We study in QCD the <math altimg='si10.svg'><mover><mrow><mtext>MS</mtext></mrow><mo stretchy='true'>&#8254;</mo></mover></math> renormalization of three-quark operators with up to two covariant derivatives, which are related to <math altimg='si11.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math> Mellin moments of baryonic light-cone distributions amplitudes. Apart from general three-quark operators, we also consider those corresponding to spin 3/2 and 1/2 states. We present in analytic form the renormalization constants and anomalous dimensions of these operators through three loops, confirming previous two- and three-loop results for <math altimg='si12.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Furthermore, we evaluate through two loops their amputated four-point Green&#8217;s functions with RI&#8242;/SMOM four-momentum assignment, which are required for the matching of lattice results with perturbative calculations. We work in linear covariant gauge and find the anomalous dimensions to be gauge independent as expected.

Germany

Bernd A. Kniehl

Oleg L. Veretin

Renormalization of three-quark operators with up to two derivatives at three loops

Tiny neutrino masses can be explained by the type-II seesaw mechanism, where a triplet scalar under <italic>SU</italic>(2) <inf><italic>L</italic></inf> is predicted. Collider searches for this exotic scalar have been extensively conducted, especially for its doubly charged component &#916; &#8239;&#177;&#8239;&#8239;&#177;&#8239;. Utilizing the forward detectors at the Large Hadron Collider (LHC), we study the probing sensitivity for the elastic photon fusion production of the scalars <math altimg='si44.svg'><mrow><mi>p</mi><mi>p</mi><mo>&#8594;</mo><mi>p</mi><mo>(</mo><mi>&#947;</mi><mi>&#947;</mi><mo>&#8594;</mo><msup><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mrow><mo>+</mo><mo>+</mo></mrow></msup><msup><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mrow><mo>&#8722;</mo><mo>&#8722;</mo></mrow></msup><mo>)</mo><mi>p</mi></mrow></math> followed by the lepton-flavor-violating (LFV) decay channels &#916; &#8239;&#177;&#8239;&#8239;&#177;&#8239;&#8239;&#8594;&#8239; <italic>e</italic> &#8239;&#177;&#8239; <italic>&#956;</italic> &#8239;&#177;&#8239;. With a high center-of-mass energy of 100 TeV and several luminosity scenarios, we can broaden the exclusion bounds in the parametric space of Br(&#916; &#8239;&#177;&#8239;&#8239;&#177;&#8239;&#8239;&#8594;&#8239; <italic>e</italic> &#8239;&#177;&#8239; <italic>&#956;</italic> &#8239;&#177;&#8239;) versus the triplet scalar mass <italic>m</italic> <inf>&#916;</inf>. Specifically, at the 100 TeV LHC with an integrated luminosity of 3 ab <math altimg='si4.svg'><msup><mrow /><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></math>, the mass exclusion limit at 95% C.L. based on the approximated significance formula can reach around 1150&#8239;GeV with the assumption of inverted neutrino mass hierarchy.

China

Hang Zhou

Ning Liu

Testing lepton-flavor-violating decay of doubly charged Higgs bosons in type-II seesaw via photon fusion at the high-energy LHC

We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an <math altimg='si16.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> SCFT in four dimensions. Up to date, this spin chain model remains unfathomable; the standard coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of particular subclasses of our solution, together with the position-dependent corrections, obey an infinite tower of modified Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the standard coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.

Deniz N Bozkurt

Juan Miguel Nieto García

Elli Pomoni

Long-range to the rescue of Yang-Baxter

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>The generalized <italic>n</italic>-component Sasa-Satsuma (GNSS) equation is systematically investigated within the framework of the Dbar-dressing method.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>The Lax pair, symmetry constraints of the spectral transformation matrix, and infinitely many conservation laws have been established.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>A hierarchy of GNSS equations with a source term is constructed via the recursion operator under a generalized temporal constraint.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>Multi-soliton solutions are derived in a compact form whose dynamics are illustrated graphically, highlighting the influence of parameters.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>The results provide a unified view of Sasa-Satsuma type equations and enhance understanding of multi-component nonlinear waves.</para></list-item></list>

Qi Chen

Tao Deng

Chunxia Li

Yuqin Yao

Integrable properties and soliton dynamics for the generalized <italic>n</italic>-component Sasa-Satsuma equation via the Dbar-dressing method

Black-hole thermodynamic topology assigns integer charges to equilibrium branches as zeros of an off-shell reservoir-mismatch one-form. We formulate this construction for a specified thermodynamic potential, active variables, fixed reservoir intensities and admissible compactified state space. The total charge is its Brouwer degree, equivalently the Morse degree of the potential and the oriented intersection number of the equation-of-state and reservoir Lagrangians. Regular Legendre changes of polarization preserve this degree after orientation transport; this covariance does not imply ensemble independence. We prove homotopy rigidity and boundary-jump formulae and relate auxiliary-angle windings, residues and gradient-flow representatives to the same degree. Standard Schwarzschild, Schwarzschild–AdS, fixed-charge RN–AdS, BTZ and logarithmically corrected examples follow from endpoint data. For grand-canonical RN–AdS and dyonic sectors, a positive-determinant desingularization of the coupled charge coordinates extends smoothly to zero size and identifies <math altimg='si13.svg'><mrow><mrow><mo stretchy='false'>|</mo></mrow><msub><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>0</mn></msub><mrow><mo>|</mo><mo>=</mo><mn>1</mn></mrow></mrow></math> and <math altimg='si42.svg'><mrow><msubsup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>e</mi><mn>2</mn></msubsup><mo linebreak='goodbreak'>+</mo><msubsup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>m</mi><mn>2</mn></msubsup><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> as boundary walls of the reservoir intersection problem, not local-stability walls or coordinate artifacts. A mixed dyonic window realizes the Poincar&#233;&#8211;Hopf count on the physical fluctuation plane. In Kerr&#8211;Newman&#8211;AdS, one reservoir supports a coupled size&#8211;spin saddle and a companion minimum. At the saddle both diagonal curvatures in the extensive ( <italic>S, J</italic>) variables are positive, whereas the Hessian determinant is negative. Thus the restricted radius index is <math altimg='si6.svg'><mrow><mo>+</mo><mn>1</mn></mrow></math> while the full fixed-potential Hessian index is <math altimg='si49.svg'><mrow><mo>&#8722;</mo><mn>1</mn></mrow></math>, exhibiting information accessible only on the multi-variable fluctuation space.

Ruiliang Li

Legendre-covariant thermodynamic topology of black holes

In this paper, we investigate the structural and analytic properties of the two-parameter telephone polynomials. Starting from the exponential generating function and the recurrence relation, we derive an explicit formula, an operational representation, and the raising and lowering operators of the family. We then examine its differential identities, a Rodrigues-type formula, several integral formulas, and its connections with some special polynomial families. For the Gaussian weight we obtain a closed form for the weighted inner product, together with a contour orthogonality relation on the imaginary axis. Finally, we investigate their zeros for some selected parameter values and present graphical illustrations of their distribution.

Kuwait

Bulgaria

Carlos M. da Fonseca

Türkiye

Can Kızılateş

Yasin Ünsal

On two-parameter telephone polynomials and their structural properties

We focus on the rogue waves and their predictions of the space shifted nonlocal Zakharov equation. By employing the Kadomtsev-Petviashvili (KP) hierarchy reduction method, the purely algebraic expressions of the general ( <italic>N</italic> <inf>1</inf>, <italic>N</italic> <inf>2</inf>, <italic>M</italic> <inf>1</inf>, <italic>M</italic> <inf>2</inf>)th rogue wave solutions are derived. Two distinct structures of the rogue waves are studied and simulated, including the line rogue waves and the rogue waves with spatiotemporal locality. The extreme lines and amplitudes of the line rogue waves are analyzed, the collapse locations of the spatiotemporally localized rogue waves are discussed. Line rogue waves only exist during specific time periods, while spatiotemporally localized rogue waves emerge with the value of <italic>x</italic> or <italic>y</italic> fixed. Patterns of the latter type of rogue waves can be predicted by the root structures of the Adler-Moser polynomials. Internal parameters <math altimg='si54.svg'><mrow><msub><mi>a</mi><mrow><mn>2</mn><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#954;</mi><mi>j</mi></msub><msup><mi>A</mi><mrow><mn>2</mn><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></math> and <math altimg='si55.svg'><mrow><msub><mi>b</mi><mrow><mn>2</mn><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#955;</mi><mi>j</mi></msub><msup><mi>B</mi><mrow><mn>2</mn><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow></math> respectively determine the middle and the outer structures of the rogue waves with <math altimg='si47.svg'><mrow><msup><mi>A</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mi>O</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></math>, which is the opposite of the case <math altimg='si51.svg'><mrow><msup><mi>B</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mi>O</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow></math>. In the inner region, the rogue waves possess three different structures according to whether zero is the root of two Adler-Moser polynomials <math altimg='si56.svg'><mrow><msubsup><mstyle mathvariant='normal'><mi>&#920;</mi></mstyle><mrow><msub><mi>&#948;</mi><mi>N</mi></msub></mrow><mrow><mo>[</mo><mi>&#954;</mi><mo>]</mo></mrow></msubsup><mrow><mo>(</mo><mi>&#950;</mi><mo>)</mo></mrow></mrow></math> or <math altimg='si57.svg'><mrow><msubsup><mstyle mathvariant='normal'><mi>&#920;</mi></mstyle><mrow><msub><mi>&#948;</mi><mi>M</mi></msub></mrow><mrow><mo>[</mo><mi>&#955;</mi><mo>]</mo></mrow></msubsup><mrow><mo>(</mo><mi>&#950;</mi><mo>)</mo></mrow></mrow></math>. The error analyses suggest the high accuracy of the predictions. It is worth pointing out that we have expanded the range of the relative magnitude of internal parameters in the predictions of rogue wave patterns and provided corresponding error estimates. These results can contribute to describing and predicting diverse rogue wave structures in nonlocal integrable systems.

Hai-Fang Song

Ji Lin

Bo Ren

Diverse rogue waves and their predictions in the space shifted nonlocal Zakharov equation

We present an exact analysis of black hole (BH) solutions in the two-dimensional (2D) dilaton gravity model with action <math altimg='si55.svg'><mrow><mi>I</mi><mo linebreak='goodbreak'>=</mo><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>/</mo><mn>2</mn><mi>G</mi><mo>)</mo></mrow><mo>&#8747;</mo><msup><mi>d</mi><mn>2</mn></msup><mi>x</mi><mspace width='0.16em' /><msqrt><mrow><mo>&#8722;</mo><mi>g</mi></mrow></msqrt><mspace width='0.16em' /><mrow><mo>(</mo><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='badbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup><mo>)</mo></mrow></mrow></math>. Identifying the dilaton as the radial coordinate, we obtain the metric function <math altimg='si1.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mrow><mo>(</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mo linebreak='badbreak'>/</mo><mn>3</mn><mo>)</mo></mrow><mspace width='0.16em' /><msup><mi>x</mi><mn>3</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><mn>2</mn><mi>G</mi><mi>M</mi></mrow></math> and derive closed-form expressions for the mass, Wald entropy, Hawking temperature, heat capacity, and Helmholtz free energy. For &#923;&#8239;&lt;&#8239;0 and <italic>M</italic>&#8239;&gt;&#8239;0 the solution admits a single non-degenerate horizon with <math altimg='si46.svg'><mrow><mi>C</mi><mo linebreak='goodbreak'>=</mo><mi>S</mi><mo linebreak='goodbreak'>/</mo><mn>2</mn><mo linebreak='goodbreak'>&gt;</mo><mn>0</mn></mrow></math>, globally negative free energy, and no phase transitions. A nonperturbative exponential entropy correction preserves stability for <italic>&#951;&#947;</italic>&#8239;&lt;&#8239;1 but triggers a temperature divergence and negative heat capacity for <italic>&#951;&#947;</italic>&#8239;&gt;&#8239;1. The topological analysis of the off-shell free-energy landscape yields a total topological charge <math altimg='si29.svg'><mrow><mi>W</mi><mo linebreak='goodbreak'>=</mo><mo>+</mo><mn>1</mn></mrow></math> in the classical regime, while strong corrections drive a transition to <math altimg='si56.svg'><mrow><mi>W</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, signaling an additional unstable branch. We derive the quasinormal mode (QNM) master equation for probe-scalar perturbations and compute the cavity spectrum, confirming the universal scaling |Im( <italic>&#969;</italic>)|&#8733; <italic>T</italic> and a quality factor <math altimg='si52.svg'><mrow><mi mathvariant='script'>Q</mi><mo>&#8776;</mo><mn>0.43</mn></mrow></math>&#8211;0.48. Because 2D dilaton gravity arises from the spherical reduction of four-dimensional Einstein&#8211;Maxwell theory and governs near-extremal BH throats, our results establish the <math altimg='si54.svg'><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='goodbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup></mrow></math> model as a transparent laboratory for exact BH thermodynamics, quantum corrections, topological classification, and dynamical response.

Iraq

Aram Bahroz Brzo

Peshwaz Abdulkareem Abdoul

Azerbaijan

Iran

Behnam Pourhassan

Saeed Noori Gashti

İzzet Sakallı

Exact black-hole solutions in <math altimg='si54.svg'><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mi>R</mi><mo linebreak='goodbreak'>&#8722;</mo><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup></mrow></math> dilaton gravity: Thermodynamics, stability, topology, and dynamical probes

Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static) spacetime. Apparently, this seems to enable the principles of GR and quantum mechanics (QM) to be reconciled into a coherent relativity and quantum theory. A canonical geometric quantization approach that presents kinematics of free-falling quantum particles within a tangent bundle, expands QM to incorporate relativistic gravitational fields, and generalizes the four-dimensional Riemann manifold into an eight-dimensional one likely discretizes, if not fully quantizes, the Finsler and Hamilton structures. The Finsler and Hamilton metrics can be directly derived from the Hessian matrix. As introduced in [Physics, 7 (2025) 52], the quantized four-dimensional metric tensor can be deduced by means of approximations including proper parameterization of coordinates and the equating line elements on all these manifolds including Riemann manifold. This research, on the contrary, goes beyond all these approximations and proposes the incorporation of a phase-space metric tensor into GR. The derivation of a quantized eight-dimensional metric tensor is not only presented, but also the implications of it and the corresponding relative spacetime are examined.

Egypt

Kareem Mubaidin

India

Debarshi Mukherjee

Saudi Arabia

Saleh O. Allehabi

Azzah A. Alshehri

Mahmoud Nasar

Ashraf F. El-Sherif

Abdel Nasser Tawfik

The derivation of phase-space metric in a geometric quantization approach: General relativity with quantized phase-space metric and relative spacetime

We examine the power-series method employed by Mustafa [Nucl. Phys. B 1006 (2024) 116629] to solve the radial Schrödinger-like equation associated with the Klein-Gordon oscillator in a Som-Raychaudhuri spacetime. We prove that the proposed truncation conditions for the three-term recurrence relation do not produce polynomial solutions but infinite series. The correct truncation conditions are presented and shown to differ from those reported in the original paper.

Argentina

Francisco M. Fernández

Comment on “KG- oscillators in Som-Raychaudhuri rotating cosmic string spacetime in a mixed magnetic field”