Recent software advances now allow large-scale lattice studies of the Corrigan--Ramond large-$N_C$ limit of Yang-Mills theory coupled with a two-index antisymmetric fermion, providing a path to SUSY Yang-Mills. We are currently generating ensembles for $N_C=4,5,6$ for lattice spacings in the range $0.11 - 0.08$ fm. We report on two aspects of our work: the study of topological properties as well as estimates of discretisation effects. The first aspect is relevant since naively, fractional topological charges might be expected in our simulations. Using a gluonic definition of the topological charge combined with gradient flow, we perform an analysis of the effect of different discretisations of the kernel action, from which we identify and interpret quantitative differences between Wilson and over-improved flows such as DBW2. The second aspect is addressed by considering ratios of different reference flow times. We conclude that our current simulations might be affected by discretisation effects of order 10\%.

In this EPJ-Special Topics issue, we collect lecture notes from a summer school held at CERN in 2024. We provide a brief motivation for the selected topics and the format of the school as well as a short summary of each of the four lecture courses. The topics that were covered are “Dispersive Methods” (by Gilberto Colangelo), “Inverse problems” (by Luigi Del Debbio), “Quantum Computing” (by Zohreh Davoudi), and “Resurgence” (by Gerald Dunne).

We study SU(N_C) gauge theories with a single fermion in the two-index antisymmetric representation to predict the mesonic spectrum of supersymmetric 𝒩=1 SYM theories. Using gradient flow methods, we investigate fractional topological charges in N_C = 4 ensembles with varying lattice spacings. We show that the use of overimproved gauge actions (specifically the DBW2 action) in the smearing kernel stabilises the values of the topological charge already at moderate values of the flow time, while this is not the case for the standard Wilson flow.

We investigate properties of the topological charge for several SU(NC) gauge field ensembles for NC = 4, 5, 6 with a single fermion in the two-index antisymmetric representation, covering multiple lattice spacings at otherwise approximately constant physical parameters. Comparing the topological charge defined by the Wilson flow and the overimproved DBW2 flow we find that already at small flow times the latter stabilizes on discrete values. We provide evidence that as the lattice spacing is lowered the Wilson flow also separates into discrete sectors at earlier flow times. Adopting the DBW2 definition in the remainder of the analysis, we do not see any evidence of fractional topological charges, which could in principle appear at finite lattice spacing.

We examine one-flavour $SU(N_c)$ gauge theories, where $N_c$ denotes the number of colors, with one fermion in the antisymmetric representation as a candidate to approximate $\mathcal{N}=1$ super Yang Mills due to their equivalence in the large-$N_c$ limit. Summarising results on spectral evaluations of $N_c=3$, we will report on the progress of dynamical calculations for $N_c>3$. We discuss cut-off effects and challenges in configuration generation.

We use one-flavour QCD ($N_c=3$) as a proxy to understand $\mathcal{N}=1$ SYM. For our simulations, we use tree-level improved Wilson fermions and Symanzik improved gauge action. The hadron spectrum is obtained by using LapH smearing for different masses and simulation volumes. We also report on our efforts to increase the number of colours in our simulations, where we find that the simulations show increasing topological freezing for larger $N_c$.

The stochastic Laplacian Heaviside (LapH) method has proven to be successful in hadronic calculations. In this work, with charm-light spectroscopy in mind, we set up and optimise the LapH procedure limiting ourselves to the evaluation of two-point mesonic correlation functions. The calculations are performed on CLS ensembles with $N_f=2+1$ Wilson-Clover fermions on a $32^3\times64$ lattice with open boundary conditions. We analyse the interplay between the LapH parameters and the boundary effects, and implement a fitting procedure to isolate excitations coming from the border.

We discuss the main issues in dealing with heavy quarks on the lattice and shortly present the different approaches used. We discuss a selection of computations covering first the b-quark mass and the B(s) meson decay constants as the consolidated results (neglecting isospin breaking corrections). In the second part we consider recent calculations of form factors for tree-level semileptonic decays with emphasis on the tensions between the results produced by different collaborations. We propose benchmark quantities and tests suited to investigate the origin of such tensions. Finally, we review computations of the bag parameters parameterising neutral meson mixing and provide an overview on a few recent developments in the field.

We compute the spectrum of the low-lying mesonic states with vector, scalar and pseudoscalar quantum numbers in QCD with one flavour. With three colours the fundamental and the two-index anti-symmetric representations of the gauge group coincide. The latter is an orientifold theory that maps into the bosonic sector of $\mathcal{N} = 1$ super Yang-Mills theory in the large number of colours limit. We employ Wilson fermions along with tree-level improvement in the gluonic and fermionic parts of the action. In this setup the Dirac operator can develop real negative eigenvalues. We therefore perform a detailed study in order to identify configurations where the fermion determinant is negative and eventually reweight them. We finally compare results with effective field theory predictions valid in the large $N_C$ limit and find reasonably consistent values despite $N_C$ being only three. Additionally,the spin-one sector provides a novel window for supersymmetric dynamics.

The (semi)leptonic decay and mixing processes of B(s) mesons have been playing a crucial role in flavour physics. In particular, they contain important information for the investigation of the b−d unitarity triangle in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, and can be ideal probes of physics beyond the Standard Model. The charged-current decay channels B+ → lνl and B0 → πlνl, where l+ is a charged lepton with νl being the corresponding neutrino, are essential in extracting the CKM matrix element |Vub|. Similarly, the B to D(∗) semileptonic transitions can be used to determine |Vcb|. The flavour-changing neutral current (FCNC) processes, such as B → K(∗)l+l− and Bd(s) → l+l−, occur only beyond the tree level in weak interactions and are suppressed in the Standard Model. Therefore, these processes can be sensitive to new physics, since heavy particles can contribute to the loop diagrams. They are also suitable channels for the extraction of the CKM matrix elements involving the top quark that can appear in the loop. The decays B → D(∗)lν and B → K(∗)ll can also be used to test lepton flavour universality by comparing results for l = e, μ and τ . In particular, anomalies have been seen in the ratios R(D(∗)) = B(B → D(∗)τν)/B(B → Dlν)l=e,μ and R(K(∗)) = B(B → K(∗)μμ)/B(B → K(∗)ee). In addition, the neutral Bd(s)-meson mixings are FCNC processes and are dominated by the 1-loop “box” diagrams containing the top quark and the W bosons. Thus, using the experimentally measured neutral B0 d(s)-meson oscillation frequencies, ∆Md(s), and the theoretical calculations for the relevant hadronic mixing matrix elements, one can obtain |Vtd| and |Vts| in the Standard Model. At the Large Hadron Collider, decays of b quarks can also be probed with Λb and other bottom baryons, which can provide complementary constraints on physics beyond the Standard Model. The most important processes are the charged-current decays Λb → plν̄ and Λb → Λclν̄, and the neutral-current decay Λb → Λl+l−. Accommodating the light quarks and the b quark simultaneously in lattice-QCD computations is a challenging endeavour. To incorporate the pion and the b hadrons with their physical masses, the simulations have to be performed using the lattice size L̂ = L/a ∼ O(102), where a is the lattice spacing and L is the physical (dimensionful) box size. The most ambitious calculations are now using such volumes; however, many ensembles are smaller. Therefore, in addition to employing Chiral Perturbation Theory for the extrapolations in the light-quark mass, current lattice calculations for quantities involving b hadrons often make use of effective theories that allow one to expand in inverse powers of mb. In this regard, two general approaches are widely adopted. On the one hand, effective field theories such as Heavy-Quark Effective Theory (HQET) and Nonrelativistic QCD (NRQCD) can be directly implemented in numerical computations. On the other hand, a relativistic quark action can be improved à la Symanzik to suppress cutoff errors, and then re-interpreted in a manner that is suitable for heavy-quark physics calculations. This latter strategy is often referred to as the method of the Relativistic Heavy-Quark Action (RHQA). The utilization of such effective theories inevitably introduces systematic uncertainties that are not present in light-quark calculations. These uncertainties can arise from the truncation of the expansion in constructing the effective theories (as in HQET and NRQCD), or from more intricate cutoff effects (as in NRQCD and RHQA). They can also be introduced through more complicated renormalization procedures which often lead to significant systematic effects in matching the lattice operators to their continuum counterparts. For instance, due to the use of different actions for the heavy and

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon g-2 Theory Initiative to update the Standard Model prediction.

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.

The current precision reached by lattice QCD calculations of low-energy hadronic observables, requires not only the introduction of electromagnetic corrections, but also control over all the potential systematic uncertainties introduced by the lattice version of QED. Introducing a massive photon as an infrared regulator in lattice QED, provides a well defined theory, dubbed QEDM, amenable to numerical evaluation [arXiv:1507.08916]. The photon mass is removed through extrapolation. In this contribution we scrutinise aspects of QEDM such as the presence and fate of the zero modes contributions and we describe the determination of the photon mass corrections in finite and infinite volume. We demonstrate that the required extrapolations are well controlled using numerical data obtained on two ensembles which only differ in volume.

We numerically study QCD with a single quark flavour on the lattice probing predictions from effective field theories that are equivalent to minimal super-symmetric Yang-Mills theory in the large $N_c$ limit. The hadronic spectrum including excited states is analysed using one gauge coupling and several physical volumes and fermion masses. We use the LapH method and also compute disconnected diagrams. Lattice simulations with an odd number of Wilson fermions give rise to regions of configuration space with a negative fermionic weight entailing a sign problem. We perform a detailed analysis on the spectrum of the Wilson-Dirac operator and report on observed cases of a negative fermion determinant in our ensembles.

Infectious diseases are a threat for human health with tremendous impact on our society at large. The recent COVID-19 pandemic, caused by the SARS-CoV-2, is the latest example of a highly infectious disease ravaging the world, since late 2019. It is therefore imperative to develop efficient mathematical models, able to substantially curb the damages of a pandemic by unveiling disease spreading dynamics and symmetries. This will help inform (non)-pharmaceutical prevention strategies. For the reasons above we wrote this report that goes at the heart of mathematical modelling of infectious disease diffusion by simultaneously investigating the underlying microscopic dynamics in terms of percolation models, effective description via compartmental models and the employment of temporal symmetries naturally encoded in the mathematical language of critical phenomena. Our report reviews these approaches and determines their common denominators, relevant for theoretical epidemiology and its link to important concepts in theoretical physics. We show that the different frameworks exhibit common features such as criticality and self-similarity under time rescaling. These features are naturally encoded within the unifying field theoretical approach. The latter leads to an efficient description of the time evolution of the disease via a framework in which (near) time-dilation invariance is explicitly realised. As important test of the relevance of symmetries we show how to mathematically account for observed phenomena such as multi-wave dynamics. The models presented here are of immediate relevance for different realms of scientific enquiry from medical applications to the understanding of human behaviour. Our review offers novel perspectives on how to model, capture, organise and understand epidemiological data and disease dynamics for modelling real-world phenomena.

The ongoing pandemic has prompted the overexposure of Presidents of the Region and the antagonistic tension that some of these they showed against the Government, subjecting to a considerable stress test the principle of loyal cooperation. One reason in addition to critically rethink the form of regional government.

We generalise the epidemic Renormalization Group framework while connecting it to a SIR model with time-dependent coefficients. We then confront the model with COVID-19 in Denmark, Germany, Italy and France and show that the approach works rather well in reproducing the data. We also show that a better understanding of the time dependence of the recovery rate would require extending the model to take into account the number of deaths whenever these are over 15% of the cumulative number of infected cases.