Nuclear Physics B最新文献

{"title":"Thermodynamic topology of black hole in Massive gravity with generalized Barrow modification of entropy","authors":"Tehreem Aslam ,&nbsp;Muhammad Yasir ,&nbsp;Shahid Qaisar ,&nbsp;Faisal Javed ,&nbsp;Bander Almutairi","doi":"10.1016/j.nuclphysb.2025.116985","DOIUrl":"10.1016/j.nuclphysb.2025.116985","url":null,"abstract":"<div><div>The goal of our work is to explore the topology classifications of black holes in Massive gravity. We use Duan's <em>ϕ</em>-mapping theory to study the topology classes. This tool helps us to compute the integer numbers to characterize the topological features of the black hole. Our analysis is carried out across two different thermodynamic ensembles. These statistical ensembles are the canonical ensemble and the mixed canonical ensemble. Every ensemble corresponds to a different thermodynamic condition, allowing us to investigate how the black holes respond to other physical conditions. Thus, employing these analytical techniques, it is expected that further insights into topological and thermodynamic aspects of black holes in these modified gravity frameworks can be explored. This work helps to shed light on black hole dependencies on gravitational theories and conditions in thermal processes and thus expands the knowledge, proposing a new essence of black holes.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116985"},"PeriodicalIF":2.5,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatially flat FLRW spacetimes with a Big Bang from matrix geometry","authors":"Christian Gaß,&nbsp;Harold C. Steinacker","doi":"10.1016/j.nuclphysb.2025.116988","DOIUrl":"10.1016/j.nuclphysb.2025.116988","url":null,"abstract":"<div><div>We present an expanding, spatially flat (<span><math><mi>k</mi><mo>=</mo><mn>0</mn></math></span>) FLRW quantum spacetime with a Big Bang, considered as a background in Yang-Mills matrix models. The FLRW geometry emerges in the semi-classical limit as a projection from the fuzzy hyperboloid. We analyze the propagation of scalar fields, and demonstrate that their Feynman propagator resembles the Minkowski space Feynman propagator in the semi-classical regime. Moreover, the higher spin modes predicted by the matrix model are described explicitly. These results are compared to recent results on <span><math><mi>k</mi><mo>=</mo><mo>−</mo><mn>1</mn></math></span> FLRW quantum spacetimes with a Big Bounce.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116988"},"PeriodicalIF":2.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unitarity constrains the quantum information metrics for particle interactions","authors":"Shanmuka Shivashankara,&nbsp;Hobbes Sprague","doi":"10.1016/j.nuclphysb.2025.116989","DOIUrl":"10.1016/j.nuclphysb.2025.116989","url":null,"abstract":"<div><div>Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of measurement. For the first time, the language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. We show that unitarity allows for finding the latter's cross section without using the scattering amplitude or the Lippmann-Schwinger equation plus Green's function. We also show the language of relativistic quantum mechanics can be used to derive the momentum entropy or Sackur-Tetrode equation for the inelastic scattering of an electron from a proton. The latter entropy derives from a Shannon entropy and an additional entropy that evokes the uncertainty principle. This article's presentation allows particle physicists to readily begin calculating quantum information metrics such as correlations and mutual information for any particle interaction.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116989"},"PeriodicalIF":2.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144365054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anisotropic compact stars in quadratic f(R) gravity and influence of quadratic parameter on properties of compact stars","authors":"Rajesh Kumar ,&nbsp;S.K. Maurya ,&nbsp;Y. Sekhmani ,&nbsp;Akram Ali ,&nbsp;Farruh Atamurotov","doi":"10.1016/j.nuclphysb.2025.116984","DOIUrl":"10.1016/j.nuclphysb.2025.116984","url":null,"abstract":"<div><div>In this article, we explore an anisotropic model to describe the Buchdahl compact star with a spherically symmetric matter distribution within the framework of modified <span><math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> gravity. To achieve this, we consider the Starobinsky model <span><math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>α</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <em>α</em> is a model parameter. To solve the Einstein Field equations, we adopt the embedded class-I geometry that satisfies the Karmarkar condition. Our analysis includes the generalized Darmois-Israel junction conditions, which are crucial for seamlessly matching the star's interior to the Schwarzschild exterior metric at the boundary in <span><math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> gravity. These conditions have been employed to calculate the constant parameters by analyzing observational data from multiple compact stars, including <em>Cen X-3, PSR J1903+327, Vela X-1</em>, and <em>PSR J1614-2230</em>. This novel approach enables us to conduct a detailed analysis of Buchdahl compact star models and assess their physical viability. We also perform various physical tests, including equilibrium conditions and stability to evaluate the models' validity. The analysis of mass and radius reveals that the <span><math><mi>M</mi><mo>−</mo><mi>R</mi></math></span> relationship is based on the Buchdahl limit and is sensitive to variations in the parameter <em>α</em>. With <span><math><mi>α</mi><mo>=</mo><mn>0</mn></math></span> representing General Relativity, the maximum mass and radius for different <em>α</em> values were calculated and compared with observational data from the five aforementioned neutron stars. The range of maximum mass and radii are: <span><math><mo>[</mo><mn>2.51</mn><mo>−</mo><mn>2.54</mn><mspace></mspace><msub><mrow><mi>M</mi></mrow><mrow><mo>⊙</mo></mrow></msub><mo>]</mo></math></span> and <span><math><mn>8.71</mn><mo>−</mo><mn>9.33</mn><mspace></mspace><mtext>km</mtext></math></span>. The obtained values of radii align well with observed neutron star radii in X-ray binaries from spectroscopic studies, confirming the validity of the model.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116984"},"PeriodicalIF":2.5,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The minimal cosmological standard model","authors":"Gabriela Barenboim ,&nbsp;Pyungwon Ko ,&nbsp;Wan-Il Park","doi":"10.1016/j.nuclphysb.2025.116983","DOIUrl":"10.1016/j.nuclphysb.2025.116983","url":null,"abstract":"<div><div>We propose a novel minimal scenario which simultaneously addresses the following theoretical/cosmological/phenomenological puzzles: (i) the origin of scales, (ii) primordial inflation, (iii) matter-antimatter asymmetry, (iv) tiny neutrino masses, (v) dark matter, and (vi) the strong CP-problem. Exact scale-symmetry was assumed. A global <span><math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>PQ</mi></mrow></msub></math></span>-symmetry was also assumed but only in the matter sector. The novelty of the scenario is the introduction of explicit <span><math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>PQ</mi></mrow></msub></math></span>-breaking terms with field-dependent coefficients in the gravity sector. Such a term does not disturb the axion solution whereas naturally realizes an axi-majoron hybrid inflation which allows a natural realization of Affleck-Dine mechanism for generating Peccei-Quinn number asymmetry. The asymmetry can be transferred to the visible sector via the right-handed neutrino portal through non-thermal decay and thermal processes, even without the presence of a CP-violating phase in the matter sector. Dark matter and dark radiation are obtained by cold and hot components of axi-majorons, respectively.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116983"},"PeriodicalIF":2.5,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Probing Starobinsky-Bel-Robinson gravity: Gravitational lensing, thermodynamics, and orbital dynamics","authors":"Erdem Sucu,&nbsp;İzzet Sakallı","doi":"10.1016/j.nuclphysb.2025.116982","DOIUrl":"10.1016/j.nuclphysb.2025.116982","url":null,"abstract":"<div><div>This paper investigates the implications of Starobinsky-Bel-Robinson (SBR) gravity on gravitational lensing and geodesic dynamics around black holes. By incorporating higher-order curvature corrections through the Bel-Robinson tensor, we derive a modified spherically symmetric metric with a dimensionless coupling parameter <em>β</em> that significantly alters black hole properties. Applying the Gauss-Bonnet theorem, we calculate the weak deflection angle of light in both vacuum and plasma environments, demonstrating that increasing <em>β</em> enhances the bending of light, particularly in high-curvature regions. Our analysis reveals frequency-dependent effects in plasma media that could provide observational signatures distinguishing SBR gravity from general relativity. Additionally, we examine the stability of geodesic orbits using Lyapunov exponents and explore the concept of effective surface gravity through inaffinity analysis, showing how higher-curvature terms influence the behavior of particle trajectories near black holes. We also derive modified expressions for Hawking temperature, revealing how quantum corrections in SBR gravity affect black hole thermodynamics.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116982"},"PeriodicalIF":2.5,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"D-brane and exponential potentials inspire warm inflation and swampland conjecture","authors":"Shama Sadiq ,&nbsp;Nadeem Azhar ,&nbsp;N. Myrzakulov ,&nbsp;S. Toktarbay ,&nbsp;A. Muratkhan ,&nbsp;Sanjar Shaymatov ,&nbsp;Abdul Jawad","doi":"10.1016/j.nuclphysb.2025.116981","DOIUrl":"10.1016/j.nuclphysb.2025.116981","url":null,"abstract":"<div><div>This research explores the rapid expansion period of the early universe by applying the Chaplygin gas model, an alternative cosmological framework, to analyze the dynamics of inflationary processes. This study assesses the compatibility of three widely studied scalar field potentials with the latest observational constraints derived from the Planck datasets. Our analysis includes inflationary parameters such as slow-roll parameters, scalar power spectrum <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>, scalar spectral index <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, dissipative ratio <em>R</em>, tensor-to-scalar ratio <em>r</em> and running of the scalar spectral index <span><math><mfrac><mrow><mi>d</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mi>d</mi><mi>ln</mi><mo>⁡</mo><mi>k</mi></mrow></mfrac></math></span>, within the theoretical frameworks of canonical scalar field dynamics and the Chaplygin gas cosmological model. These parameters help to paint a comprehensive picture of the inflationary epoch and its impact on the observable Universe. We also address the generalized ratio of the swampland de-Sitter conjecture through the expression of <span><math><mfrac><mrow><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>V</mi></mrow><mrow><msup><mrow><mi>V</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>T</mi></mrow></mfrac></math></span> for three different potentials. We analyze inflation driven by a scalar field <em>ϕ</em> with decay rate <span><math><mi>Γ</mi><mo>(</mo><mi>ϕ</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mfrac><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>a</mi></mrow></msup></mrow><mrow><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>a</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac></math></span>, where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></math></span> is a dimensionless coupling and <em>a</em> controls dissipation strength. Working in the strong dissipative regime (<span><math><mi>R</mi><mo>≫</mo><mn>1</mn></math></span>), we systematically investigate the background evolution and perturbation spectrum, deriving inflationary observables.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116981"},"PeriodicalIF":2.5,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cosmological constant from canonical transformation in quantum cosmology","authors":"Andronikos Paliathanasis","doi":"10.1016/j.nuclphysb.2025.116980","DOIUrl":"10.1016/j.nuclphysb.2025.116980","url":null,"abstract":"<div><div>We explore the introduction of the cosmological constant via canonical transformations in cosmology. We consider the Wheeler-DeWitt equation for the cold dark matter (CDM) universe and we construct the Hamilton-Jacobi action for the ΛCDM model, where Λ is the cosmological constant. We discuss how this approach allows us to relate different physical systems, providing insights into the role of the cosmological constant in cosmology. More precisely the de Sitter universe emerges from the vacuum solution of the spatially flat Friedmann–Lemaître–Robertson–Walker geometry under the application of canonical transformations within quantum cosmology.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116980"},"PeriodicalIF":2.5,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bulk reconstruction for anti-symmetric and symmetric gauge fields: p-forms and the graviton","authors":"Budhaditya Bhattacharjee,&nbsp;Jyotirmoy Mukherjee","doi":"10.1016/j.nuclphysb.2025.116979","DOIUrl":"10.1016/j.nuclphysb.2025.116979","url":null,"abstract":"<div><div>We consider the HKLL bulk reconstruction procedure for <em>p</em>-form fields and graviton in empty AdS<span><math><msub><mrow></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>. We derive spacelike bulk reconstruction kernels for the <em>p</em>-forms and the graviton in the Poincaré patch of <span><math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>. The kernels are first derived via a mode-sum approach in arbitrary even dimensions. The appropriate AdS-covariant fields are identified and corresponding kernels obtained via the mode sum approach for these fields. We present arguments for casting these kernels in terms of the AdS chordal distance. Introducing an antipodal-like mapping, the kernels are cast in a spacelike form. An alternative derivation is presented for these kernels, by using a chordal Green's function approach. From the asymptotic expansion of the bulk fields and using Green's theorem, we determine the spacelike kernels for both modes of <em>p</em>-forms and the graviton, which are shown to agree with the kernels obtained by the mode-sum approach. The massive <em>p</em>-form fields, as well as the relevant Brietenlohner-Freedman bounds are also discussed.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116979"},"PeriodicalIF":2.5,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dispersive determination of neutrino mass ordering","authors":"Hsiang-nan Li","doi":"10.1016/j.nuclphysb.2025.116978","DOIUrl":"10.1016/j.nuclphysb.2025.116978","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We argue that the mixing phenomenon of a neutral meson formed by a fictitious massive quark will disappear, if the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale. This disappearance is taken as the high-energy input for the dispersion relation, which must be obeyed by the width difference between two meson mass eigenstates. The solution to the dispersion relation at low energy, i.e., in the symmetry broken phase, then connects the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements to the quark masses involved in the box diagrams responsible for meson mixing. It is demonstrated via the analysis of the &lt;em&gt;D&lt;/em&gt; meson mixing that the typical &lt;em&gt;d&lt;/em&gt;, &lt;em&gt;s&lt;/em&gt; and &lt;em&gt;b&lt;/em&gt; quark masses demand the CKM matrix elements in agreement with measured values. In particular, the known numerical relation &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/span&gt; with the &lt;em&gt;s&lt;/em&gt; (&lt;em&gt;b&lt;/em&gt;) quark mass &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) can be derived analytically from our solution. Next we apply the same formalism to the mixing of the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; states through similar box diagrams with intermediate neutrino channels. It is shown that the neutrino masses in the normal hierarchy (NH), instead of in the inverted hierarchy or quasi-degenerate spectrum, match the observed Pontecorvo-Maki-Nakagawa-Sakata matrix elements. The lepton mixing angles larger than the quark ones are explained by means of the inequality &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;≫&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; being the neutrino masses in the NH. At last, the solution for the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; mixing specifies the mixing ang","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1018 ","pages":"Article 116978"},"PeriodicalIF":2.5,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}