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A summary of the recent ATLAS results at the LHC in Quantum Chromodynamics is given, covering a number of areas that reflect the work of the collaboration on the Bose–Einstein correlations in multi-particle events, the inclusive jet production, the measurements of jet substructure quantities in di-jet events, and the photon–photon scattering exclusive processes.

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Recently, a Pavia–Padova–Parma–Frascati group of theoreticians has suggested a novel approach to determine the leading order of hadronic contribution \(a_\mu ^{\rm (LO)had}\) to the muon \(g-2\) anomaly, consisting in a measurement of the running QED fine structure constant in the space-like region by the Bhabha \(\mu e\to \mu e\) scattering at CERN and an extraction of \(\Delta \alpha _{\rm had}^{(5)}(s)\) from the latter, to be crucial in determination of \(a_\mu ^{\rm (LO)had}\). In this contribution, it is demonstrated how, by one elaborated Unitary and Analytic model of electromagnetic structure of hadrons, one can predict behavior of \(\Delta \alpha _{\rm had}^{(5)}(s)\) before measurements carried out at CERN.

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Universal vector-meson coupling constants \(f_{\rho ^0}, f_\omega , f_\phi \) appear in the lepton decay widths of the corresponding vector mesons in a quadratic form, therefore, in their numerical evaluation from experimental values on \({\mit \Gamma }(V \to e^+e^-)\) one does not know their signs. It is demonstrated strong dependence of the signs of \(f_{\rho ^0}, f_\omega , f_\phi \) on the \(\omega \)–\(\phi \) mixing forms. However, by an application of the \(\omega \)–\(\phi \) mixing directly to the electromagnetic currents of \(\omega \) and \(\phi \) vector mesons and by a comparison of obtained results with the Kroll–Lee–Zumino electromagnetic current to be identified with a linear combination of the re-normalized \(\rho ^0\), \(\omega \) and \(\phi \) fields, signs of all coupling constants \(f_{\rho ^0}, f_\omega , f_\phi \) are specified.

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We scrutinize various holographic estimations of the deconfinement temperature within the bottom-up AdS/QCD models. A special emphasis is put on the recent idea of isospectral potentials in the holographic approach. It is demonstrated that different models from an isospectral family (i.e. , the models leading to identical predictions for the spectrum of hadrons with fixed quantum numbers) result in different predictions for the deconfinement temperature. This difference is found to be quite small in the scalar glueball channel but very large in the vector-meson channel which is often used for fixing parameters of holographic models. The observed stability in the former case clearly favors the choice of the glueball channel for thermodynamic predictions in AdS/QCD models, with the scalar glueball trajectory being taken from lattice simulations and used as a basic input in improved versions of the Soft Wall holographic model.

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In this paper, we review our recent series of works where we determine the parameters of light strange resonances using data on \(\pi K\rightarrow \pi K\) and \(\pi \pi \rightarrow K\bar K\) and model-independent dispersive methods or techniques based on complex analysis. We also advance some preliminary results on a model-independent determination of the \(\kappa \) or \(K^*_0(700)\) resonance parameters.

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In this paper, we review a recent analysis of the \(\eta ^{(\prime )}\pi \) system using COMPASS data. The extracted relative phases and intensities are fitted with a coupled-channel formalism fulfilling both unitarity and analyticity. As a result, a robust extraction of a single isolated exotic \(\pi _1(1600)\) is provided, decaying to both \(\eta ^{(\prime )}\pi \) final states, together with the determination of the resonance parameters of the \(a_2(1320)\) and \(a'_2(1700)\). No statistical significance for a second exotic state is found.

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An unambiguous definition of meson resonance masses requires a description of the associated phase shifts in terms of a manifestly unitary S-matrix and its complex poles. However, the commonly used Breit–Wigner (BW) parametrisations can lead to appreciable deviations. We demonstrate this for a simple elastic resonance, viz. \(\rho (770)\), whose pole and BW masses turn out to differ by almost 5 MeV. In the case of the very broad \(f_0(500)\) and \(K_0^\star (700)\) scalar mesons, the discrepancies are shown to become much larger, while also putting question marks at the listed PDG BW masses and widths. Furthermore, some results are reviewed of a manifestly unitary model for meson spectroscopy, which highlight the potentially huge deviations from static model predictions. Finally, a related unitary model for production amplitudes is shown to explain several meson enhancements as non-resonant threshold effects, with profound implications for spectroscopy.

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The center vortex model of the QCD vacuum is very successful in explaining the non-perturbative properties of QCD, especially confinement, chiral symmetry breaking and the topological charge of vacuum configurations. On the other hand, the center vortex model still suffers from a Gribov problem: Direct maximal center gauge and center projection can lead to an underestimation of the string tension in smooth configurations or after persistent simulated annealing. We discuss methods to identify center regions, whose boundaries evaluate to center elements, and want to improve the vortex detection: these regions might help to recognize vortices in configurations where maximal center gauge lost the vortex finding property.

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Modulo the scale of spontaneous breaking of Peccei–Quinn symmetry, the axion mass \(m_{a}(T)\) is given by the QCD topological susceptibility \(\chi (T)\) at all temperatures \(T\). From an approach tying the U\(_A(1)\) and chiral symmetry breaking and getting good \(T\)-dependence of \(\eta \) and \(\eta '\) mesons, we get \(\chi (T)\) for an effective Dyson–Schwinger model of nonperturbative QCD. Comparison with lattice results for \(\chi (T)\), and thus also for \(m_{a}(T)\), shows good agreement for temperatures ranging from zero up to the double of the chiral restoration temperature \(T_{\rm c}\).

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The Skyrme model is a low-energy effective field theory of strong interactions where nuclei and baryons appear as topological solitons, more concretely as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models have been proposed to overcome two of the main drawbacks of the theory, namely, the too large binding energies and the lack of cluster structures. In this paper, we shortly review how to address both issues by extending the standard Skyrme model with the inclusion of the rho meson and how important the pion mass contribution is.

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We discuss the photoproduction of resonances observed in the \(\pi ^+\pi ^-\) system. For the \(\gamma p\to \pi ^+\pi ^- p\) reaction, we consider two production mechanisms: the one-pion exchange known in the literature as the Deck mechanism and collective contribution of all other short-range exchanges which we parametrize in terms of a smooth function of \(s_{\pi \pi }\). We have found a very good agreement of the model with experimental mass distributions for partial waves \(S\), \(P\) and \(D\). Our calculations are in line with the expectation that while the \(P\)- and \(D\)-wave resonances \(\rho (770)\) and \(f_2(1270)\) are conventional \(q\bar {q}\) states, the \(S\)-wave \(f_0(980)\) resonance is rather a more loosely bound \(qq\bar {q}\bar {q}\) state.

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When an unstable ordinary quark–antiquark state couples strongly to other low-mass mesons (such as pions, kaons, \(D\)-mesons, etc.), the quantum fluctuations generated by the decay products dress the bare ‘seed’ \(\bar {q}q\) state and modify its spectral functions. The state is associated to a pole on the complex plane. When the coupling to the decay products is sufficiently large, a remarkable and interesting phenomenon takes place: dynamically generated companion states (or poles) might emerge. Some resonances listed in the PDG, such as the \(a_{0}(980)\), the \(K_{0}^{\ast }(700)\), and the \(X(3872)\), can be well-understood by this mechanism that we briefly review in these proceedings. On the other hand, we show that the \(Y(4008)\) and \(Y(4260)\) are not independent resonances (or poles), but manifestations of \(\psi (4040)\) and \(\psi (4160)\), respectively.

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NA48/2 results related to ChPT testing are presented. The most precise measurement of the charged kaon semileptonic form factors has been obtained from \(4.4 \times 10^6\) the \(K^\pm \rightarrow \pi ^0 e^\pm \nu _e\) (\(K^\pm _{e3}\)) and \(2.91 \times 10^6\) the \(K^\pm \rightarrow \pi ^0 \mu ^\pm \nu _\mu \) (\(K^\pm _{\mu 3}\)) events collected in 2004. In addition, the branching ratio of the \(K^\pm \to \pi ^\pm \pi ^0 e^+ e^-\) decay, that has not been observed so far, has been obtained from a sample of 4919 decay candidates with \(4.9\%\) background. The branching ratio in the full kinematic region is measured to be \((4.24 \pm 0.15) \times 10^{-6}\), which is in agreement with ChPT predictions.

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The decay \(K^{+} \rightarrow \pi ^{+}\nu \bar {\nu }\) with a very precisely predicted branching ratio of less than \(10^{-10}\) is one of the best candidates to reveal indirect effects of new physics at the highest mass scales. The NA62 experiment at CERN SPS is designed to measure the branching ratio of the \(K^{+} \rightarrow \pi ^{+}\nu \bar {\nu }\). In 2016, the first data set good for physics has been collected. The preliminary result on BR\((K^{+} \rightarrow \pi ^{+}\nu \bar {\nu })\) from the full 2016 data set is presented here. Due to the high beam energy and hermetic detector coverage, NA62 has also the opportunity to directly search for a multitude of long-lived beyond-Standard-Model particles, such as dark photons, dark scalars, axion-like particles, and heavy neutral leptons. An overview of the broader NA62 physics program with status and prospects will be illustrated.

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With the discovery of a doubly charmed \({\mit \Xi }_{cc}\) baryon, a somewhat forgotten issue of tetraquarks containing two heavy and two light (anti)quarks, \({\cal T}_{QQ}\), triggered theorist’s interest. We discuss quark model estimates of \({\cal T}_{QQ}\) masses and a model where the light sector is treated as a soliton. We show that this model has different large-\(N_{\mathrm {c}}\) limit than other approaches.

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Hot and dense QCD matter created in high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) manifests properties of strongly coupled liquid with very low viscosity. High statistics data and major upgrades of the STAR experiment started a new era of tomography of the QCD matter at RHIC using hard probes. In particular, the Heavy Flavor Tracker (HFT) enables precision measurements of open heavy-flavor hadrons and the Muon Telescope Detector (MTD) greatly improves quarkonium measurements. These studies are complemented by measurements of jet properties that provide further insights into the partonic energy loss in the QCD matter. In these proceedings, an overview of recent results on open heavy-flavor hadron, quarkonium, and jet production in Au+Au collisions at the top RHIC collision energy \(\sqrt {s_{NN}} = 200\) GeV in the center of mass per nucleon–nucleon pair measured with STAR is presented.

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We discuss the advantages of carrying out ultra-relativistic collisions of heavy projectiles on polarized deuteron targets, which allows to study the build up of elliptic flow through one-body observables. Predictions are extended to the case of other light nuclei with spin \(\ge 1\). We also mention the forthcoming experimental prospects. Results would shed light on the build-up of collectivity in light systems.

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While importance sampling Monte Carlo algorithms have proved to be a crucial tool for numerical studies in modern physics, they fail when we consider complex action systems. The density of states approach provides a way to simulate such systems and reduce the sign problem that afflicts them to a 1-dimensional oscillatory integral. In this work, we shall review the density of states approach as well as the Linear Logarithmic Relaxation algorithm and present some recent development concerning the control of systematics in this algorithm. The results of a benchmark study on the relativistic Bose gas shall be presented as well.

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We study the phase diagram of the 1+1 dimensional Gross–Neveu model at finite number of fermion flavors using the lattice field theory. Numerical results are presented, which indicate the existence of an inhomogeneous phase, where the chiral condensate is a spatially oscillating function.

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Correlation functions of the Landau gauge Yang–Mills theory are calculated from their equations of motion. Solutions for the three- and four-gluon vertices and the role of two-loop diagrams in the gluon propagator equation are discussed.

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We discuss previous results for the light scalar mesons as four-quark states as well as recent results for the heavy–light axialvector states using the Dyson–Schwinger and Bethe–Salpeter equations. We introduce a new technique for solving the axialvector heavy–light four-quark system.

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We discuss the description of chiral imbalance imprint in pion matter. It is based on the Chiral Perturbation Theory supplemented by medium induced chiral chemical potential in the covariant derivative. Such an implementation of chiral imbalance recently explored was in linear sigma model inspired by QCD. The relationship between two sigma models is examined. A possible experimental detection of chiral imbalance in charged pion decays inside the fireball is pointed out.

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While string models describe initial-state radiation in ultra-relativistic nuclear collisions well, they mainly differ in their end-point positions of the strings in spatial rapidity. We present a generic model where wounded constituents are amended with strings whose both end-point positions fluctuate and analyze semi-analytically various scenarios of string-end-point fluctuations. In particular, we constrain the different cases to experimental data on rapidity spectra from collisions at \(\sqrt {s_{NN}}=200\) GeV, and explore their respective two-body correlations, which allows to partially discriminate the possible solutions.