Papers

Modern machine learning is leading to substantial gains in precision, flexibility, and computational efficiency in fundamental physics. Statistical validation, uncertainty quantification, and robustness assessment are less systematically addressed. The VERaiPHY initiative (Validation & Evaluation for Robust AI in PHYsics) is a series of articles developed within the PHYSTAT programme, aimed at establishing statistical standards for the development, evaluation, and deployment of ML techniques. Each article focuses on a specific methodological domain from a statistics perspective and clarifies statistical questions, tests, and the interpretation of results. This opening article establishes the probabilistic, statistical, and machine learning foundations that the later contributions assume, together with the notation used throughout.

We investigate the polarization correlation of back-to-back gluon pairs in unpolarized $pp$ collisions and compute their density matrix. For gluon pairs produced through $q\bar{q}$ annihilation, the linear polarization correlation is sizable, even reaching unity when the final-state gluons are emitted perpendicular to the beam direction in the $q\bar{q}$ rest frame. Combining with the fact that their helicity remains maximally correlated across different scattering angle, the gluon pair system thus resides in a maximally entangled Bell state in this configuration. In contrast, for the $gg\to gg$ channel, both the helicity and linear polarization correlations are considerably suppressed, producing a separable state. Nonetheless, it still retains an appreciable linear polarization correlation of about $11\%$ at central scattering in unpolarized collisions. The linearly polarization correlation of the back-to-back gluon pair can further increase when the incoming gluons are circularly polarized. Employing the anisotropy of energy correlators, we demonstrate that the linear polarization correlation of gluon pairs can be extracted from the $\cos 2\Delta\Phi$ modulation.

Recently, the Super-Kamiokande Collaboration reported an indication of the diffuse supernova neutrino background (DSNB) with a statistical significance of $2.6\sigma$. Motivated by this possible discovery, we investigate the impact of axion cooling on the DSNB flux on the basis of long-term neutrino-radiation hydrodynamic simulations. We compare the observed flux and our models and obtain a $1\sigma$ upper limit $|g_{ap}|<1.3\times10^{-9}$ on the axion-proton coupling constant, which is comparable to the conventional limit based on the SN 1987A neutrino burst. In contrast to the SN 1987A bound, the DSNB constraint does not rely on the properties of a single observed supernova, because the DSNB represents the cumulative neutrino emission from a cosmic population of core-collapse events. More generally, this approach can be applied to other feebly interacting particles that modify protoneutron-star cooling.

Currently, the CP-violating phase $\delta$ is the least precisely known among the neutrino mixing parameters. In the coming years, accelerator neutrino experiments such as DUNE and Hyper-K will measure $\delta$, significantly increasing the precision. Such a measurement is usually performed by comparing the oscillation probabilities in the neutrino and antineutrino sectors, thereby directly observing the CP violation. This approach, however, has some downsides: in particular, it is more challenging to obtain good statistics in the antineutrino sector, leading to increased statistical errors. In principle, however, it is possible to determine $\delta$ by looking only at the neutrino sector, studying the energy dependence of the oscillation probability. We investigate this possibility in detail; we find that, if this approach is used, the main issue would be the degeneracies with other mixing parameters, which affect the sensitivity to $\delta$. Those parameters, however, have already been measured with great precision, which will increase even more in the next few years; if those constraints are taken into account by introducing Gaussian penalty terms in the $\chi^2$, it is possible to achieve better results focusing only on the neutrino sector, rather than using the standard approach. Those degeneracies could also be broken by exploring a wider range of $L/E$: this can be achieved, for instance, by increasing the neutrino energy. In this way, the total beam intensity could also increase due to the relativistic boost (however, the conversion efficiency could decrease, affecting the total luminosity). We find that if the relativistic boost increases the number of events in the high-energy configuration, the best performance would be achieved in such a set-up; otherwise, the optimal approach would be to focus only on the neutrino mode without changing the beam energy.

We investigate the axial Ward identity for massive fermions under a constant magnetic field at arbitrary strength, maintaining an arbitrary spacetime configuration of a perturbative electric field. We show that a spatially modulated electric field prevents the exact cancellation between the anomaly and pseudoscalar terms, generating a local axial-charge source even in the adiabatic regime where the frequency is subthreshold to massive-fermion production. Remarkably, unlike conventional magnetic responses, this charge generation is dominated not by the contribution of the lowest Landau level, but by those of the higher Landau levels. Our findings provide a microscopic foundation for anomaly-induced transport and anomalous optical responses in gapped systems. In particular, we find that the spatially modulated chiral magnetic effect in weakly gapped Weyl semimetals that exhibits a linear suppression of the magneto-resistance by the magnetic-field strength instead of the renowned quadratic suppression.

The origin of fermion masses and flavor mixing is often obscured by standard Euler-angle parameterizations, which mask the underlying connection between physical observables and Yukawa couplings. We prove that introducing a single, remarkably weak yet physically grounded commutation hypothesis, $[\mathbf{M}_R^2, \mathbf{M}_I^2] = 0$, on the Hermitian mass-squared matrix $\mathbf{M}^2 = M \cdot M^\dagger$ systematically reduces a general 18-parameter complex mass matrix $M$ down to a 5-parameter form per sector that admits exact analytic diagonalization. The resulting mass eigenvalues are closed-form algebraic expressions that completely bypass the transcendental Cardano trigonometric reduction required for generic Hermitian matrices, while the diagonalizing unitary matrix $U_f$ depends solely on two parameters that form a dimensionless 2D geometric flavor-ratio vector $\mathbf{v}_f=(x,y)$. Combining two such sectors yields the physical CKM/PMNS mixing matrix directly as $V = U_1^\dagger(\mathbf{v}_1) \cdot U_2(\mathbf{v}_2)$, establishing a direct, first-principles analytical bridge from raw Yukawa couplings to fermion masses and mixing matrices without intermediate phenomenological inputs. Finally, we highlight that this exact leading-order baseline enforces an exact four-fold moduli degeneracy among mixing elements, pointing directly toward non-commuting extensions for full phenomenological precision.

The leptonic decays of the $D_s^+$-meson have received considerable attention in recent years. In this work, we perform a precise calculation of the decay constant $f_{D_s^+}$ using the QCD sum rules method within the background field theory framework. In our calculation, we fully include the quark propagator contributions up to dimension-six condensates. By adopting two different constraint schemes, we obtain $f_{D_s^+}^{\text{(I)}} = 253.0_{-3.1}^{+3.3}\ \text{MeV}$ and $f_{D_s^+}^{\text{(II)}} = 251.8_{-1.3}^{+1.4}\ \text{MeV}$, respectively, both of which are in good agreement with existing theoretical and experimental results. The conventional scheme follows the standard Borel window criteria, while the derivative scheme reduces the dependence of the decay constant on the Borel parameter through an auxiliary function. Based on these decay constants and incorporating the NLO electroweak radiative corrections, we further calculate the branching fractions for the three leptonic decay channels for both schemes. Combined with the latest branching fraction $\mathcal{B}(D_s^+ \to \mu^+ \nu_\mu)$ from the PDG, we extract the CKM matrix elements $|V_{cs}|^{\text{(I)}} = 0.967 \pm 0.012$ and $|V_{cs}|^{\text{(II)}} = 0.970 \pm 0.005$ from the two schemes, respectively.

Neutron-star cores hold the only known matter in the universe that is simultaneously cold and strongly interacting, compressed beyond nuclear density into a state of unknown composition. The equation of state links stellar masses, radii and tidal deformabilities to this regime, but recovering this key quantity from sparse observations is an ill-posed inverse problem. Existing analyses bury a prior in a fixed functional form, unevenly weighting admissible solutions and biasing the result. We reconstruct the equation of state with a denoising diffusion model that keeps prior, physics and data separate: it learns an inspectable, physically motivated prior anchored to first-principles nuclear theory, while perturbative-QCD and astrophysical constraints are imposed exactly. Future measurements therefore will update the posterior by reweighting alone, without retraining or resampling. The inferred radius of 12.6 km and tidal deformability of 469 at 1.4 solar masses reproduce Gaussian-process and heavy-ion-informed inferences despite a far broader prior. We find near-conformal but still stiff matter in the heaviest stars, consistent with a gradual hadron-quark crossover and disfavouring a strong first-order phase transition. More broadly, coupling a learned prior to exactly enforced physics establishes a template for ill-posed inverse problems where theory and data constrain different regions.

In this study, we investigate the ground-state masses, magnetic moments, transition magnetic moments, radiative decays, and heavy-to-heavy semileptonic decay rates, including their corresponding branching fractions of triply heavy baryons (THBs). The ground-state masses of the involved baryons are evaluated by numerically solving the six-dimensional hyperradial Schrödinger equation within the hypercentral constituent quark model (hCQM), incorporating both hyper-Coulomb and linear confinement potentials along with spin-dependent interactions. The electromagnetic properties are calculated using the spin-flavour wave functions and the effective constituent quark masses of the baryon. The semileptonic $b \rightarrow c$ decay widths are computed using the Isgur–Wise function within the heavy-quark spin symmetry, from which the corresponding branching ratios and lepton flavour universality ratios are also determined.

We investigate density-induced conversion of neutrons into a neutral dark baryon $\chi$ in cold, charge-neutral, $\beta$-equilibrated neutron-star matter containing hyperons and all $\Delta(1232)$ quartet. The hadronic sector is modeled within a density-dependent covariant density-functional framework using the DDME2 parametrization. A scalar Higgs portal is included as a possible interaction channel between the visible and dark sectors, although its mean-field contribution is negligible for the couplings adopted here. Unlike fixed dark-matter admixture models or scenarios in which nucleon-to-DM conversion is driven by Higgs exchange, the $\chi$ abundance is determined self-consistently from chemical equilibrium and baryon-number conservation. We find that hyperons and $\Delta$ resonances alter the neutron chemical potential, delay the onset of $\chi$, and suppress its abundance relative to nucleonic matter. This competition induces characteristic changes in the equation of state, particle fractions, sound speed, and adiabatic index. For $m_\chi=1250$, $1300$, and $1400$ MeV, the maximum masses of the complete $N+Y+\Delta+\chi$ configurations are $1.806$, $1.899$, and $2.024,M_\odot$, respectively, indicating that the massive-pulsar constraint disfavors the lighter dark-baryon benchmarks. The radial profiles further show that for $m_\chi=1400$ MeV, $\chi$ is confined to the inner core of the most massive stars, while canonical configurations remain essentially unaffected. Thus, the stellar modifications arise primarily from conversion-induced rearrangement of the equilibrium composition rather than from Higgs-mediated interactions. These results highlight the importance of treating conventional non-nucleonic degrees of freedom and density-generated dark baryons on an equal footing when assessing the astrophysical viability of dark-sector extensions of dense matter.

It has been proposed that primordial quark pellets or PQPs –ultra-dense quark-matter mini- stars– formed at $T\sim 1$ GeV may be a good candidate accounting for the dark matter of the universe. If correct, dark matter would consist of very compact objects with a maximum mass of $10^{-2} \ M_\odot$ and radii of approximately 100 m, although smaller objects would be much more abundant and encompass the bulk of the dark matter content. Here we describe a viable formation mechanism based on the enhancement of the local baryon density when supra-horizon Peccei-Quinn domain walls formed at an earlier epoch sweep and accumulate quarks and gluons before entering the horizon. Assuming an efficient baryon concentration by contracting Peccei-Quinn domain walls, we derive the resulting primordial quark pellet mass spectrum, minimum mass and cosmological abundance.

Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.

Ostrogradsky's theorem shows that higher-derivative dynamical systems inevitably yields a Hamiltonian featuring a ghost mode that is unbounded from below. However, we argue that this theorem is inapplicable to gravitational systems, as the Hamiltonian constraint, which encodes background independence by dictating that the total Hamiltonian vanishes, holds strictly. The ghost mode obeying this constraint constitutes an indispensable component in the construction of space and time. Nevertheless, it should be underscored that the use of the weak-field (graviton) approximation, being a background-dependent scheme presupposing the existence of absolute time, invokes this theorem; consequently, it is allowed only in the domain below the Planck scale, where second derivative terms dominate.

In the $U(1)_X$ vector-like fermion model ($U(1)_X$VLFM), the Standard Model(SM) gauge group is extended with an additional $U(1)_X$ symmetry. Vector-like fermions and right-handed neutrinos are introduced, providing new sources of lepton flavor violation(LFV). In this paper, we perform a detailed study of the LFV decays $l_j \to l_i \gamma$ (with $j = \tau, \mu$; $i = \mu, e$; $i \neq j$) in this model. The numerical results show that, in certain parameter regions, the branching ratios of these processes can become large enough to be probed in future experiments. This work provides important theoretical guidance and constraints for exploring new physics beyond the SM.

We respond to arXiv:2607.08904, which commented on our previous work constraining neutrino-dark matter interactions from IceCube observations of neutrinos from active galactic nuclei.

Modern Bayesian theory-to-data comparisons for jet-medium interactions, such as [Phys. Rev. C 111,054913 (2025)], are lacking the careful accounting of theoretical systematic uncertainties included within their uncertainty budget. Tree-level gluon-gluon scattering is revisited to establish a framework capable of quantifying theoretical systematic uncertainties to be used in Bayesian jet-medium constraints. The behavior of tree-level scattering in thermal QCD is examined in detail, finding deviations away from the commonly used approximations. Deviations in the scattering rate affect jet-medium transport coefficients at the partonic level, leading to a more intricate kinematic dependence for $\hat q$ and $\hat e$ than, say, the well-known logarithmic behavior. These deviations away from well-known behavior are used to estimate theoretical systematic uncertainties in Bayesian analysis.

We examine the behavior of tree-level scattering in thermal QCD at high energies and find significant deviations away from the commonly used approximations [Phys. Rev. D 44, 1298 (1991), Phys. Rev. D 44, R2625 (1991), Phys. Rev. D.77, 014015 (2008), Phys. Rev. D. 77.114017 (2008)]. These deviations in the scattering rate also affect jet-medium transport coefficients at the partonic level, leading to a different kinematic dependence of the transverse momentum broadening per unit length $\hat{q}$. As scattering rates and $\hat{q}$ are used by large-scale Monte Carlo simulations of jets in the quark-gluon plasma (QGP), such as [Phys. Rev. C 111,054913 (2025)], current constraints on $\hat q$ are biased owing to the approximations used therein. Besides theoretically improving $\hat q$, the differences between the $\hat q$ herein and the approximate $\hat q$ used in jet Monte Carlo simulations are used to construct a theoretical systematic uncertainty, which in turn can be employed to devise a covariance matrix for $\hat q$ and enables updating the uncertainty bands on $\hat q$ obtained by Bayesian analysis.

We study the forward-backward asymmetry in the three-body decay process $H\to Z\gamma\to\overline{f}f\gamma$, induced by complex form factors in the $HZ\gamma$ vertex. To estimate its magnitude, we derive constraints on the real and imaginary parts of the $CP$-violating form factor $h_3^{Z\gamma}$ using current LHC measurements, obtaining upper limits of about $0.9$ GeV. These bounds are of the same order of magnitude as those derived from electric dipole moments (EDM). We find that the asymmetry can reach values of order $10^{-1}$ and may be accessible at the HL-LHC.

Gauge theories like lattice QCD present a complex problem for quantum simulation. In a basis where the electric part of the Hamiltonian is simple, the magnetic part, generally expressed as a sum over the plaquette operators of the lattice, is quite complicated, producing correlated transitions between several link and site degrees of freedom. We provide an efficient block encoding of the plaquette operator in the irrep basis, a refinement of the electric basis where the internal gauge-variant degrees of freedom are integrated out. The construction removes the plaquette matrix element scaling wall which has been a significant barrier for other approaches in this basis. The algorithm leverages a convenient factorization property of the matrix elements, cheap classical precomputation, and quantum oracles built from lookup tables and programmed rotations.

We revisit the $CP$-odd form factor in the $HWW$ vertex within the Standard Model (SM), which is induced only at the one-loop level when one of the $W$ bosons is off-shell. To the best of our knowledge, the numerical evaluation of this form factor is presented for the first time. The relevant contributions from quark loops are of order $10^{-5}$, well below the current experimental sensitivity. The phenomenological implications are studied through asymmetries in unpolarized and polarized observables in three-body decays.

The nature of the $X(3872)$ exotic hadron remains one of the most debated questions in hadron spectroscopy. We calculate its magnetic moment within a non-relativistic quark model that includes the three-body force arising from the cubic Casimir operator of $SU(3)_C$ with consistent dimensional analysis. Unlike previous works that used an uncontrolled large coupling, we fix the three-body strength using the realistic value of $\sim 10$–$20$ MeV extracted from the recent analysis of Noh et al.~(2024) based on lattice QCD and baryon spectroscopy. We find that the magnetic moment predictions fall into two distinct regions: the pure color-singlet configuration yields $\mu_X = -0.99 \pm 0.02\,\mu_N$, while the compact configurations yield $\mu_X = -1.17$ to $-1.23\,\mu_N$. The difference between the two compact scenarios ($0.06\,\mu_N$) is comparable to the systematic uncertainty of the model ($\sim 0.15\,\mu_N$) and should be interpreted with caution. However, the distinction between the pure color-singlet and the compact scenarios ($\sim 0.18$–$0.24\,\mu_N$) is larger than the estimated model systematic uncertainty and may provide a qualitative structural indicator. We emphasize that the pure color-singlet configuration is a simplified proxy for a molecule and does not represent a physical $D^0\bar{D}^{*0}$ molecule with large spatial extent. A full molecular treatment would require coupled-channel dynamics and long-range pion-exchange potentials, which are beyond the scope of this work. We also resolve a long-standing dimensional inconsistency in the cubic Casimir three-body force formulation and demonstrate through a detailed sensitivity and uncertainty analysis that our conclusions are robust for the physically relevant range of the three-body coupling.

While localized astrophysical sources can generate macroscopic graviton squeezing, their observable quantum signatures at far-field detectors remain unresolved. In this work, we investigate the propagation dynamics of the squeezed states using spatial quantum optics methods to evaluate correlation functions accessible to a local observer. Crucially, we reveal a severe kinematic conflict in same-cone measurements, which highly suppresses local quantum coherence. Consequently, these macroscopically squeezed states appear classically thermal to a single detector. Our results demonstrate that global squeezing does not guarantee local observability, and the measurable quantum signatures may be significantly weaker than what would be expected from the overall squeezing parameter of the state.

Stochastic gravitational-wave backgrounds from different primordial mechanisms can exhibit identical peak frequencies and amplitudes, leaving their origin degenerate. We show that this degeneracy can be broken by the broadband spectral response of the gravitational-wave source. By comparing scalar-induced and gauge-field-induced gravitational waves with the same primordial spectral profile and cosmological evolution, we isolate the imprint of the tensor-source dynamics. Although both mechanisms exhibit the same infrared scaling, they develop distinct spectral shapes near the peak and different ultraviolet asymptotes. The local spectral index $n_{\rm gw}$ and its running $\alpha_{\rm gw}$ further characterize this source-dependent evolution, providing a spectral fingerprint beyond the peak observables. These results show that broadband, multi-frequency observations can probe the production mechanism of a primordial gravitational-wave background even when its peak frequency and amplitude are degenerate.

We investigate the production of four Higgs bosons via gluon fusion at the high-luminosity LHC. We construct a phenomenological analysis of the eight-$b$-jet final state and use a multivariate analysis to derive expected simultaneous constraints on the triple and quartic Higgs boson self-coupling modifications. At 95% confidence level, the resulting region projects onto $-10.3<c_3<11.2$ and $-222<d_4<234$, where $c_3=\kappa_3-1$ and $d_4=\kappa_4-1$. We also examine how quadruple-Higgs boson production can enter a triple-Higgs boson signal region requiring at least six $b$-tagged jets. In addition, we consider two extensions of the Standard Model scalar sector: a one-real-singlet extension yielding the direct resonant process $pp\rightarrow S\rightarrow hhhh$, and a two-real-singlet extension yielding the cascade $pp\rightarrow h_3\rightarrow h_2h_2\rightarrow (hh)(hh)$, where $S$, $h_2$ and $h_3$ are new scalar resonances. For these processes, we derive expected upper limits on the quadruple-Higgs boson production cross sections as functions of the new scalar masses.

A fundamental open question in hadron spectroscopy is whether the radial excitation ladder of quarkonia truncates at a finite level—a possibility that would challenge the conventional quark-antiquark bound-state picture and offer decisive clues to the nonperturbative strong interaction. Taking advantage of the newly observed high-mass hadronic states, we address this issue by solving a screened Godfrey–Isgur Hamiltonian for charmonium and bottomonium using the Gaussian expansion method. The calculated spectra saturate at $4.74\,\mathrm{GeV}$ ($c\bar{c}$) and $11.67\,\mathrm{GeV}$ ($b\bar{b}$), while root-mean-square radii grow to $\sim10\,\mathrm{fm}$—an order of magnitude above the confinement scale—where adjacent mass gaps drop below $10\,\mathrm{MeV}$. Combining a threshold-based mass-gap criterion, defined by the onset of mass–radius decoupling, with additional diagnostics, we locate the operational upper radial limits at $n\approx8$–$10$ for charmonium and $n\approx12$–$13$ for bottomonium. Beyond these limits, the conventional $q\bar{q}$ description ceases to apply. This work provides the first quantitative determination of these upper limits, and the proposed criterion is directly testable with forthcoming high-statistics data from BESIII, Belle II, and LHCb.

That the gluons of quantum chromodynamics self-interact with a strong coupling suggests the possibility of hadrons in which the gluonic field plays an essential role: Glueballs in which gluons stick together to produce a hadron in which no quarks are required, and hybrids in which an excited gluonic field couples to quarks. This chapter presents our contemporary theoretical understanding of such states, and the challenges associated with definitively identifying their presence within the experimental spectrum of hadrons.

We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $\epsilon$ on a lattice of volume $V$ at bare coupling $g$ is bounded as $16n_A V + 12n_f V$, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{\pi^2\epsilon} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}\pi^3\epsilon^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy $E'$, and $n_f$ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as $O(n_A^4 V^{4/3}) + O(V^{5/3})$ per Trotter step for fixed $n_f\leq 6$. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.

A warped extra dimension in a five-dimensional (5D) anti-de Sitter (AdS) background was introduced in 1999 by Lisa Randall and Raman Sundrum to solve the gauge hierarchy problem in particle physics. As a bonus, a holographic interpretation in terms of four-dimensional (4D) conformal field theories (CFTs) was found. Interestingly enough, another 5D background, linear dilaton (LD), was found to have a holographic interpretation in terms of Little String Theory. In this review, we will show how a set of 5D backgrounds, parametrized in terms of a real parameter $\nu$, generalizes both theories and gives rise, in particular, to AdS for $\nu=0$ and to LD for $\nu=1$. Furthermore, working in the 5D theory, we will consider applications of the LD background to: (i) particle physics, so that the 5D Planck scale can be lowered to sub-Planckian values, and (ii) Brane World Cosmology (BWC), based on the appearance of an extra vacuum characterized by a 5D black hole. In all cases, we find a gapped continuum for bulk propagating fields, which makes a connection with unparticles. In the case of BWC, we also point out the existence of a pressureless holographic fluid that could play the role of dark matter (DM), with feeble (gravitational) interactions with the Standard Model (SM), decoupled from the thermal SM bath, and generated by a freeze-in mechanism after inflation. We also point out the additional possibility of identifying DM with a long-lived, feebly interacting massive graviton, as an isolated resonance generated by radiative corrections to the continuum graviton propagator self-energy.

In order to exploit the full potential of the LHC and future colliders, high-precision calculations of a very wide range of observables are crucial. Automated tools for next-to-next-to-leading order calculations of perturbative scattering amplitudes are therefore a highly desirable goal. So far, we have developed several major ingredients of such a tool in the OpenLoops framework. In our approach we split the calculation of scattering amplitudes into three components: loop momentum tensor integrals, the corresponding process-dependent tensor coefficients, and the interplay of $(D-4)$-dimensional parts of the integrand with divergences of the integrals. In these proceedings, we present a new recursive algorithm to reduce arbitrary two-loop tensor integrals to scalar integrals, which has been implemented into an efficient numerical tool. We also implemented a first version of the subsequent reduction to master integrals, which allows for a full validation of the algorithm. We present a first successful validation computation and discuss its dependence on the precision of the externally computed master integrals.

It is well-established that at low baryon chemical potential, the transition from the confined hadronic phase to the deconfined partonic phase is a smooth crossover rather than a first or second-order phase transition. We develop a thermodynamically consistent hybrid equation of state to study the effect of global rotation on the equation of state across the QCD crossover that interpolates the hadronic and partonic phases. The temperature dependence of normalized thermodynamic observables, such as entropy density ($s/T^3$), pressure ($P/T^4$), energy density ($\varepsilon/T^4$), specific heat ($C_V/T^3$), and the square of speed of sound ($c_s^2$) in presence of rotation are investigated. The effect of non-zero chemical potential on thermodynamic quantities in presence of rotation is also studied. Our results show that increasing chemical potential enhances the thermodynamic quantities, whereas rotation suppresses them in the crossover region. Further, we investigate the effect of rotation on the conserved numbers susceptibilities and their correlations as a function of temperature. The susceptibilities and their correlations exhibit a systematic enhancement with increase in rotation in both the hadronic and partonic phases. These findings provide new insights into the interplay between rotation and QCD thermodynamics, which can have important implications for rapidly rotating strongly interacting matter produced in ultra-relativistic heavy-ion collisions.