We present a background-independent renormalization framework for one-loop primordial spectra. We apply it to two observables: the scalar-induced tensor spectrum sourced by a minimally coupled spectator field, and the scalar spectrum generated by potential self-interactions. In both cases, the UV part of the loops is isolated and, using the universal WKB behavior of the internal modes, the UV poles are extracted analytically and absorbed into local counterterms without having to specify either the background evolution or the full dynamics of the field running in the loop. This yields finite model-independent expressions for the renormalized spectra amenable to numerical analysis.

Spain

Guillermo Ballesteros

Jesús Egea

Italy

Flavio Riccardi

Background-independent one-loop renormalization of tensor and scalar primordial spectra

This corrigendum corrects, in Ref. [2], the closed form of the massless branch, Eq. (22), the limiting statement following Eq. (27), the coefficients of Table 2 with the consequent changes to Tables 4 and 5, and the renormalization-scale bands of Table 6. The three-sector recursion, Eq. (19), the master ODE, Eq. (21), and the dressed Lambert- <italic>W</italic> representation, Eqs. (26) and (27), are unaffected: the coefficients generated by Eq. (19) satisfy Eq. (21) identically, and Eqs. (26) and (27) reproduce the Eq. (19) series to <math altimg='si30.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>30</mn></mrow></msup></math> for <math altimg='si20.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>&#8211;4 at all couplings tested, thereby confirming the corrected coefficients given in Table 1. All values were regenerated at 30-digit precision. A companion corrigendum to Ref. <cross-ref id='crf0010' refid='bib0001'>[1]</cross-ref> corrects the same boundary term there.

Canada

Farrukh A. Chishtie

Corrigendum to “Exact scheme-independent generating function for the massive <italic>O</italic>( <italic>N</italic>) <italic>&#981;</italic> 4 two-point function in scale-factorized quantum field theory&#8221; [Phys. Lett. B 880 (2026) 140835]

Multiple lattice evidences support the existence of a confining but chirally symmetric stringy fluid regime of QCD above the chiral symmetry restoration temperature at <italic>T<inf>ch</inf></italic>&#8239;&#8771;&#8239;155 MeV. This regime is characterized by an approximate chiral spin symmetry and its extensions which means that the propagating excitations represent the chirally symmetric quarks connected into color singlets by the chromoelectric string. Clear <italic>&#960;, &#960;</italic>&#8242; peaks above <italic>T<inf>ch</inf></italic> were extracted on the lattice from the spatial and temporal correlators, which become broader with temperature and disappear roughly at 3 <italic>T<inf>ch</inf></italic>. The meson-like excitations above <italic>T<inf>ch</inf></italic> were studied within the manifestly confining and chirally symmetric model. It has been demonstrated that the chiral symmetry restoration in the confining regime happens because of Pauli blocking of the levels, required for the existence of the quark condensate, by the thermal quark excitation. The same Pauli blocking leads to a huge swelling of the low-spin mesons above <italic>T<inf>ch</inf></italic> which become infinitely large in the chiral limit. This property should be crucial for the explanation of the high collectivity and a very small mean-free path of the constituents above <italic>T<inf>ch</inf></italic> seen experimentally. Here we demonstrate that the swelling of pions above <italic>T<inf>ch</inf></italic> is a model-independent effect required by current algebra.

Austria

L. Ya. Glozman

A large size of the pion-like excitations in the stringy fluid above <italic>T<inf>ch</inf></italic> is model independent and required by current algebra

Gravitational waves provide a unique probe of the strong-field regime of gravity, offering access to physics beyond the classical black hole paradigm. We explore how space-based observations of extreme-mass-ratio inspirals (EMRIs) by the Laser Interferometer Space Antenna (LISA) can be used to test for departures from the Kerr geometry, and in particular for the breaking of its axial and equatorial symmetries, as expected in quantum-gravity-inspired alternatives to Kerr black holes such as the fuzzball proposal. By introducing generic multipolar deformations encoding potential symmetry breakings and performing a systematic parameter estimation analysis, we forecast LISA’s ability to constrain such departures from the Kerr geometry in the strong-field regime. We show that EMRI signals with realistic signal-to-noise ratios can constrain several higher-order multipoles of the primary, opening a new observational window onto strong-field deviations from the Kerr geometry. In particular, we find that LISA can constrain generic nonaxisymmetric mass quadrupole deformations at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></math> level and axisymmetric mass octupole deformations at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mn>0</mn></msup></math> level, providing concrete observational targets for strong-field deviations from the Kerr geometry, such as those that may arise in fuzzball and other exotic-compact-object scenarios. Our results demonstrate that precision measurements of EMRI waveforms will transform LISA into a powerful laboratory for fundamental physics and offer precise constraints on quantum-gravity-motivated models of compact objects.

Pablo F. Muguruza

Carlos F. Sopuerta

Probing fuzzballs and beyond: Model-independent tests of Kerr symmetry breaking with LISA

We perform a model-independent investigation of the thermodynamic evolution of the Universe by reconstructing the expansion history from observational data using Gaussian Process regression. We consider three independent combinations of datasets, namely CC32+DESI DR2+Pantheon+, CC32+DESI DR2+Union3, and CC32+DESI DR2+DES Y5, allowing us to assess the impact of different supernova samples on the reconstruction. From the reconstructed Hubble parameter and its derivatives over the reconstructed redshift range, we evaluate key thermodynamic quantities associated with the apparent horizon, including the diagnostic function $\textit{P}$($\textit{z}$), the entropy production rate $${{\dot{S}}}_{\textrm{tot}}$$ , and its second derivative $${{\ddot{S}}}_{\textrm{tot}}$$ . Within the observationally reconstructed late-time redshift range, we find that $\textit{P}$($\textit{z}$) remains positive for all dataset combinations, supporting the validity of the generalized second law of thermodynamics. Correspondingly, $${{\dot{S}}}_{\textrm{tot}} > 0$$ throughout, while $${{\ddot{S}}}_{\textrm{tot}} < 0$$ at low redshifts, indicating that the Universe evolves toward stable thermodynamic equilibrium. To assess methodological robustness, the reconstruction is performed using multiple covariance kernels, including the Squared Exponential and Matérn kernels with $$\nu = 5/2, 7/2,$$ and 9/2, all of which yield consistent results within uncertainties. We also reconstruct the dark energy equation of state in a fully model-independent manner and find that the inferred preference for dynamical dark energy is sensitive to both the adopted supernova compilation and the GP kernel, ranging from consistency with $$\Lambda $$ CDM to a moderate ( $$\sim 2$$ – $$4\sigma $$ ) preference for evolving dark energy, with all reconstructions exhibiting a crossing of the $$w=-1$$ boundary at intermediate redshifts.

India

Afaq Maqsood

Tanima Duary

Model-independent reconstruction of cosmic thermodynamics and dark energy dynamics

We derive an exact, scheme-independent generating function <math altimg='si51.svg'><mrow><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math> for the massive <italic>O</italic>( <italic>N</italic>)-symmetric <italic>&#981;</italic> 4 two-point observable <math altimg='si52.svg'><mrow><msub><mi>R</mi><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle></msub><mrow><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>,</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo>&#8801;</mo><msup><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msup><mrow><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>,</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> within Scale-Factorized Quantum Field Theory (SF-QFT). Path-integral factorization at the physical matching scale <math altimg='si5.svg'><mrow><msup><mi>Q</mi><mo>*</mo></msup><mo linebreak='goodbreak'>=</mo><mi>m</mi></mrow></math>, followed by Seeley&#8211;DeWitt heat-kernel integration of the infrared modes, extracts five universal scheme-independent inputs: the two-loop <italic>&#946;</italic>-function coefficients <italic>&#946;</italic> <inf>0</inf>, <italic>&#946;</italic> <inf>1</inf>, the mass anomalous dimension coefficients <italic>d</italic> <inf>1</inf>, <italic>d</italic> <inf>2</inf>, and the two-loop field anomalous dimension coefficient <italic>e</italic> <inf>2</inf>, in the normalization of Refs. [1,2] with <math altimg='si6.svg'><mrow><mi>a</mi><mo>&#8801;</mo><mi>&#955;</mi><mo linebreak='goodbreak'>=</mo><mi>g</mi><mo linebreak='goodbreak'>/</mo><mo>(</mo><mn>2</mn><msup><mi>&#960;</mi><mn>2</mn></msup><mo>)</mo></mrow></math>. The observable <math altimg='si46.svg'><msub><mi>R</mi><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle></msub></math> carries its own renormalization-group anomalous dimension <math altimg='si53.svg'><mrow><msub><mi>&#947;</mi><msub><mi>R</mi><mstyle mathvariant='normal'><mi>&#915;</mi></mstyle></msub></msub><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>&#945;</mi><mn>1</mn></msub><mi>a</mi><mo linebreak='goodbreak'>+</mo><msub><mi>&#945;</mi><mn>2</mn></msub><msup><mi>a</mi><mn>2</mn></msup><mo linebreak='goodbreak'>+</mo><mo>&#8943;</mo></mrow></math>, with <math altimg='si54.svg'><mrow><msub><mi>&#945;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>d</mi><mn>1</mn></msub></mrow></math> and <math altimg='si55.svg'><mrow><msub><mi>&#945;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>d</mi><mn>2</mn></msub><mo linebreak='goodbreak'>+</mo><mn>2</mn><msub><mi>e</mi><mn>2</mn></msub></mrow></math>; the factor of two on <italic>e</italic> <inf>2</inf> is the two-leg field renormalization of the two-point function. The Principle of Observable Effective Matching (POEM) at <math altimg='si5.svg'><mrow><msup><mi>Q</mi><mo>*</mo></msup><mo linebreak='goodbreak'>=</mo><mi>m</mi></mrow></math> fixes the boundary data <math altimg='si56.svg'><mrow><msub><mi>f</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#945;</mi><mn>1</mn></msub></mrow></math> and <math altimg='si57.svg'><mrow><msub><mi>f</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#945;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math> and yields a universal three-sector Effective Dynamical Renormalization (EDR) recursion whose coefficients <italic>f</italic> <inf><italic>n</italic>,0</inf> define <math altimg='si31.svg'><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub></math> exactly and converge geometrically with ratio &#8239;&#8764;&#8239;0.003 to 0.01. Summing the recursion gives the master ordinary differential equation (ODE) <math altimg='si58.svg'><mrow><msubsup><mi mathvariant='script'>G</mi><mn>0</mn><mo>&#8242;</mo></msubsup><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><mi>k</mi><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>&#945;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>+</mo><mrow><mo>[</mo><msub><mi>&#945;</mi><mn>2</mn></msub><mo linebreak='badbreak'>&#8722;</mo><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>+</mo><mi>k</mi><mo>)</mo></mrow><msubsup><mi>&#945;</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup><mo>]</mo></mrow><mi>z</mi><mo linebreak='goodbreak'>+</mo><mrow><mo>(</mo><msub><mi>&#945;</mi><mn>1</mn></msub><mo linebreak='badbreak'>+</mo><msub><mi>&#945;</mi><mn>2</mn></msub><mi>z</mi><mo>)</mo></mrow><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub></mrow></math>, with <math altimg='si18.svg'><mrow><mi>k</mi><mo>&#8801;</mo><msub><mi>&#946;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>&#8722;</mo><msub><mi>&#946;</mi><mn>0</mn></msub></mrow></math>, whose two branches are distinguished by whether the anomalous-dimension feedback is active: the massless branch ( <math altimg='si30.svg'><mrow><msub><mi>&#945;</mi><mi>i</mi></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>) integrates to the square-root <italic>F</italic> <inf>0</inf> of Ref. [3], while the massive branch is an Abel equation of the second kind that admits no elementary closed form, the obstruction being controlled by <italic>&#945;</italic> <inf>1</inf> through <math altimg='si59.svg'><mrow><mi>d</mi><mi mathvariant='script'>S</mi><mo linebreak='goodbreak'>/</mo><mi>d</mi><mi>z</mi><mo linebreak='goodbreak'>=</mo><msub><mi>&#945;</mi><mn>1</mn></msub><mi>c</mi><mo linebreak='goodbreak'>/</mo><msup><mi>&#981;</mi><mrow><mo>&#8242;</mo><mn>2</mn></mrow></msup></mrow></math> with <math altimg='si60.svg'><mrow><mi>c</mi><mo linebreak='goodbreak'>=</mo><mi>k</mi><mrow><mo>(</mo><mi>k</mi><mo linebreak='badbreak'>+</mo><mn>1</mn><mo>)</mo></mrow><msubsup><mi>&#945;</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup></mrow></math> and a non-constant Chini invariant. The Lambert- <italic>W</italic> structure nonetheless survives in renormalized form, <math altimg='si61.svg'><mrow><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>1</mn><mo linebreak='goodbreak'>+</mo><msup><mi>&#956;</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><msub><mi>W</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>&#956;</mi><mspace width='0.16em' /><msup><mi>e</mi><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mo>(</mo><mi>z</mi><mo>)</mo></mrow></msup><mo>)</mo></mrow></mrow></math> with a self-consistently dressed argument <math altimg='si62.svg'><mrow><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mo>&#8242;</mo></msup><mo linebreak='goodbreak'>=</mo><msup><mi>&#981;</mi><mo>&#8242;</mo></msup><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><mi>k</mi><mo linebreak='badbreak'>+</mo><mn>1</mn><mo>)</mo></mrow><mo linebreak='goodbreak'>&#8722;</mo><msubsup><mi>&#945;</mi><mrow><mn>1</mn></mrow><mn>2</mn></msubsup><mi>z</mi><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>+</mo><msub><mi mathvariant='script'>G</mi><mn>0</mn></msub><mo>)</mo></mrow></mrow></math>, reducing to the explicit closed form in the massless limit. Predictions for all <italic>O</italic>( <italic>N</italic>) universality classes follow from the recursion, and a direct comparison with conventional fixed-order perturbation theory shows the renormalization-scale band of the latter contracting toward the single scheme-free SF-QFT value at every loop order.

Exact scheme-independent generating function for the massive <italic>O</italic>( <italic>N</italic>) <italic>&#981;</italic> 4 two-point function in scale-factorized quantum field theory

The phase space of hadron collider events spans hundreds of dimensions, generating an intricate geometry that we are just starting to explore. The number of possible new physics signals is exponential in the number of dimensions and detecting all of them is currently impossible for any human or artificial intelligence. In this work we introduce a method to search for new physics model independently in this high-dimensional space. It is based on the measurement of the most basic property of the manifold of collider events, its dimensionality. Our proposed technique does not suffer from a look-elsewhere effect that grows exponentially with the number of dimensions of the dataset, and by construction is insensitive to energy scale uncertainties. We illustrate its potential by finding new physics in simulated events with hundreds of phase space dimensions, taking as input single particles rather than jets. This study sets the stage for new model-independent search strategies based on global properties of collider data manifolds.

France

Raffaele Tito D’Agnolo

Alfredo Glioti

Gabriele Rigo

Switzerland

Alessandro Valenti

Intrinsic dimension of collider events and model-independent searches in 100 dimensions

This paper presents a detailed description of a model-independent method for the direct measurement of the Υ(4$\textit{S}$) → $\textit{B}$ $\textit{B}$ and Υ(4$\textit{S}$) → $$ {B}^0{\overline{B}}^0 $$ production fractions at $\textit{B}$ factories. The method is based on counting single- and double-inclusive charmed meson production at the Υ(4$\textit{S}$) resonance, providing statistical tagging of $$ {B}^0{\overline{B}}^0 $$ and $\textit{B}$ $\textit{B}$ events. A feasibility study indicates that a precision comparable to the current world average can be achieved without making any underlying assumptions, as the calculations rely solely on event yields.

Russia

M. Yasaveev

P. Pakhlov

N. Peters

A. Mufazalova

A model independent method for measurement of $\textit{B}$ ± and $\textit{B}$ 0 meson production fractions at Υ(4$\textit{S}$)

In holographic duality, the total energy of the dual field theory is obtained from the holographic renormalization, which depends not only on the bulk geometry but also on the choice of quantization schemes. We point out that the validity of several widely studied holographic inequalities — including the AdS Penrose inequality, the late-time bound on entanglement entropy growth, and the growth-rate limits of CV and CA complexities — depends on the choice of quantization schemes. Motivated by this issue, we introduce a modified total energy, which is still computed via holographic renormalization but the final value is independent of the choice of quantization schemes. We verify that this modified energy removes the apparent violations of these bounds that arise from quantization-scheme dependence in the model of massive scalar field. Our results suggest that our modified total energy provides a more robust notion of energy when we talk about above inequalities in holographic settings.

China

Ze Li

Hai-Shan Liu

Zi-Qing Xiao

Run-Qiu Yang

Quantization-scheme-independent energy and its implications for holographic bounds

Extreme astrophysical environments provide unique laboratories for testing fundamental neutrino interactions. We present the first oscillation-independent astrophysical probe of nonstandard neutrino interactions (NSI), using coincident neutral-current signals across diverse detectors to break degeneracies that have long limited sensitivity reach. Using self-consistent NSI supernova simulations and flavor-independent neutral-current scattering we show that anticorrelated signatures between JUNO liquid scintillator and dark matter detectors such as DARWIN/XLZD, ARGO, or RES-NOVA enable clear discrimination between NSI and flavor-conversion effects. For a Galactic supernova at Betelgeuse distance our approach enables an independent probe of neutrino-quark NSI couplings in parameter space that can reach and extend beyond current terrestrial limits. This multidetector approach enables breaking degeneracies in terrestrial searches and is broadly applicable to a wide range of upcoming experiments, establishing a new principle for testing fundamental interactions with astrophysical data.

United States

Angela R. Beatty

Anna M. Suliga

Japan

Volodymyr Takhistov

Oscillation-independent probes of nonstandard neutrino interactions from supernovae