This is a review of gravitational instantons — solutions to Riemannian Einstein or Einstein–Maxwell equations in four dimensions which yield complete metrics on non-compact four-manifolds, and which asymptotically ‘look like’ flat space. The review focuses on examples, and is based on lectures given by the author at the Cracow School of Theoretical Physics held in Zakopane in June 2024.

United Kingdom

Gravitational Instantons, Old and New

Causal Dynamical Triangulations (CDT) is a lattice theory of quantum gravity. It is shown how to identify the IR and the UV limits of this lattice theory with similar limits studied using the continuum, functional renormalization group (FRG) approach. The main technical tool in this study will be the so-called two-point function. It will allow us to identify a correlation length not directly related to the propagation of physical degrees of freedom.

Denmark

Poland

Netherlands

IR and UV Limits of CDT and Their Relations to FRG

United States

Do \({\mit \Lambda }_{\mathrm {CC}}\) and \(G\) Run?

The QCD running coupling constant is studied in the perturbative region, considering the existing experimental data, and also in the nonperturbative region, at low-momentum transfer. A continuous phenomenological function is determined by means of three different models also calculating the corresponding finite value of the vector quark self-energy. These two quantities are used for the vector interaction of a Dirac relativistic model for the charmonium spectrum. The process required to fit the spectrum is discussed and the relationship with previous models is analyzed.

Colombia

Phenomenological Exploration of the Strong Coupling Constant in the Perturbative and Nonperturbative Regions

Detecting beyond the Standard Model (BSM) signals in high-energy particle collisions presents significant challenges due to complex data and the need to differentiate rare signal events from the Standard Model (SM) backgrounds. This study investigates the efficacy of deep learning models, specifically Deep Neural Networks (DNNs) and Graph Neural Networks (GNNs), in classifying particle collision events as either BSM signal or background. The research utilized a dataset comprising 214,000 SM background and 10,755 BSM events. To address class imbalance, an undersampling method was employed, resulting in balanced classes. Three models were developed and compared: a DNN and two GNN variants with different graph construction methods. All models demonstrated high performance, achieving Area Under the Receiver Operating Characteristic curve (AUC) values exceeding \(94\%\). While the DNN model slightly outperformed GNNs across various metrics, both GNN approaches showed comparable results despite different graph structures. The GNNs’ ability to explicitly capture inter-particle relationships within events highlights their potential for BSM signal detection.

Türkiye

Deep Learning Approaches for BSM Physics: Evaluating DNN and GNN Performance in Particle Collision Event Classification

We compute amplitudes for the \(g^* g^* \to q \bar q V^*\) process (two virtual gluons into a quark, an antiquark, and a boson) at the tree level using the spinor-helicity formalism. The resulting analytic expressions are much shorter than squared amplitudes obtained using trace methods. Our results can be used to expedite numerical calculations in phenomenological studies of the Drell–Yan process in high-energy factorization framework.

Spinor-helicity Calculation of the \(g^* g^* \to q \bar q V^*\) Amplitude at the Tree Level

The spin polarization of \({\mit \Lambda }\) hyperons produced in inclusive reactions with unpolarized protons on unpolarized targets has been studied for almost 40 years. The NA61/SHINE experiment at the CERN SPS has a great potential to study transverse polarization in \(p\)–\(p\) and \(p\)–\(A\) collisions. In this work, we discuss the impact of magnetic field and limited detector acceptance on the possible polarization measurement by this experiment. Our analysis shows that the magnetic field impact on the \({\mit \Lambda }\) polarization due to precession is one order of magnitude smaller than the detector acceptance-based polarization bias, and the identification of an experimental signal similar to that observed before by other experiments is possible.

Lambda Transverse Polarization in NA61/SHINE at the CERN SPS: Feasibility Studies

The fractal and phase transitional properties of each type of pions (i.e. \(\pi ^{\pm ,0}\)) through one-dimensional \(\eta \)-space, at an energy of \(\sqrt {s}=13\) TeV, have been studied with the help of the Scaled Factorial Moment (SFM) framework. To generate simulated data sets for \(pp\) collisions under the minimum bias (MB) condition at \(\sqrt {s}=13\) TeV, we have employed the Monte Carlo-based event simulator PYTHIA. Various parameters such as the Levy index \((\mu )\), degree of multifractality \((r)\), anomalous fractal dimension \((d_q)\), multifractal specific heat \((c)\), and critical exponent \((\nu )\) have been calculated. To study the Bose–Einstein (BE) effect due to identical particles (here pions), we have also derived these parameters for mixed-pion pairs (i.e. \(\{\pi ^{+},\pi ^{-}\}\), \(\{\pi ^{+},\pi ^{0}\}\), and \(\{\pi ^{-},\pi ^{0}\}\)) and we find that the effects of identical particles weakened for the mixture with respect to the individual distributions. The quest for the quark–hadron phase transition has also been conducted within the framework of the Ginzburg–Landau (GL) theory of second-order phase transition. Analysis revealed that for PYTHIA-generated MB events, there is a clear indication of the quark–hadron phase transition according to the GL theory. Furthermore, the values of the multifractal specific heat (\(c\)) for each \(\pi ^{+}, \pi ^{-}, \pi ^{0}\), and the mixture-pair data sets of pions generated by the PYTHIA model at MB condition indicate a transition from multifractality to monofractality in \(pp\) collisions at \(\sqrt {s}=13\) TeV.

India

Egypt

The Study of Strongly-intensive Observables for \(\pi ^{\pm ,0}\) in \(pp\) Collisions at LHC Energy in the Framework of PYTHIA Model

Weakly nonlocal (WNL) Quantum Field Theories (QFTs) may define a new class of UV-completions in particle physics and gravity, without introducing any new elementary particle. One problematic issue is how to realize spontaneous symmetry breaking without introducing an infinite tower of ghosts in the perturbative spectrum. In this article, a WNL extension of the Standard Model (SM) is proposed: the Fuzzy Standard Model (FSM). It is a smooth deformation of the SM based on covariant star-products of fields. This new formalism realizes electroweak symmetry breaking without ghosts at tree-level. We give evidence that the FSM exhibits Vainshtein screening, aka classicalization, in the deep-UV. This could solve the electroweak hierarchy problem if it occurs at the TeV-scale.

France

Ghost-free Electroweak Symmetry Breaking with Weakly Nonlocal Interactions

We show that the rank decomposition of a real matrix \(r\), which is a Spin(3,1) tensor, leads to \(2k\) Majorana bispinors, where \(k= \mathrm {rank}\: r\). The Majorana bispinors are determined up to local GL\((k, \mathbb {R})\) transformations. The bispinors are combined in pairs to form \(k\) complex Dirac fields. We analyze in detail the case \(k=1\), in which there is just one Dirac field with the well-known standard Lagrangian. The GL\((1, \mathbb {R})\) symmetry gives rise to a new conserved current, different from the well-known U(1) current. The U(1) symmetry is present too. All global continuous internal symmetries in the \(k=1\) case form the SO(2,1) group. As a side result, we clarify the discussed in literature issue whether there exist algebraic constraints for the matrix \(r\) which would be equivalent to the condition \(\mathrm {rank}\: r=1\).