We determine the minimum value of thrust for a number of \(N\)-particle configurations. For \(N=5\) in three dimensions, an exact result is found for the first time. For larger \(N\), we obtain numerical results through optimisation. When a definite value cannot be reliably identified, the results are analysed in the context of Extreme Value Theory, using a Maximum Likelihood Estimate and a Bayesian analysis. Results are given for three spatial dimensions, two dimensions, and selected cases in \(d\) dimensions. Abstract Published by the Jagiellonian University 2026 authors

France

M. Cacciari

A Thrust to Trust Minimum Thrust

A study of retardation models for the hadronic quark interaction is performed starting from a coordinate-space calculation that elaborates a classical electrodynamics procedure. The possibility of constructing a corresponding quantum operator is critically analyzed also performing some numerical matrix element calculations. A comparison of the developed model with the Feynman diagram interaction at tree-level is studied, showing a substantial physical correspondence of the two models. Possible applications and generalizations are discussed. Abstract Published by the Jagiellonian University 2026 authors

Colombia

M. De Sanctis

A study of Retardation Models for Phenomenological Interactions in Hadronic Physics

We study free open fermionic strings on a non-commutative phase-space. Modified super-Virasoro algebras in both the Ramond and Neveu–Schwarz sectors acquire non-commutativity anomalies, and this non-commtativity breaks also the Lorentz symmetry and give a non-diagonal mass operator. Redefining the Fock space diagonalizes the mass operator. Extra constraints on non-commutativity parameters cancel the anomalies, restore the standard spectrum, and make the GSO projection possible. Abstract Published by the Jagiellonian University 2026 authors

Algeria

M.A. Abdelmoumene

N. Belaloui

Non-commutative Phase-space Effects in Fermionic String Theory

We study the thermodynamics of the quark–gluon plasma using an effective 2-flavor Polyakov–Nambu–Jona-Lasinio (PNJL) model extended by a quasiparticle description for quarks and gluons, incorporating temperature-dependent quark masses within the PNJL framework. Two variants, Quasiparticle Model-I and Quasiparticle Model-II, are implemented to investigate bulk thermodynamic observables such as pressure, energy density, entropy density, specific heat, and the speed of sound. The combined framework yields a robust baseline for the description of hot QGP dynamics in the high-temperature regime at vanishing chemical potential and zero magnetic field. Systematic comparison with lattice QCD results shows excellent agreement and a clear improvement over conventional PNJL implementations. We observe that both variants complement each other, offering mutually consistent insight into quasiparticle mass effects and medium response in the deconfined phase. This mutual consistency validates the physical foundation of the overall quasiparticle mechanism, reinforcing the credibility of the calculated Equation of State. Finally, the quasiparticle model extension improves PNJL from a descriptive tool to a more qualitative phenomenological approach, enabling an improved description of the strongly interacting quark–gluon plasma. Abstract Published by the Jagiellonian University 2026 authors

India

Y. Kumar

H. Aggarwal

R.S. Laishram

P. Jain

O. Prakash

S. Tyagi

P. Bangotra

V. Kumar

Y. Goswami

M.K. Sahu

Thermodynamical Analysis of QGP Using Effective PNJL Model with Quasiparticle Approach

Where do gauge symmetries come from? This article develops the idea that the Standard Model might be emergent, with its gauge symmetries dissolving in some phase transition deep in the ultraviolet. The (meta)stability of the Higgs vacuum may be pointing to some new critical phenomena at very high energy scales, with the Higgs connecting physics at LHC laboratory energies to that in the deep ultraviolet. In the emergence scenario, the dark energy scale comes out similar to the size of light Majorana neutrino masses. These two quantities appear at the same order in a low-energy expansion in inverse powers of the scale of emergence, about \(10^{16}\) GeV. Dark matter candidates include axions and phonon-like excitations of degrees of freedom above the scale of emergence. Possible tests of these ideas involve neutrinos as well as gravitational-waves-related signals from the early Universe observables, which are sensitive to physics at very high energy scales. Abstract Published by the Jagiellonian University 2026 authors

Poland

S.D. Bass

Emergent Gauge Symmetries in Particle Physics and Cosmology

The internal structure of hadrons is characterized by form factors which correspond to matrix elements of currents. Among those, the stress-energy-momentum tensor is a universally conserved quantity providing the gravitational form factors, from which mechanical properties may be derived via the response to the space-time fluctuations. They have received much attention due to their role as moments of the Generalized Parton Distributions, where the stress-energy-momentum tensor couples to two photons, and more recently, due to the explicit lattice QCD determination for the pion and nucleon. In these lectures, we attempt a pedagogical review of the topic from a purely hadronic point of view, based on the notion of dispersion relations, meson dominance, and parton–hadron duality. We show that despite the overwhelming simplicity of the approach, a rather successful description of the lattice QCD data is achieved. Abstract Published by the Jagiellonian University 2026 authors

Spain

E. Ruiz Arriola

W. Broniowski

Particle Seismology: Mechanical and Gravitational Properties from Parton–Hadron Duality

This year marks the \(350^{\mathrm {th}}\) anniversary of the discovery of the first animalcula (little animals) by van Leeuwenhoek in 1676. Flavour physics makes it possible to search for new animalcula at distance scales far shorter than those resolved by van Leeuwenhoek in 1676, and even shorter than those directly accessible at the Large Hadron Collider and the planned colliders in this century. I summarize various strategies for achieving this goal. While precise measurements of a wide variety of observables and their precise theoretical calculations, both within the Standard Model (SM) and beyond it, are indispensable in this context, in my view, it is crucial to develop strategies for the search for New Physics (NP) that go beyond the global fits that are very popular today. While effective field theories such as WET and SMEFT are formulated in terms of Wilson coefficients of the relevant operators, with correlations characteristic of the SM and of specific NP scenarios, the most direct tests of the SM and its extensions are, in my opinion, correlations among different observables, like branching ratios of numerous decays, that are characteristic of particular new animalcula at work. Abstract Published by the Jagiellonian University 2026 authors

Germany

A.J. Buras

Hunting New Animalcula with Flavour Changing Processes

In a recently proposed approach to testing models of inflation by Cosmic Microwave Background (CMB) radiation, the reheating temperature is directly expressed in terms of the CMB observables. Its model-independent bounds translate in a given model into narrow ranges of those observables. In that approach, we analyse the polynomial class of the \(\alpha \)-attractor inflaton potential models (P-models), in a broad range of polynomials and with the inflaton decays and fragmentation in the reheating period taken into account. The predictions for the CMB observables, the scalar spectral index \(n_{\mathrm {s}}\) and tensor-to-scalar ratio \(r\), are compared with the Planck and Planck combined with ACT data. Both can be accommodated by that class of the \(\alpha \)-attractor models. The sensitivity of the results of that comparison to the reheating temperature and to the upper bound on the ratio \(r\) is clearly demonstrated. Abstract Published by the Jagiellonian University 2026 authors

M. Marciniak

M. Olechowski

S. Pokorski

Testing \(\alpha \)-attractor P-model of Inflation by Cosmic Microwave Background Radiation

We examine the Regge theoretical properties for the scaling observed in \(pp\) elastic scattering differential cross sections at the LHC. A positive signature amplitude (&lt;span class="it"&gt;i.e.&lt;/span&gt; the Pomeron) with scaling properties has been derived. It is found to describe the dip–bump region of momentum transfer at LHC energies in agreement with data. We derive the analytic continuation in the whole plane of the \(t\)-channel partial waves of index \(l_t\) specific to the Regge formalism. The analytic form of the partial-wave amplitude exhibits a specific scaling property without singularities, except for a series of poles in the \(l_t\) real axis at fractional values. Abstract Published by the Jagiellonian University 2026 authors

R. Peschanski

B.G. Giraud

The Scaling Pomeron

This contribution reviews recent progress in the low-lying scalar mesons and glueballs. We propose a new classification for the scalar nonet that includes \(f_0(980)\) and \(a_0(980)\) as the lowest states, while we identify \(f_0(1500)\) as a primary glueball candidate. We demonstrate that the production yields of these states in heavy-ion collisions are mutually consistent across statistical, coalescence, and S-matrix frameworks. To investigate their internal structure, we move beyond standard phenomenology by describing glueballs as topological solitons. This approach yields an energy spectrum in excellent agreement with lattice QCD and experimental data, while interpreting \(f_0(2470)\) as a tightly bound glueballonium to explain its anomalously long lifetime. This non-perturbative framework provides a predictive basis for the future experimental verification of exotic scalar states. Abstract Published by the Jagiellonian University 2026 authors

C. Sasaki

Selected Topics in Quark–Hadron Physics: From Scalar Nonets to Topological Glueballs