About 18 years ago, the BABAR and the Belle Collaborations reported evidence for a new $$c\bar{c}$$ structure near $$3900~\textrm{MeV}$$ in $$e^{+}e^{-} \rightarrow D\bar{D}$$ , triggering debate over whether it represents a genuine hadronic state or arises from interference effects and the opening of the $$D^{*}\bar{D}$$ threshold. The issue remained unsettled until 2024, when BESIII, with an enlarged $$e^{+}e^{-} \rightarrow D\bar{D}$$ sample, confirmed the presence of the $\textit{G}$(3900) structure, reviving discussion of its nature. Although it has been proposed as a $\textit{P}$-wave $$D\bar{D}^{*}$$ molecular state, no consensus has emerged, and interference effects remain a plausible explanation. In this Letter, we show that analyzing the $$e^{+}e^{-}\rightarrow D\bar{D}$$ cross section as a function of the transverse momentum of the final-state $\textit{D}$ meson reveals a prominent Jacobian peak. This feature cannot be generated by interference effects alone and thus provides direct evidence for the existence of $\textit{G}$(3900). Moreover, the peak position is highly sensitive to the actual mass of $\textit{G}$(3900), offering a precise determination method. The criterion illustrated by $\textit{G}$(3900) can be extended to other hadronic systems, offering a powerful tool to identify genuine resonances.

China

Yin Huang

Xurong Chen

Criterion for the existence of the $\textit{G}$(3900) resonance

We formulate a systematic on-shell construction of perturbative amplitudes by combining the Feynman–tree theorem with BCFW recursion. Amplitudes are built entirely from on-shell tree amplitudes generated by BCFW and are supplemented by additional unobservable state-conjugate on-shell pairs, called vacuum pairs, whose momenta are integrated over Lorentz-invariant phase space. At fixed coupling order, the contributing tree amplitudes are classified by polygon bookkeeping, while their products form forests whose relative signs are fixed by inclusion–exclusion. We show that these signs coincide with the signs assigned by the full Feynman–tree-theorem cut expansion, so that the construction reproduces the ordinary perturbative loop expansion order by order. The dynamical tree input consists of the allowed three-point on-shell amplitudes; the particle spectrum, couplings, and color data are taken as given, and no off-shell object is introduced at any stage.

Chile

M. Maniatis

Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order $\textit{g}$ 6

The beyond-the-standard-model scenario presented in this work is motivated by the observations of neutrino masses, the anomalous magnetic moments of the electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all of which are odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams featuring the same fields also explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without conflicting with direct detection constraints, or those from big bang nucleosynthesis or cosmic microwave background observations. Finally, prospective signatures at the LHC are discussed.

India

Vandana Sahdev

Neutrino masses, anomalous magnetic moments and dark matter with vector-like fermions and an inert scalar doublet * V.S. acknowledges the support from research grant no. CRG/2018/004889 of the SERB, India; T.R. Seshadri for providing resources during the initial stages of the work; and Brajesh Choudhary for providing access to computers bought under the aegis of Grant No. SR-MF/PS-0212014-DUB (G) of the DST (India)

In this paper, we investigate the motion of test particles in the vicinity of a static, non-rotating black hole (BH) described in the framework of Proca–Gauss–Bonnet (PGB) gravity endowed with primary hair, focusing on how the parameters of the BH model affect their trajectories. The geometry of this BH is determined by four quantities: the hair parameter <italic>q</italic>, the BH mass <italic>M</italic>, and the two coupling constants <italic>&#945;</italic> and <italic>&#946;</italic>. The stability conditions for equatorial circular trajectories are analyzed using the effective potential approach. Explicit analytical formulae for both the angular momentum and the conserved energy of the test particles are obtained in terms of the BH parameters. The behavior of the innermost stable circular orbits (ISCOs) is also addressed in detail. Furthermore, we examine small perturbations of circular motion and derive analytic forms of the oscillatory frequencies, such as radial, vertical, and orbital frequencies, close to the equatorial plane. The periastron precession frequency is also evaluated. The results show how the BH parameters influence the orbital dynamics of the test particles, providing new insights into their motion in the context of PGB gravity.

Rana Muhammad Zulqarnain

Pakistan

Saadia Mumtaz

Kuwait

Orhan Donmez

Azerbaijan

G. Mustafa

Algeria

Abdelmalek Bouzenada

Uzbekistan

Ikhtiyor Saidov

Epicyclic frequencies around Proca-induced black holes with primary hair

Inflationary production of ultralight vector dark matter can be amplified by a brief non-slow-roll phase, yet instantaneous mass transitions generate ultraviolet ringing and leave finite-time predictions unresolved. We replace the sharp transition with a smooth profile and derive the momentum-response kernel of the longitudinal mode. Finite duration preserves the infrared enhancement, suppresses modes that resolve the transition, and introduces a profile-dependent correction to the relic abundance. After fixing the dark matter abundance, the induced gravitational-wave signal retains an independent transverse-traceless source dependence, so abundance rescaling alone leaves residual profile information. Numerical mode evolution and radiation-era tensor integration support the finite-width treatment. Transition duration therefore links microscopic inflationary dynamics to ultralight vector abundance and its low-frequency gravitational-wave signal.

Imtiaz Khan

Niamat Ullah

Chengxun Yuan

Farruh Atamurotov

Ahmadjon Abdujabbarov

Finite-duration non-slow-roll effects in inflationary production of ultralight vector dark matter

We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with $\textit{N}$ = 2 + 1 flavors of O($\textit{a}$)-improved Wilson fermions, covering six lattice spacings between 0$\textit{.}$039 and 0$\textit{.}$097 fm and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain as our final, continuum-extrapolated result $$ {a}_{\mu}^{\mathrm{hvp},\kern0.30em \mathrm{nlo}} $$ = −101.57(26) (54) × 10 . It lies below the estimate provided by the 2025 White Paper of the Muon ($\textit{g}$ – 2) Theory Initiative by 1.4$\textit{σ}$ but is two times more precise. It also exhibits a strong tension of 4.6$\textit{σ}$ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.

Germany

Arnau Beltran

Alessandro Conigli

Switzerland

Simon Kuberski

Harvey Meyer

Konstantin Ottnad

Hartmut Wittig

Higher-order hadronic vacuum polarization contribution to the muon $\textit{g}$ − 2 from lattice QCD

We investigate the behavior of the nonradial gravity-pulsation discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode in neutron stars with a strong first-order phase transition which give rise to hybrid star configurations. These modes are of utmost relevance, since they can be potentially excited in isolated as well as binary neutron star systems in the inspiral phase, thus allowing us to indirectly detect the presence of a deconfinement transition. In order to do this, we consider four categories of hybrid stars that present distinctive features in their equations of state. We employ the constant speed of sound parametrization, which accounts for a sharp phase transition between confined hadronic matter and deconfined quark matter. Then, working within the relativistic Cowling approximation to obtain the frequencies of nonradial oscillations, we find that, depending on the hybrid star category, the relations between discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode frequencies and masses as well as tidal deformabilities display a highly distinct behavior across the diverse hybrid star categories that appear in the slow hadron-quark conversion regime. This distinct phenomenology provides smoking-gun evidence to clearly distinguish and further classify hybrid stars with a strong transition from purely hadronic stars using upcoming gravitational-wave data. In addition, we present for each of the categories studied the relation between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode frequency and the normalized energy density jump. Finally, we present a novel universal relation for the discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode able to encompass the four categories, including long branches of slow stable hybrid stars and address its asteroseismological capability.

Argentina

M.C. Rodriguez

Brazil

José C. Jiménez

Ignacio F. Ranea-Sandoval

Classification of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-modes for neutron stars with a strong transition: Novel universal relation including slow stable hybrid stars

According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$\textit{G}$ gravity theory in which the effective gravitational constant $\textit{G}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $\textit{G}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $\textit{G}$ , which may ameliorate the “arrow of time” problem. We make some comparisons with the constant-$\textit{G}$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.

Chen-Hao Wu

Yen Ong

Cosmology with logarithmic corrected horizon entropy according to the generalized entropy and variable-$\textit{G}$ correspondence

We developed a unified framework based on a special (non-regular) embedding of the exceptional group $$E_6$$ in which the main stage of symmetry breaking chain realizes $$E_6\rightarrow G(2) \times SU(3)_A$$ . The exceptional factor $\textit{G}$(2) plays the role of a hidden strong sector, while $$SU(3)_A$$ acts as an ancestor of the electroweak gauge group. A minimal scalar sector is organized around a $$\textbf{650}$$ -based $$E_6$$ Higgs sector. Its $$G(2)\times SU(3)_A$$ components $$(\textbf{7},\textbf{1})$$ and $$(\textbf{1},\textbf{8})$$ implement the subsequent breaking steps $$G(2)\rightarrow SU(3)_C$$ and $$SU(3)_A\rightarrow SU(2)_L\times U(1)_A$$ . The $\textit{speciality}$ of this symmetry breaking establishes the feature of $\textit{darkness}$. Defining a hypercharge from the $$t_{8}$$ generator of $$SU(3)_A$$ is not sufficient to recover the exact Standard Model hypercharges and the correct Weinberg weak angle, leading to the necessity of an $$E_7$$ uplift which introduces only a proper additional $$U(1)_X$$ factor to fix the abelian sector. The special embedding naturally suppresses tree-level leptoquark couplings that typically mediate proton decay in regular grand unified theories. The scalar potential for the Higgs sectors has been constructed, deriving the heavy gauge-bosons spectrum and presenting a consistent one-loop running of the gauge couplings across the intermediate scales, which is shown to satisfy an $$E_6$$ unification. The exotic states are organized in $$E_7$$ -derived vectorlike pairs and are made ultraheavy, while a chirality-selecting projection keeps only the desired Standard Model zero modes. All non-Standard Model Higgs fields and $\textit{broken}$ massive vectors are found to be invisible to colliders searches. The $\textit{G}$(2) gluons ensemble confines into heavy dark glueballs with parametrically suppressed communication with $$SU(3)_A$$ and $$U(1)_X$$ sectors. Cosmological history is analyzed in details, including topological defects, inflation and reheating, demonstrating that monopole relics are naturally diluted. The resulting framework provides a minimal and internally consistent exceptional apparatus which includes the Standard Model and a dark matter sector which is secluded by the group-theoretic orthogonality.

Italy

Nicolò Masi

Toward a special $$E_6\rightarrow G(2) \times SU(3)_A$$ embedding for Standard Model and dark matter and an $$E_7$$ completion proposal

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

United States

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>