values of T and S. However, the cases with scalars in a complex representation under   $S U(2)_L$   with a general hypercharge can explain the   $S U(2)_L$   excess observed by CDF-II owing to nonzero T and S. We further consider the strong constraints from the perturbativity and EW global fit of the precision data and vary the isospin representation and hypercharge of the additional scalar multiplet to assess the extent of the model to solve the W-boson mass anomaly. It turns out that these constraints play important roles in setting limits on the model parameter space. We also briefly describe the collider signatures of the extra scalar multiplet, especially when it contains long-lived, heavy, highly charged states.

 -boson Mass Anomaly From a General (2) Scalar Multiplet  

We investigate the possibility to interpret the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly in terms of a massive spin-2 particle, <math><mi>G</mi></math>, which can be identified as the first Kaluza-Klein graviton in the generalized Randall-Sundrum model. In particular, we obtain the leading-order contributions to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> by calculating the relevant one-loop Feynman diagrams induced by <math><mi>G</mi></math>. The analytic expression is shown to keep the gauge invariance of the quantum electrodynamics and to be consistent with the expected UV divergence structure. Moreover, we impose the theoretical bounds from the perturbativity and the experimental constraints from LHC and LEP-II on our model. Especially, we derive novel perturbativity constraints on nonrenormalizable operators related to <math><mi>G</mi></math>, which are the natural generalization of the counterpart for the renormalizable operators. As a result, we show that there exists a substantial parameter space, which can accommodate the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly allowed by all constraints. Finally, we also make comments on the possible explanation of the electron <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomalies with the massive spin-2 particle.

Muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly from a massive spin-2 particle

We examine contributions to the muon dipole moment g − 2 from a 3-form field Ω, which naturally arises from many fundamental theories, such as the string theory and the hyperunified field theory. In particular, by calculating the one-loop Feynman diagram, we have obtained the leading-order Ω-induced contribution to the muon g − 2, which is found to be finite. Then we investigate the theoretical constraints from perturbativity and unitarity. Especially, the unitarity bounds are yielded by computing the tree-level μ + μ  −  scattering amplitudes of various initial and final helicity configurations. As a result, despite the strong unitarity bounds imposed on this model of Ω, we have still found a substantial parameter space which can accommodates the muon g − 2 data.

Yong Tang

Contributions to the muon g − 2 from a three-form field

We discuss two models that are part of a class providing a common explanation for lepton flavor universality violation in <math><mrow><mi>b</mi><mo>→</mo><mi>s</mi><msup><mrow><mi>l</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>l</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> decays, the dark matter (DM) problem and the muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) anomaly. The <math><mi>B</mi></math> meson decays and the muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) anomalies are explained by additional one-loop diagrams with DM candidates. The models have one extra fermion field and two extra scalar fields relative to the Standard Model. The <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> quantum numbers are fixed by the interaction with the Standard Model fermions in a new Yukawa Lagrangian that connects the dark and the visible sectors. We compare two models, one where the fermion is a singlet and the scalars are doublets under <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math> and another one where the fermion is a doublet and the scalars are singlets under <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math>. We conclude that both models can explain all of the previously mentioned issues simultaneously, while satisfying all other flavor and DM constraints. However, there are crucial differences between how the DM constraints affect the two models leading to a noticeable difference in the allowed DM mass range.

Portugal

Rodrigo Capucha

Tomás Lopes

Rui Santos

Impact of electroweak group representation in models for <math><mi>B</mi></math> and <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomalies from dark loops

Although searches for dark matter have lasted for decades, no convincing signal has been found without ambiguity in underground detections, cosmic ray observations, and collider experiments. We show by example that gravitational wave (GW) observations can be a supplement to dark matter detections if the production of dark matter follows a strong first-order cosmological phase transition. We explore this possibility in a complex singlet extension of the standard model with CP symmetry. We demonstrate three benchmarks in which the GW signals from the first-order phase transition are loud enough for future space-based GW observations, for example, BBO, U-DECIGO, LISA, Taiji, and TianQin. While satisfying the constraints from the XENON1T experiment and the Fermi-LAT gamma-ray observations, the dark matter candidate with its mass around ∼1 TeV in these scenarios has a correct relic abundance obtained by the Planck observations of the cosmic microwave background radiation.