We study a five-leg scattering amplitude on the special Coulomb branch of planar N=4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N=(1,1) super Yang-Mills theory and reducing it down to four space-time dimensions with extra-dimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in 't Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the `square root' of a five-point correlation function of infinitely-heavy half-BPS operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

We apply the method of regions to the evaluation of dual conformal integrals with small off-shellness. In contrast to conventional approach, where the separation of regions is performed via dimensional regularization breaking the dual conformal invariance (DCI), we use a sufficiently generic combination of dimensional and analytic regularizations which preserves the DCI. Within this regularization (dubbed as DCI regularization), the contribution of each region becomes DCI. We show that our method dramatically simplifies the calculations. As a demonstration, we calculate the slightly off-shell DCI pentabox integral up to power corrections. The contributions of all 32 regions appear to be expressible in terms of products/ratios of $\Gamma$-functions multiplied by some powers of DCI cross-ratios. Therefore, after removing the regularization, we obtain the final expression in terms of cross-ratios logarithms only. We have checked that our result for pentabox integral numerically agrees with the result of the recent Belitsky\&Smirnov paper [arXiv:2508.14298] which has essentially more complicated form.

Electron-positron colliders operating in the GeV region of center-of-mass energies or the Tau-Charm energy region, have been proven to enable competitive frontier research, due to its several unique features. With the progress of high energy physics in the last two decades, a new-generation Tau-Charm factory, Super Tau Charm Facility (STCF) has been actively promoting by the particle physics community in China. STCF holds great potential to address fundamental questions such as the essence of color confinement and the matter-antimatter asymmetry in the universe in the next decades. The main design goals of STCF are with a center-of-mass energy ranging from 2 to 7 GeV and a peak luminosity surpassing 5*10^34 cm^-2s^-1 that is optimized at a center-of-mass energy of 4 GeV, which is about 50 times that of the currently operating Tau-Charm factory - BEPCII. The STCF accelerator is composed of two main parts: a double-ring collider with the crab-waist collision scheme and an injector that provides top-up injections for both electron and positron beams. As a typical third-generation electron-positron circular collider, the STCF accelerator faces many challenges in both accelerator physics and technology. In this paper, the conceptual design of the STCF accelerator complex is presented, including the ongoing efforts and plans for technological R&D, as well as the required infrastructure. The STCF project aims to secure support from the Chinese central government for its construction during the 15th Five-Year Plan (2026-2030) in China.

Based on $10.64~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic $D^+_s$ decays using the $e^+e^-\to D^{*+}_{s} D^{*-}_{s}$ process. The branching fractions of $D_s^+\to\ell^+\nu_{\ell}\,(\ell=\mu,\tau)$ are measured to be $\mathcal{B}(D_s^+\to\mu^+\nu_\mu)=(0.547\pm0.026_{\rm stat}\pm0.016_{\rm syst})\%$ and $\mathcal{B}(D_s^+\to\tau^+\nu_\tau)=(5.60\pm0.16_{\rm stat}\pm0.20_{\rm syst})\%$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_{D_s^+}|V_{cs}|=(246.5\pm5.9_{\rm stat}\pm3.6_{\rm syst}\pm0.5_{\rm input})_{\mu\nu}~\mathrm{MeV}$ and $f_{D_s^+}|V_{cs}|=(252.7\pm3.6_{\rm stat}\pm4.5_{\rm syst}\pm0.6_{\rm input}))_{\tau \nu}~\mathrm{MeV}$, respectively. Taking the value of $|V_{cs}|$ from a global fit in the Standard Model, we obtain ${f_{D^+_s}}=(252.8\pm6.0_{\rm stat}\pm3.7_{\rm syst}\pm0.6_{\rm input})_{\mu\nu}$ MeV and ${f_{D^+_s}}=(259.2\pm3.6_{\rm stat}\pm4.5_{\rm syst}\pm0.6_{\rm input})_{\tau \nu}$ MeV, respectively. Conversely, taking the value for $f_{D_s^+}$ from the latest lattice quantum chromodynamics calculation, we obtain $|V_{cs}| =(0.986\pm0.023_{\rm stat}\pm0.014_{\rm syst}\pm0.003_{\rm input})_{\mu\nu}$ and $|V_{cs}| = (1.011\pm0.014_{\rm stat}\pm0.018_{\rm syst}\pm0.003_{\rm input})_{\tau \nu}$, respectively.

We present the first computation of next-to-next-to-leading order (NNLO) pure QED and mixed QCD$\otimes$QED corrections to unpolarized and polarized semi-inclusive deep-inelastic scattering (SIDIS). Building on our previous NNLO QCD results, these corrections are crucial for improving the theoretical precision. The coefficient functions are derived within the QCD factorization framework using dimensional regularization, with consistent renormalization and mass factorization. A detailed phenomenological analysis shows that the NNLO QED and QCD$\otimes$QED terms enhance perturbative stability and reduce scale uncertainties. These results are essential for high-precision SIDIS predictions at future facilities such as the Electron-Ion Collider.

The recent precise measurements of the $e^+e^-\to K_SK_L$ and $e^+e^-\to K^+K^-$cross sections and the hadronic spectral function of the$\tau^-\to K^-K_S\nu_\tau$ decay are used to extract the isoscalar and isovector electromagnetic kaon form factors and their relative phase in a model independent way. The experimental results are compared with a fit based on the vector-meson-dominance model.

One of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor and measurements and theoretical interpretations of their results have advanced tremendously: apart from masses and quantum numbers of flavor particles, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. Till early 1990s observations of CP violation were confined to neutral $K$ mesons, but since then a large number of CP-violating processes have been studied in detail in neutral $B$ mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of $K, D$, and $B$ mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field.

In the recent years, argon-based experiments looking for Dark Matter in the Universe have explored the non-standard scenario in which Dark Matter is made by low-mass Weakly Interacting Massive Particles, of mass in the range of 1-10 GeV instead of the canonical hundreds of GeV. Detecting such particles is challenging, as their expected signatures are nuclear recoils with energies below 10 keV, observable solely via ionization. This necessitates a precise understanding of the detector response in this energy regime, which remains incomplete for argon. To address this, the ReD experiment was developed within the framework of the DarkSide-20k Collaboration to produce and characterize few-keV nuclear recoils. A compact dual-phase argon Time Projection Chamber (TPC) was irradiated with neutrons from a Cf252 source, to produce Ar recoils in the energy range of interest via (n,n') elastic scattering. A downstream spectrometer composed of 18 plastic scintillators detected the neutrons scattered off Ar nuclei, enabling recoil energy reconstruction via two-body kinematics. The ionization yield Qy of argon, defined as the number of electrons produced per unit energy deposit, was measured in a model-independent way between 2 and 10 keV. These measurements extend direct experimental coverage well below the previous limit of approximately 7 keV. The results are consistent with existing data above 7 keV, while they indicate a higher Qy at lower energies.

We calculate a subset of two-loop master integrals relevant for the differential cross section of $e^+e^-\to \mu^+\mu^-$ process. We consider only those families for which the account of the electron mass $m$ is necessary. Our results have the form of the Frobenius series in $m$ with coefficients expressed via Goncharov's polylogarithms.

Heavy-flavour physics is an essential component of the particle-physics programme, offering critical tests of the Standard Model and far-reaching sensitivity to physics beyond it. Experiments such as LHCb, Belle II, and BESIII drive progress in the field, along with contributions from ATLAS and CMS. The LHCb Upgrade II and upgraded Belle II experiments will provide unique and highly sensitive measurements for decades, playing a key role in the searches for new physics. Future facilities with significant heavy-flavour capabilities will further expand these opportunities. We advocate for a European Strategy that fully supports Upgrade II of LHCb and an upgrade of Belle II, along with their subsequent exploitation. Additionally, we support a long-term plan that fully integrates flavour physics in an $e^+e^-$ collider to run as a $Z$ factory.

We report on an improved measurement of the Cabibbo-Kobayashi-Maskawa {\it CP}-violating phase $\gamma$ through a Dalitz plot analysis of neutral $D$ meson decays to $K_S^0 \pi^+ \pi^-$ and $K_S^0 K^+ K^-$ in the processes $B^\mp \to D K^\mp$, $B^\mp \to D^* K^\mp$ with $D^* \to D\pi^0,D\gamma$, and $B^\mp \to D K^{*\mp}$ with $K^{*\mp} \to K_S^0 \pi^\mp$. Using a sample of 383 million $B\bar{B}$ pairs collected by the BABAR detector, we measure $\gamma=(76 \pm 22 \pm 5 \pm 5)^\circ$ (mod $180^\circ$), where the first error is statistical, the second is the experimental systematic uncertainty and the third reflects the uncertainty on the description of the Dalitz plot distributions. The corresponding two standard deviation region is 29^\circ < \gamma < 122^\circ. This result has a significance of direct {\it CP} violation ($\gamma \ne 0$) of 3.0 standard deviations.

We present a method for high-precision numerical evaluations of Lauricella functions, whose indices are linearly dependent on some parameter $\varepsilon$, in terms of their Laurent series expansions at zero. This method is based on finding analytic continuations of these functions in terms of Frobenius generalized power series. Being one-dimensional, these series are much more suited for high-precision numerical evaluations than multi-dimensional sums arising in approaches to analytic continuations based on re-expansions of hypergeometric series or Mellin--Barnes integral representations. To accelerate the calculation procedure further, the $\varepsilon$ dependence of the result is reconstructed from the evaluations of given Lauricella functions at specific numerical values of $\varepsilon$, which, in addition, allows for efficient parallel implementation. The method has been implemented in the $\texttt{PrecisionLauricella}$ package, written in Wolfram Mathematica language.

Calculation results for the HQET field anomalous dimension and the QCD cusp anomalous dimension, as well as their properties, are reviewed. The HQET field anomalous dimension $\gamma_h$ is known up to 4 loops. The cusp anomalous dimension $\Gamma(\varphi)$ is known up to 3 loops, and its small-angle and large-angle asymptotics -- up to 4 loops. Some (but not all) color structures at 4 loops are known with the full $\varphi$ dependence. Some simple contributions are known at higher loops. For the $\varphi\to\infty$ asymptotics of $\Gamma(\varphi)$ (the light-like cusp anomalous dimension) and the $\varphi^2$ term of the small-$\varphi$ expansion (the Bremsstrahlung function), the $\mathcal{N}=4$ SYM results are equal to the highest-weight parts of the QCD results. There is an interesting conjecture about the structure of $\Gamma(\varphi)$ which holds up to 3 loops; at 4 loops it holds for some color structures and breaks down for other ones. In cases when it holds it related highly non-trivial functions of $\varphi$, and it cannot be accidental; however, the reasons of this conjecture and its failures are not understood. The cusp anomalous dimension at Euclidean angle $\phi\to\pi$ is related to the static quark-antiquark potential due to conformal symmetry; in QCD this relation is broken by an anomalous term proportional to the $\beta$ function. Some new results are also presented. Using the recent 4-loop result for $\gamma_h$, here we obtain analytical expressions for some terms in the 4-loop on-shell renormalization constant of the massive quark field $Z_Q^{\text{os}}$ which were previously known only numerically. We also present 2 new contribution to $\gamma_h$, $\Gamma(\varphi)$ at 5 loops and to the quark-antiquark potential at 4 loops.

We introduce the $\texttt{PrecisionLauricella}$ package, a computational tool developed in Wolfram Mathematica for high-precision numerical evaluations of Lauricella functions with indices linearly dependent on a parameter, $\varepsilon$. The package leverages a method based on analytical continuation via Frobenius generalized power series, providing an efficient and accurate alternative to conventional approaches relying on multi-dimensional series expansions or Mellin--Barnes representations. This one-dimensional approach is particularly advantageous for high-precision calculations and facilitates further optimization through $\varepsilon$-dependent reconstruction from evaluations at specific numerical values, enabling efficient parallelization. The underlying mathematical framework for this method has been detailed in our previous work, while the current paper focuses on the design, implementation, and practical applications of the $\texttt{PrecisionLauricella}$ package.

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

A precise measurement of the cross section of the process $e^+e^-\to\pi^+\pi^-(\gamma)$ from threshold to an energy of 3GeV is obtained with the initial-state radiation (ISR) method using 232fb$^{-1}$ of data collected with the BaBar detector at $e^+e^-$ center-of-mass energies near 10.6GeV. The ISR luminosity is determined from a study of the leptonic process $e^+e^-\to\mu^+\mu^-(\gamma)\gamma_{\rm ISR}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^+e^-\to\pi^+\pi^-(\gamma)$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi\pi$ cross section from threshold to 1.8GeV is $(514.1 \pm 2.2({\rm stat}) \pm 3.1({\rm syst}))\times 10^{-10}$.

We search for the neutrinoless, lepton-flavor-violating tau decays tau -> l V^0, where l is an electron or muon and V^0 is a vector meson reconstructed as phi -> K^+K^-, rho -> pi^+pi^-, K^* -> K^+pi^-, or K^*bar -> K^-pi^+. The analysis has been performed using 451 fb^{-1} of data collected at an e^+e^- center-of-mass energy near 10.58 GeV with the BaBar detector at the PEP-II storage rings. The number of events found in the data is compatible with the background expectation, and upper limits on the branching fractions are set in the range (2.6-19) x 10^{-8} at the 90% confidence level.

Using data samples of $(10087\pm 44)\times10^{6}$ $J/\psi$ events and $(2712.4\pm 14.3)\times10^{6}$ $\psi(3686)$ events collected with the BESIII detector at the BEPCII collider, we search for the CP violating decays $J/\psi\rightarrow K^{0}_{S}K^{0}_{S}$ and $\psi(3686)\rightarrow K^{0}_{S}K^{0}_{S}$. No significant signals are observed over the expected background yields. The upper limits on their branching fractions are set as \mathcal{B}(J/\psi\rightarrow K^{0}_{S}K^{0}_{S}) <4.7\times 10^{-9} and \mathcal{B}(\psi(3686)\rightarrow K^{0}_{S}K^{0}_{S}) <1.1\times 10^{-8} at the 90% confidence level. These results improve the previous limits by a factor of three for $J/\psi\rightarrow K^{0}_{S} K^{0}_{S}$ and two orders of magnitude for $\psi(3686)\rightarrow K^{0}_{S} K^{0}_{S}$.

Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which one needs to perform Laurent expansions. Moreover such expansions are desirable to be expressed in terms of well known functions which can be evaluated with arbitrary precision. To solve this problem we use the differential equation method and the reduction of corresponding differential systems to canonical basis. Specifically we will be interested in the generalized hypergeometric functions of one variable together with Appell and Lauricella functions and their expansions in terms of Goncharov polylogarithms. Particular attention will be given to the case of rational indices of considered hypergeometric functions when the reduction to canonical basis involves nontrivial variable change. The article comes with a Mathematica package Diogenes, which provides algorithmic implementation of the required steps.