In the Cachazo-He-Yuan (CHY) representation, many tree-level scattering amplitudes are written as integrals localized by the scattering equations, where the CHY integrand encodes the theory and must reproduce the physical factorization pattern of Mandelstam singularities. The inverse CHY problem therefore asks for a rational integrand whose physical poles match a prescribed set of factorization channels, a task that becomes rapidly combinatorial at higher multiplicity. We present an algorithmic approach that makes the subset structure of pole data explicit by assigning each particle subset <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> a generalized pole degree <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow></math>, realized as a signed internal-edge count in a colored integrand graph. Additivity under integrand multiplication and an elementary face recursion on the subset lattice imply that all higher-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></math> are linear functions of the two-particle integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">{</mo><mi>K</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">}</mo></math>, so the inverse step becomes a mixed-integer linear feasibility problem. The same subset lattice provides a fixed computation graph for exact constraint satisfaction: pole requirements and recursion identities are treated as hard constraints, updates are restricted to those that preserve feasibility, and whenever a proposed change would enter a fixed node its constraint residual is rerouted and redistributed through unfixed degrees of freedom so that all constraints remain satisfied throughout. After a factorial rescaling, every local propagation update is purely integral, keeping the entire procedure exact in integer arithmetic and avoiding a posteriori reconstruction from numerical evaluations. Since physical tree-level amplitudes must contain only simple factorization poles as dictated by unitarity and locality, we further organize generalized integrands by an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-regular grading under multiplication, where degree-zero factors act as Möbius-invariant insertions admitting a decomposition into products of four-point cross ratios, which guides efficient higher-order pole reduction. We illustrate the construction at six and eight points, including pole selection and higher-order pole reduction.

China

Simeng Li

Yaobo Zhang

Inverse Cachazo-He-Yuan integrand construction from factorization channels with exact integer constraint propagation

We point out that relic neutrinos from the Big Bang may induce the parametric fluorescence in atomic or molecular systems, which offers a novel way to discover cosmic neutrino background. By coherently scattering with molecular energy levels, a massive neutrino can spontaneously “decay” into a lighter neutrino and an infrared signal photon; i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mi>M</mi><mo stretchy="false">→</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow></msub><mo>+</mo><mi>M</mi></mrow></math>, where the molecular state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>M</mi></mrow></math> remains unchanged after the scattering. Because the amplitudes of different radiants are matched in phase, the rate is coherently enhanced and proportional to the squared density of ambient dipoles. When the energy transfer from neutrinos coincides with the energy-level difference, the fluorescence will be on resonance. Near the resonance, the rate is proportional to the square of the coherence time <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub></mrow></math> of the ensemble. For a nominal target volume of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>), the signal rate can reach <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>yr</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>ns</mi></mrow></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mrow><mi mathvariant="normal">μ</mi><mi mathvariant="normal">s</mi></mrow></mrow></math>). This event rate appears to be very promising in consideration of an even longer coherence time that is achievable in solid systems.

Guo-yuan Huang

Shun Zhou

Probing the Cosmic Neutrino Background through Parametric Fluorescence

In this work, we investigate the resonance structures in the $ \Sigma(1/2^-) $ system from both three-quark and five-quark perspectives within the framework of the chiral quark model. An accurate few-body computational approach, the Gaussian expansion method, is employed to construct the orbital wave functions of multiquark states. To reduce the model dependence on parameters, we fit two sets of parameters to check the stability of the results. The calculations show that our results remain stable despite changes in the parameters. In the three-quark calculations, two $ \Sigma(1/2^-) $ states are obtained with energies around 1.8 GeV, which are good candidates for the experimentally observed $ \Sigma(1750) $ and $ \Sigma(1900) $ . In the five-quark configuration, several stable resonance states are identified, including $ \Sigma \pi $ , $ N \bar{K} $ , and $ N \bar{K}^{*} $ . These resonance states survive the channel-coupling calculations under the complex-scaling framework and manifest as stable structures. Our results support the existence of a two-pole structure for the $ \Sigma(1/2^-) $ system, predominantly composed of $ \Sigma \pi $ and $ N \bar{K} $ configurations, analogous to the well-known $ \Lambda(1380) $ - $ \Lambda(1405) $ ( $ \Sigma \pi $ - $ N \bar{K} $ ) system. On the other hand, although the energy of the $ N \bar{K}^{*} $ configuration is close to that of $ \Sigma(1750) $ and $ \Sigma(1900) $ , the obtained width is not consistent with the experimental values. This suggests that the $ N \bar{K}^{*} $ state needs to mix with three-quark components to better explain the experimental $ \Sigma(1750) $ and $ \Sigma(1900) $ states. According to our decay width calculations, the predicted two resonance states are primarily composed of $ \Sigma \pi $ and $ N \bar{K} $ , with their main decay channel being $ \Lambda \pi $ . Therefore, we encourage experimental groups to search for the predicted two-pole structure of the $ \Sigma(1/2^-) $ system in the invariant mass spectrum of $ \Lambda \pi $ .

Yu Yao

Xuejie Liu

Xiaoyun Chen

Yuheng Wu

Jialun Ping

Yue Tan

Qi Huang

Investigation of resonances in the Σ(1/2$^{–}$) system based on the chiral quark model * Supported partly by the National Science Foundation of China (12205249, 12305087). Yue Tan is supported by the Funding for School-Level Research Projects of Yancheng Institute of Technology (xjr2022039) and the Qinglan Project Fund of Jiangsu Province. Qi Huang is supported by the Start-up Funds of Nanjing Normal University (184080H201B20)

It has been claimed that the coherent scattering of relic neutrinos with the Earth will result in a neutrino-antineutrino asymmetry of $$ \mathcal{O} $$ (10 ) on the Earth surface, which is five orders of magnitude larger than the naive model expectation. In this work we show that this overdensity was overestimated for the perfectly round Earth by solving the exact solution with partial waves. After summing over all the angular modes, the maximal asymmetry is only around 10 above the ground. To achieve the proposed asymmetry of $$ \mathcal{O} $$ (10 ), a special geography may be needed as the experimental site. The code for a fast evaluation of Bessel functions with large orders through asymptotic expansions has been attached along with this work as supplementary material.

Germany

Neutrino-antineutrino asymmetry of C$\textit{ν}$B on the surface of the round Earth

We infer the ultrahigh energy neutrino source by using the Glashow resonance candidate event recently identified by the IceCube Observatory. For the calculation of the cross section for the Glashow resonance, we incorporate both the atomic Doppler broadening effect and initial state radiation <math> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>e</mi> </msub> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>→</mo> <msup> <mi>W</mi> <mo>−</mo> </msup> <mi>γ</mi> </math> $$ {\overline{\nu}}_e{e}^{-}\to {W}^{-}\gamma $$ , which correct the original cross section considerably. Using available experimental information, we have set a generic constraint on the <math> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>e</mi> </msub> </math> $$ {\overline{\nu}}_e $$ fraction of astrophysical neutrinos, which excludes the μ-damped pγ source around 2σ confidence level under the assumption that neutrino production is dominated by the ∆-resonance. While a weak preference has been found for the pp source, next-generation measurements will be able to distinguish between ideal pp and pγ sources with a high significance assuming an optimistic single power-law neutrino spectrum. The inclusion of multi-pion production at very high energies for the neutrino source can weaken the discrimination power. In this case additional multimessenger information is needed to distinguish between pp and pγ sources.

Manfred Lindner

Nele Volmer

Inferring astrophysical neutrino sources from the Glashow resonance

We explore beta decays in a dark background field, which could be formed by dark matter, dark energy or a fifth force potential. In such scenarios, the neutrino's dispersion relation will be modified by its collective interaction with the dark field, which can have interesting consequences in experiments using tritium beta decays to determine the absolute neutrino mass. Among the most general interaction forms, the (pseudo)scalar and (axial-)vector ones are found to have interesting effects on the spectrum of beta decays. In particular, the vector and axial-vector potentials can induce distinct signatures by shifting the overall electron energy scale, possibly beyond the usually defined endpoint. The scalar and pseudoscalar potentials are able to mimic a neutrino mass beyond the cosmological bounds. We have placed stringent constraints on the dark potentials based on the available experimental data of KATRIN. The sensitivity of future KATRIN runs is also discussed.

Werner Rodejohann

Tritium beta decay with modified neutrino dispersion relations: KATRIN in the dark sea

The question of how heavy a sterile neutrino can be probed in experiments leads us to investigate the Primakoff production of heavy sterile neutrinos from ultrahigh-energy neutrinos via the magnetic dipole portal. Despite the suppression from the small magnetic moment, the transition is significantly enhanced by tiny t-channel momentum transfers, similar to the resonant production of pions and axions in an external electromagnetic field. Based on the current IceCube measurement of astrophysical neutrinos up to PeV energies, strong constraints can already be derived on the transition magnetic moments of sterile neutrinos up to TeV masses. Moreover, we investigate the sensitivity of future tau neutrino telescopes, which are designed for EeV cosmogenic neutrino detection. We find that sterile neutrino masses as large as <math><mn>30</mn><mspace width="0.25em"></mspace><mtext>TeV</mtext></math> can be probed at tau neutrino telescopes such as GRAND, POEMMA, and Trinity.

Sudip Jana

Probing heavy sterile neutrinos at neutrino telescopes via the dipole portal

In light of the exciting campaign of cosmogenic neutrino detection, we investigate the double and multiple tau bangs detectable at future tau neutrino telescopes. Such events are expected from the Standard Model (SM) higher-order processes, which can be easily identified with broad techniques anticipated at future tau neutrino telescopes. We find that SM perturbative processes can already contribute observable double-bang events to telescopes with a sensitivity of collecting $${\mathcal {O}}(100)$$ <math> <mrow> <mi>O</mi> <mo>(</mo> <mn>100</mn> <mo>)</mo> </mrow> </math> cosmogenic neutrino events. The detectable but suppressed rate in fact makes the double and multiple bangs an excellent probe of SM unknowns and possible new physics beyond. As a case study, the nonperturbative sphaleron process, which can copiously produce multiple tau bangs, is explored.

Double and multiple bangs at tau neutrino telescopes

Whether the neutrino mass ordering is normal or inverted remains an experimentally open issue in neutrino physics. The knowledge of neutrino mass ordering has great importance for neutrinoless double-beta ( $$ 0\nu \beta \beta $$ <math> <mrow> <mn>0</mn> <mi>ν</mi> <mi>β</mi> <mi>β</mi> </mrow> </math> ) decay experiments, which can establish the nature of massive neutrinos, i.e., whether they are Dirac or Majorana fermions. Recently, the KamLAND-Zen 800 measurement has reached for the first time the parameter space of the inverted ordering with a vanishing lightest neutrino mass. By assuming the inverted ordering, we attempt to derive the physical information of the neutrino nature and Majorana CP phases from a negative or positive observation of $$ 0\nu \beta \beta $$ <math> <mrow> <mn>0</mn> <mi>ν</mi> <mi>β</mi> <mi>β</mi> </mrow> </math> decays in the near future. Moreover, the possibility of extracting the nuclear matrix element in the case of a positive observation is also examined.To avoid the ambiguity from unknown priors of neutrino masses, we adopt the maximum likelihood method instead of the Bayesian approach usually considered in previous works.

Italy

Newton Nath

Inference of neutrino nature and Majorana CP phases from $$\mathbf{0}{\nu \beta \beta }$$ <math> <mrow> <mn>0</mn> <mrow> <mi>ν</mi> <mi>β</mi> <mi>β</mi> </mrow> </mrow> </math> decays with inverted mass ordering

We investigate a consistent scenario of time-varying neutrino masses, and discuss its impact on cosmology, beta decay, and neutrino oscillation experiments. Such time-varying masses are assumed to be generated by the coupling between a sterile neutrino and an ultralight scalar field, which in turn affects the light neutrinos by mixing. We demonstrate how various cosmological bounds, such as those coming from big bang nucleosynthesis, the cosmic microwave background, as well as large scale structures, can be evaded in this model. This scenario can be further constrained using multiple terrestrial experiments. In particular, for beta-decay experiments like KATRIN, nontrivial distortions to the electron spectrum can be induced, even when time-variation is fast and it gets averaged. Furthermore, the presence of time-varying masses of sterile neutrinos will alter the interpretation of light sterile neutrino parameter space in the context of the reactor and gallium anomalies. In addition, we also study the impact of such time-varying neutrino masses on results from the BEST collaboration, which have recently strengthened the gallium anomaly. If confirmed, we find that the time-varying neutrino mass hypothesis could give a better fit to the recent BEST data.