We present an investigation of the structural properties of heavy-light ( $$D, D_s, B, B_s$$ ) and heavy-heavy ( $$B_c$$ ) mesons by incorporating the $\textit{V}$-scheme strong coupling constant $$\alpha _V$$ up to the third-loop order ( $$N^3$$ LO). The inclusion of three-loop radiative corrections is critical to achieving perturbative convergence and effectively canceling renormalon-induced instabilities. A central feature of this work is the rigorous calibration of the string tension $\textit{b}$ using the universal scaling ratio $$R_{n_f} = \Lambda _{\overline{\text {MS}}}^{(n_f)}/\sqrt{b}$$ , matched to the non-perturbative Sommer scale $$r_0$$ from FLAG 2024 averages. By integrating these flavor-dependent $$N^3$$ LO refinements ( $$b \approx 0.1951 \pm 0.0369$$ GeV $$^2$$ ) into a variational Cornell potential framework, we demonstrate a systematic“stiffening”of the internal structure and a physical spatial contraction across successive loop orders. Our $$N^3$$ LO results for root-mean-square (RMS) matter radii and charge radii exhibit remarkable agreement with established benchmarks: specifically, the $$B_c$$ charge radius (0.191 fm) and matter radius (0.2967 fm) align closely with light-front predictions and relativistic quark model studies. Evaluation of the Isgur–Wise function reveals that while higher-order corrections primarily reshape the light-quark spectator cloud, the heavy core localization remains dominated by the constituent mass scale.

India

Rishan Choudhury

Pritom Nath

Jugal Lahkar

Variationally improved structure of heavy-light mesons at $$N^3$$ LO: stiffening effects and universal form factors in the $\textit{V}$-scheme

In a previous paper [Flores-Baez et al., <a href="http://dx.doi.org/10.1103/PhysRevD.76.096010">Phys. Rev. D 76, 096010 (2007)</a>] we have calculated the radiative corrections to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> decays, aiming to estimate the width difference between charged and neutral rho mesons. There, we have used the scalar quantum electrodynamics approximation and considered the convection terms to keep the loop contributions finite in the case of charged rho meson decays. Here we compute the radiative corrections by considering the electromagnetic structure of charged mesons and we also include the full Lorentz structure of the electromagnetic vertices. We reevaluate the width difference of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>±</mo></msup><mo>−</mo><msup><mi>ρ</mi><mn>0</mn></msup></math> vector mesons and calculate the structure-dependent contributions to final state radiation terms in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> cross section. Both effects are important inputs for evaluating the isospin breaking corrections in the dominant hadronic vacuum polarization contributions to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> when using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton data.

Mexico

F.V. Flores-Baez

G. López Castro

Genaro Toledo

Beyond scalar QED radiative corrections: The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>±</mo></msup><mo>−</mo><msup><mi>ρ</mi><mn>0</mn></msup></math> width difference, final state radiation corrections, and their impact on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup><mo stretchy="false">[</mo><mi>τ</mi><mo stretchy="false">]</mo></math>

We present a generalization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>-space candia algorithm to next-to-next-to-next-to-leading order (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">N</mi><mn>3</mn></msup><mi>LO</mi></math>) accuracy in quantum chromodynamics (QCD) for solving the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for unpolarized parton densities in the nucleon. The algorithm is based on logarithmic expansions of the solution and can be extended to all orders in QCD. An expansion equivalent to the exact solution of the DGLAP equation at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">N</mi><mn>3</mn></msup><mi>LO</mi></math> is presented in the non-singlet sector. Results for approximate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">N</mi><mn>3</mn></msup><mi>LO</mi></math> parton distribution functions, evolved using the most recent approximations to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">N</mi><mn>3</mn></msup><mi>LO</mi></math> DGLAP splitting functions, are provided for benchmarking. The new version of the code, candia-v2, is publicly available [github, candia-v2, (2025).].

United States

Casey Hampson

Marco Guzzi

DGLAP evolution at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">N</mi><mn>3</mn></msup><mi>LO</mi></math> with the candia algorithm

The Jiangmen Underground Neutrino Observatory (JUNO) started physics data taking on 26 August 2025. JUNO consists of a 20-kton liquid scintillator central detector, surrounded by a 35 kton water pool serving as a Cherenkov veto, and almost 1000 m$^{2}$ of plastic scintillator veto on top. The detector is located in a shallow underground laboratory with an overburden of 1800 m.w.e. This paper presents the performance results of the detector, extensively studied during the commissioning of the water phase, the subsequent liquid scintillator filling phase, and the first physics runs. The liquid scintillator achieved an attenuation length of 20.6 m at 430 nm, while the high coverage PMT system and scintillator together yielded about 1785 photoelectrons per MeV of energy deposit at the detector centre, measured using the 2.223 MeV $\textit{γ}$ from neutron captures on hydrogen with an Am-C calibration source. The reconstructed energy resolution is 3.4% for two 0.511 MeV $\textit{γ}$ at the detector centre and 2.9% for the 0.93 MeV quenched $^{214}$Po alpha decays from natural radioactive sources. The energy non-linearity is calibrated to better than 1%. Intrinsic contaminations of $^{238}$U and $^{232}$Th in the liquid scintillator are below 10$^{-16}$ g/g, assuming secular equilibrium. The water Cherenkov detector achieves a muon detection efficiency better than 99.9% for muons traversing the liquid scintillator volume. During the initial science runs, the data acquisition duty cycle exceeded 97.8%, demonstrating the excellent stability and readiness of JUNO for high-precision neutrino physics.

Chile

Angel Abusleme

France

Thomas Adam

Germany

Kai Adamowicz

China

David Adey

Pakistan

Shakeel Ahmad

Rizwan Ahmed

Finland

Timo Ahola

Italy

Sebastiano Aiello

Fengpeng An

Guangpeng An

United Kingdom

Costas Andreopoulos

Giuseppe Andronico

João Pedro Athayde Marcondes de André

Russia

Nikolay Anfimov

Vito Antonelli

Tatiana Antoshkina

Thailand

Burin Asavapibhop

Didier Auguste

Margherita Buizza Avanzini

Slovakia

Andrej Babic

Jingzhi Bai

Weidong Bai

Nikita Balashov

Roberto Barbera

Andrea Barresi

Davide Basilico

Eric Baussan

Beatrice Bellantonio

Marco Bellato

JeanLuc Beney

Marco Beretta

Antonio Bergnoli

Enrico Bernieri

Nikita Bessonov

David Biaré

Daniel Bick

Lukas Bieger

Svetlana Biktemerova

Thilo Birkenfeld

David Blum

Simon Blyth

Sara Boarin

Manuel Boehles

Anastasia Bolshakova

Mathieu Bongrand

Aurélie Bonhomme

Clément Bordereau

Matteo Borghesi

Augusto Brigatti

Timothee Brugiere

Riccardo Brugnera

Riccardo Bruno

Jonas Buchholz

Antonio Budano

Max Buesken

Mario Buscemi

Severino Bussino

Jose Busto

Ilya Butorov

Marcel Büchner

Anatael Cabrera

Barbara Caccianiga

Boshuai Cai

Hao Cai

Xiao Cai

Yanke Cai

Yi-zhou Cai

Zhiyan Cai

Stéphane Callier

Steven Calvez

Antonio Cammi

Agustin Campeny

Dechang Cai

Chuanya Cao

Dewen Cao

Guofu Cao

Jun Cao

Yaoqi Cao

Rossella Caruso

Aurelio Caslini

Cédric Cerna

Vanessa Cerrone

Daniele Cesini

Chi Chan

Jinfan Chang

Yun Chang

Milo Charavet

Tim Charissé

Auttakit Chatrabhuti

Chao Chen

Guoming Chen

Haitao Chen

Haotian Chen

Jiahui Chen

Jian Chen

Jing Chen

Junyou Chen

Lihao Chen

Mali Chen

Mingming Chen

Initial performance results of the JUNO detector * We acknowledge financial and institutional supportfrom the Chinese Academy of Sciences, the National KeyR&D Program of China, the People's Government of Guangdong Province, and the Tsung–Dao Lee Institute of Shanghai Jiao Tong University in China.We appreciate the contributions from the Institut Na-tional de Physique Nucléaire et de Physique des Partic-ules (IN2P3) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, the Fonds de la Recherche Sci-entifique (F.R.S.–FNRS) and the Institut Interuni-versitaire des Sciences Nucléaires (IISN) in Belgium, and the Conselho Nacional de Desenvolvimento Científico eTecnológico (CNPq) in Brazil.We also acknowledge the support of the AgenciaNacional de Investigación y Desarrollo (ANID) and the ANID–Millennium Science Initiative Program (ICN2019044) in Chile; the European Structural and In-vestment Funds, the Ministry of Education, Youth and Sports, and the Charles University Research Center inthe Czech Republic; the Deutsche Forschungsgemeinsch-aft (DFG), the Helmholtz Association, and the Cluster ofExcellence PRISMA+ in Germany; and the Joint Insti-tute for Nuclear Research (JINR) and Lomonosov Mo-scow State University in Russia.We further thank the Slovak Research and Develop-ment Agency in the Slovak Republic, the National Science and Technology Council (NSCT) and MOE, China, the Program Management Unit for Hu-man Resources & Institutional Development, Research and Innovation (PMU–B), Chulalongkorn University, and Suranaree University of Technology in Thailand, the Science and Technology Facilities Council (STFC) in the United Kingdom, and the University of California atIrvine and the National Science Foundation (NSF) in the United States

Momentum maps connecting phase spaces of different multiplicities are widely used in precision calculations in QCD and collider phenomenology in general. The antenna mapping is a colour-ordered map which allows to absorb the recoil of an arbitrary number of emissions onto two hard radiators. Due to the rapid convergence in soft and collinear configurations, the antenna mapping is extensively used for fixed-order calculations within the antenna subtraction method, as well as in parton showers such as the VINCIA shower. However, colour-ordered momentum mappings cannot be directly applied in the presence of multiple unordered emissions of quarks and gluons, which typically appear beyond the leading-colour approximation. To address this technical challenge, we present, in the context of the antenna subtraction method, a simple decomposition of the phase space into sectors to isolate classes of infrared configurations which can be unambiguously assigned to a specific momentum ordering. In each sector, the singularities of any matrix element can be subtracted relying on a colour-ordered map. We illustrate the required phase-space sectors for up to three unordered emissions. The mapping algorithm described here has been recently employed for the first differential N $$^3$$ LO calculation of jet production at electron–positron colliders.

Xuan Chen

Matteo Marcoli

Phase-space sectors for colour-ordered momentum mappings in local subtraction up to N $$^3$$ LO

We present a determination of the strong coupling $$\alpha _s(m_Z)$$ from a global dataset including both fixed-target and collider data from deep-inelastic scattering and a variety of hadronic processes, with a simultaneous determination of parton distribution functions (PDFs) based on the NNPDF4.0 methodology. This determination is performed at NNLO and approximate $${\textrm{N}}^3$$ LO ( $${\textrm{aN}}^3$$ LO) perturbative QCD accuracy, including QED corrections and a photon PDF up to NLO accuracy. We extract $$\alpha _s$$ using two independent methodologies, both of which take into account the cross-correlation between $$\alpha _s$$ and the PDFs. The two methodologies are validated by closure tests that allow us to detect and remove or correct for several sources of bias, and lead to mutually consistent results. We account for all correlated experimental uncertainties, as well as correlated theoretical uncertainties related to missing higher order perturbative corrections (MHOUs). We study the perturbative convergence of our results and the impact of QED corrections. We assess individual sources of uncertainty, specifically MHOUs and the value of the top quark mass. We provide a detailed appraisal of methodological choices, including the choice of input dataset, the form of solution of evolution equation, the treatment of the experimental covariance matrix, and the details of Monte Carlo data generation. We find $$\alpha _s(m_Z)=0.1194^{+0.0007}_{-0.0014}$$ at $${\textrm{aN}}^3$$ $${\textrm{LO}}_{\textrm{QCD}}\otimes {\textrm{NLO}}_{\textrm{QED}}$$ accuracy, consistent with the latest PDG average and with recent lattice results.

Richard Ball

Andrea Barontini

Switzerland

Juan Cruz-Martinez

Stefano Forte

Felix Hekhorn

Emanuele Nocera

Netherlands

Juan Rojo

Roy Stegeman

A determination of $$\alpha _s(m_Z)$$ at $${{\textrm{aN}}}^3{{\textrm{LO}}}_{{\textrm{QCD}}}\otimes {{\textrm{NLO}}}_{{\textrm{QED}}}$$ accuracy from a global PDF analysis

Spain

Daniel Castillo

Canada

Lotta Jokiniemi

Pablo Soriano

Javier Menéndez

Corrigendum to “Neutrinoless ββ decay nuclear matrix elements complete up to N 2LO in heavy nuclei&#8221; [Physics Letters B 860 (2025) 139181]

We present a method for obtaining an initial-state parton shower model where the (backward) evolution fully consistent with the (forward) evolution of the collinear parton density used. As a proof-of-concept we use parton densities obtained with the parton branching (PB) approach, and modify the default initial-state shower in 8 with this method to be consistent with them. PB is ideally suited for checking the validity of our method since, in addition to producing collinear parton densities, it also produces the corresponding transverse-dependent (TMD) ones, and these can then be directly compared to the transverse momentum distribution obtained from the parton shower. We show that TMD distributions which we in this way obtain from our modified 8 shower using leading order (LO) parton densities and splitting functions are fully consistent with the corresponding leading order TMD densities. At next-to-leading order (NLO) it is not possible to achieve the same consistency using the built-in LO splitting functions in the shower, but we show that by introducing NLO splitting functions using a reweighting procedure, we can achieve consistency also at NLO. The method presented here, which we have named , can be easily extended to any collinear parton densities, as long as the exact conditions for the evolution are known. With the method we obtain an initial-state parton shower which in principle has no free parameters, and is fully consistent with collinear parton densities at LO and NLO.

H. Jung

Sweden

L. Lönnblad

M. Mendizabal

Sara Taheri Monfared

A parton shower consistent with parton densities at LO and NLO:

In this paper, we explore the properties of the Ellis-Jaffe Sum Rule (EJSR) by employing the Principle of Maximum Conformality (PMC) approach to address its perturbative part up to next-to-next-to-next-to-leading order ( <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>N</mi></mrow><mrow><mn mathvariant='normal'>3</mn></mrow></msup><mi mathvariant='normal'>LO</mi></math>) QCD contributions. By applying the PMC, we achieve a precise perturbative QCD prediction for the EJSR, free from conventional ambiguities associated with the renormalization scale choices. Considering the presence of the <math altimg='si2.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub></math> Landau pole near the asymptotic scale, we incorporate the low-energy <math altimg='si2.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub></math> model based on analytic perturbation theory (APT) to refine the EJSR behavior in the infrared region. By combining the PMC approach with the low-energy APT model, the agreement between theoretical calculations and experimental measurements of EJSR is significantly improved, as evidenced by the reduced discrepancy from <math altimg='si3.svg'><msup><mrow><mi>&#967;</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mi>d</mi><mo>.</mo><mi>o</mi><mo>.</mo><mi>f</mi><msub><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi mathvariant='normal'>Conv</mi><mo>.</mo></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.86</mn></math> to <math altimg='si4.svg'><msup><mrow><mi>&#967;</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mi>d</mi><mo>.</mo><mi>o</mi><mo>.</mo><mi>f</mi><msub><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi mathvariant='normal'>PMC</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.19</mn></math>, thereby validating the effectiveness of our approach.

Hua Zhou

Qing Yu

Xing-Gang Wu

Updated determination of Ellis-Jaffe sum rules up to N 3LO QCD corrections

We discuss the modeling of the hadronic phase of QCD at finite magnetic field in the framework of hadron resonance gas (HRG). We focus on the statistical description of particle yields that include contribution from resonance decays. We demonstrate that the swift increase in the number of protons with magnetic field predicted in the HRG is due to the assumption of structureless resonances. We discuss fluctuations of conserved charges and show that at present the qualitative comparison of the model predictions with the lattice QCD data should be treated with care. We also discuss the principle of detailed balance which allows us to study the magnetic field dependence of neutral resonances.