Papers

We generalise the SoftSERVE framework for the automated computation of soft functions involving final-state heavy quarks in back-to-back kinematics up to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our algorithm employs suitable phase-space parameterisations for both massive and mixed massless-massive contributions, allowing for an efficient numerical evaluation. Focusing on SCET$_\mathrm{I}$ observables that satisfy non-Abelian exponentiation, we present explicit results for the 0-jettiness soft function in hadronic top-quark pair production in the form of two-dimensional grids. We describe the renormalisation procedure in detail and discuss the singular behaviour of the tripole colour correlations in the threshold limit.

We assess the prospects for inclusive heavy-quark-pair electroproduction in electron-proton ($ep$) and electron-nucleus ($e$A) collisions, alongside double-charm-pair ($D^0 \bar{D}^0$ and $D^0D^0$) electroproduction in $ep$ collisions, during the early operational phase of the Electron-Ion Collider (EIC). Based on the anticipated beam energies and luminosities of the EIC, we estimate the total cross sections and differential distributions for photon virtuality $Q^2$, heavy-quark transverse momentum, and rapidity. This analysis evaluates different Bjorken-$x$ ($x_{\rm Bj}$) intervals across a range of $Q^2$ values. Expected event yields are estimated from the projected integrated luminosities of the early science programme, demonstrating the substantial improvement in statistical precision over previous HERA measurements at moderate and large $x_{{\rm Bj}}$. For electron–nucleus collisions, we compute the nuclear modification ratio $R^{e\text{A}}$ within collinear factorisation using nuclear parton distribution functions, and identify the kinematic regimes in which shadowing, anti-shadowing, and EMC-like suppression are accessible with early EIC data. These results are intended to serve as a parton-level baseline to support feasibility studies and to provide a reference for future higher-order theoretical and experimental investigations at the EIC.

We started the Living Review of Machine Learning for Particle Physics (HEP-ML Living Review) in 2020 as a community-maintained, near-comprehensive bibliography of machine learning in particle physics. The field was then growing faster than any single researcher could follow, finding the relevant papers was hard, and a structured, continuously updated reference paid off immediately. Since then the literature has grown by more than an order of magnitude, the methods reach far beyond the classification and generation tasks of the early years, and the community has built its own ecosystem of topic-specific reviews, benchmark papers, and software frameworks. The original model no longer serves this field well, and we can no longer sustain it. We therefore change direction. We freeze the Living Review as an archival reference covering the literature up to 1 June 2026, where it remains a stable record of the first phase of HEP-ML. A new resource, the HEP-ML Living Guide, replaces it. It does not list everything. It curates, it annotates, and it points readers to foundational and representative work, so that researchers can find their way into a mature and rapidly diversifying field. In this article we explain why we make this change and how the new resource works.

Within a holographic QCD framework, we numerically investigate chiral symmetry breaking and the associated phase transition at finite temperature and chemical potential. The model is constructed on a nonlinear charged Born-Infeld black hole background. The chiral condensate, extracted from the asymptotic behavior of the bulk scalar field, serves as the primary order parameter. At zero chemical potential, we find a chiral crossover transition for physical quark masses with a pseudocritical temperature of $T_{pc}=0.1477$ GeV. In the chiral limit, the transition becomes first-order with a critical temperature of $T_{c}=0.1337$ GeV. A critical strange quark mass of $m_s=37$ MeV, at zero light quark mass, separates first- and second-order transition regions. For finite chemical potential ($\mu$) and a physical strange mass ($m_s=95$ MeV) with massless light quarks, the transition remains second-order, with $T_c$ decreasing as $\mu$ increases. These results are further supported by the behavior of meson susceptibilities $(\chi_{\pi}-\chi_{\sigma})$, which exhibit a rapid thermal decay and convergence across the phase boundary. Introducing the Born-Infeld parameter $\beta$ shifts the second-order phase boundary to higher temperatures for smaller $\beta$ (stabilizing the chirally broken phase) but does not alter the transition order or introduce a critical endpoint within the studied range. Our findings are consistent with previous soft-wall model studies and highlight the significant role of nonlinear bulk electrodynamics in modifying the chiral phase diagram.

We investigate the geodesic dynamics, eikonal quasinormal modes (QNMs), and extended phase space thermodynamics of a Schwarzschild-de Sitter-like black hole coupled with a global monopole in Bumblebee gravity. Our analysis reveals that spontaneous Lorentz symmetry breaking and topological defects modify the effective radial dynamics, leading to lower effective potential barriers and a reduced magnitude of the effective force. For null geodesics, higher monopole parameters expand the photon sphere and critical impact parameter, implying an enlarged black hole shadow, while mitigating dynamical instability. For massive particles, the stable circular orbit window narrows significantly as the Outermost Stable Circular Orbit (OSCO) shrinks, alongside a marked enhancement in perihelion precession. In addition, we examine the correspondence between the eikonal QNMs and the properties of null geodesics. The excellent agreement between the eikonal approximation and the WKB method for scalar and electromagnetic perturbations supports the validity of the correspondence for the spacetime under consideration. In the extended thermodynamic phase space, we evaluate the black hole as a holographic heat engine. We demonstrate that classical efficiency is mathematically blind to Lorentz violation; however, introducing a quantum-corrected modified entropy tightly couples the macroscopic work output to the symmetry-breaking framework. Ultimately, the necessity to respect the Carnot bound imposes a strict macroscopic constraint on the Lorentz-violating parameter, safeguarding the Second Law of Thermodynamics.

We develop a multipole description of transverse distributions of the energy-momentum tensor for a spin-$3/2$ baryon in frames connected by a longitudinal boost. In the transverse Breit frame, the $T^{00}$, $T^{03}$, and $T^{33}$ matrix elements are expressed through seven multipole form factors for energy, angular momentum, and stress. At finite longitudinal momentum, we factorize the Lorentz mixing of these three components from the spin-$3/2$ Wigner rotations of the external states. The resulting elastic-frame matrix elements contain six transverse multipoles, whose Fourier transforms define the distributions of energy, longitudinal momentum, and longitudinal momentum flux. We also calculate $T^{++}$, $T^{+-}$, and $T^{--}$ directly with light-front Rarita-Schwinger spinors. The elastic-frame construction provides a continuous interpolation from the transverse Breit frame to the infinite-momentum frame. In this limit, the Wigner rotation becomes the Melosh rotation, and the leading elastic-frame matrix elements reproduce the corresponding light-front results. Using the $\Delta$-baryon gravitational form factors obtained in the Skyrme model as a representative numerical input, we find that the energy distribution is dominated by the energy monopole defined in the transverse Breit frame and changes only weakly under longitudinal boosts. Through boost mixing, this monopole provides the dominant contribution to the longitudinal momentum distribution and its flux at finite $P_z$. For a longitudinally polarized spin-$3/2$ target, the distributions contain only the monopole contributions, whereas those of a transversely polarized target exhibit spin-dependent quadrupole and octupole deformations and a dipole that shifts their maxima.

The quark spin-orbit correlation probes the alignment of quark helicity with longitudinal kinetic orbital angular momentum inside a hadron. This correlation is defined by a QCD operator: the position moment of the asymmetric parity-odd quark energy-momentum tensor. The matrix element of this rank-two tensor decomposes into symmetric-traceless, antisymmetric, and trace parts. The symmetric-traceless part is matched to moments of axial generalized parton distributions. The QCD equations of motion relate the antisymmetric part to vector and tensor form factors and set the trace to zero. Using these relations, we derive two gauge-invariant sum rules for the spin-orbit correlation in a spin-$1$ hadron. One gives the correlation in an unpolarized target. The other gives its tensor-polarization dependence, which is absent for spin-$0$ and spin-$1/2$ targets. We estimate the unpolarized spin-orbit correlations for the $\rho$ meson and deuteron using existing lattice and phenomenological inputs, respectively.

We present a model in which asymptotically de Sitter universes of various types, and de Sitter (dS) radii $R_n$, live in the interiors of black holes in a maximally entropic flat $p = \rho$ Friedmann-Robertson-Walker universe. These dS universes clearly have many quantum states. We argue that they decay and equilibrate with the maximal entropy universe on time scales of order $\alpha_n R_n {\rm ln} (R_n /\delta_n)$, where $\alpha_n$ are model-dependent dimensionless constants and $\delta_n$ are the initial distances between the shell, satisfying the Israel junction conditions, and the dS horizon. These are time-scales as viewed by a detector following a trajectory far from the would-be cosmological horizon. These times are all exponentially shorter than dS recurrence times, which have no meaning in this model. It is impossible for a detector inside one of the dS universes to determine whether it is actually part of such a structure. This model could be used as the basis for claiming that certain constants of nature or cosmological initial conditions were chosen to have mathematically unnatural values because other values could not lead to any form of intelligent life.

Reconstructing the analytic structure of a function from finite datasets is a fundamental problem across theoretical, numerical, and experimental physics. While Padé approximants provide a natural framework, finite-information effects, as well as statistical and systematic uncertainties, may obscure the underlying analytic structure and limit reconstruction reliability. In this work, we reinterpret the appearance of Froissart doublets not merely as numerical artifacts but as diagnostic objects carrying information about the analytic consistency of the input data. Accordingly, we develop a general Padé-based algorithm that exploits the dynamics of Froissart doublets along Padé sequences to identify localized inconsistencies and iteratively reconstruct the analytic structure most compatible with the data. The method requires no model for the origin of the inconsistencies and distinguishes genuine analytic features from spurious structures induced by finite-information effects. We validate it using Stieltjes functions, realistic pseudo-experimental datasets with statistical and systematic uncertainties, and general holomorphic functions. The complete algorithm is provided as a supplementary Mathematica notebook in an open GitLab repository.

We present a study of transverse momentum broadening for high-energy partons propagating through the quark-gluon plasma (QGP), extending the Gyulassy-Levai-Vitev (GLV) formalism to include both all-path-length (APL) corrections and improved sub-Regge kinematics. The standard GLV framework relies on the large separation distance and large formation time approximations, which are well justified in large nuclei but may become unreliable in small collision systems, where the relevant length and coherence scales are comparable. Working to first order in the opacity expansion, we derive analytic expressions for the transverse momentum broadening distribution and the corresponding momentum transport coefficient, $\hat{q}$, while systematically relaxing these approximations. The APL correction arises from relaxing the large separation distance approximation, whereas the sub-Regge and combined sub-Regge-APL corrections are obtained using an improved set of Regge kinematics beyond the strict Regge limit. We find that these corrections can substantially modify both the transverse momentum broadening distribution and the momentum transport coefficient, particularly for short path lengths and high exchanged momentum, providing a more complete theoretical description of momentum broadening in the QGP.

We investigate whether squeezing can provide an observable signature of quantum gravitational waves. Because a realistic detector couples only to a particular wave-packet mode, squeezing in global source modes need not remain observable. We show that inflationary two-mode squeezing reduces to an unsqueezed thermal state in the accessible one-mode sector, phase incoherence washes out squeezing in stochastic backgrounds, and the limited coverage of the solid angle of detectors strongly suppresses squeezing from isolated sources. We then show that source squeezing is not essential, i.e., a quantized gravitational wave can generate a positive squeezing witness if the detector state is initially prepared in a squeezed state, whereas a classical external gravitational field cannot, producing only a displacement. However, the resulting signal is bounded by the extremely small graviton–detector coupling. Thus, detector squeezing can remove the need for squeezed incident waves, but not the suppression caused by weak gravitational interaction.

Near-threshold resonances have been discovered in many hadron pair production processes, resulting in a significant increase in reaction cross sections at low relative velocities of the produced particles. The natural cause of such resonances is the interaction between slow hadrons in the final state. Our review demonstrates that, in virtually all known cases, final-state interactions successfully explain the results of numerous experiments demonstrating a nontrivial energy dependence of cross sections for processes near reaction thresholds. A comprehensive study of near-threshold resonances in various processes can provide new information about the interaction between hadrons at large distances.

We comment on various statements in a recent document (A.~Deur, S.~J.~Brodsky, C.~D.~Roberts and B.~Terzić, Regarding the Rotational Unruh Effect, arXiv:2607.25004v1 [hep.ph], (2026)). The examples cited treat electrons (or positrons) circulating and emitting photons in high-energy storage rings. The topic is also of interest in astrophysics, for electrons orbiting in magnetic fields around neutron stars.

We present a new avenue to the usual Schwinger effect via the open string pair production for a system of two Dp branes with $1 \le p \le 6$ in Type II superstrings. The two Dp are placed parallel at a separation with one of them carrying the most general constant electromagnetic background allowed for the pair production. By taking the so-called field theory limit, we obtain systematically, from the open string pair production rate, the respective explicit Lorentz invariant QED pair production rate in diverse dimensions for a pair of charged/anti-charged massive particles, which can be scalars, spinors or vectors.

We construct a realization of sneutrino tribrid inflation within the $R$-symmetric flipped $SU(5)$ grand unified theory. A vector-like pair of matter multiplets, $10_V+\overline{10}_V$, provides a $D$-flat inflaton direction along the right-handed sneutrino component, with an additional $Z_2$ symmetry forbidding a direct inflaton mass term so that the leading inflationary interaction is a non-renormalizable Kähler-driven operator. Unlike previous studies, we treat the superpotential cutoff scale $M_s$ as independent of the reduced Planck mass, $m_P$, substantially enlarging the viable parameter space. Confronting the model with the ACT DR6/Planck determination $n_s=0.9734\pm0.0034$ and the $2\sigma$ bound on the running of the spectral index, we identify broad regions of viable parameter space in which the flipped $SU(5)$ symmetry-breaking scale can approach the conventional GUT scale, $M\simeq M_{\rm GUT}$, and the tensor-to-scalar ratio can reach observable values, $r\gtrsim10^{-3}$, within reach of forthcoming CMB $B$-mode experiment such as LiteBIRD. We further study the post-inflationary dynamics, identifying the inflaton with the lightest right-handed sneutrino in a conventional type-I seesaw sector, whose out-of-equilibrium decay generates a lepton asymmetry that is converted into the observed baryon asymmetry via non-thermal leptogenesis and electroweak sphalerons, for a reheating temperature consistent with both successful leptogenesis and the gravitino constraint.

In this contribution, we present thermal photon production mechanisms within a magnetized quark-gluon plasma, utilizing the framework of Landau-level quantization. We examine the specific influences of the magnetic field, chemical potential, and chiral chemical potential on photon yield and polarization. By providing a more comprehensive theoretical description of photon production across the full evolution of heavy-ion collisions, our study offers a promising new avenue for resolving the photon $v_2$ puzzle and potentially detecting the signature of magnetic fields in heavy-ion collision experiments.

In this paper, we study the impact of different cross-section models in the measurement of the neutrino oscillation parameters in DUNE. In particular, for the quasi-elastic (QEL) region, we considered the Llewellyn-Smith formalism (LS) and the Hartree-Fock Continuum Random Phase Approximation (HF-CRPA) and for the resonance (RES) region, we consider the Rein-Sehgal (RS) and the Berger-Sehgal (BS) models, and compare our results with the DUNE cross-section tune (Valencia model for QEL and RS model for RES), which was considered in their technical design report. Our results show that while the DUNE tune is best for QEL, the best model for RES is BS. As the DUNE energy region is mainly dominated by RES, for the total cross-section, the HF-CRPA+BS model provides the best strength in the cross-section, whereas the DUNE tune is the weakest among all the configurations considered in our work. Regarding the neutrino mass ordering, CP violation and octant sensitivity, the HF-CRPA+BS model provides $(25- 30)$% improvement, and regarding the precision of the $\theta_{23}$ and $\Delta m^2_{32}$, the same model provides $(15 - 20)$% improvement as compared to the DUNE tune.

We investigate small-instanton contributions to the axion potential across a range of KSVZ models containing vector-like quarks~(VQs), using naive dimensional analysis. We consider scenarios containing a single VQ, multiple identical copies, and sets of distinct VQs, requiring in each case that the gauge couplings remain perturbative up to the Planck scale under the two-loop gauge running. The associated fermion zero-mode content varies between these cases, requiring different combinations of mass insertions and scalar–Yukawa contractions for its saturation. Increasing the copies of VQs can render the instanton-size integral dominated by instantons of the smallest size, corresponding to the scale near the ultraviolet~(UV) cut-off. The resulting contribution then becomes sensitive to the UV completion and the induced potential can compete with, or dominate over, the ordinary QCD contribution. Assuming that the QCD and small-instanton potentials are aligned, we determine the resulting axion-mass shift and its consequences for the axion–photon coupling. When the small-instanton induced susceptibility becomes comparable to or larger than the QCD susceptibility, the physical axion mass of $m_a$ is enhanced at fixed decay constant~$f_a$, while the axion-photon of $g_{a\gamma\gamma}$ coupling remains controlled by $f_a$ and the anomaly ratio of $E/N$. The standard QCD relation among $m_a$, $f_a$ and $g_{a\gamma\gamma}$ is consequently modified, opening new regions of the $(m_a,g_{a\gamma\gamma})$ plane for axion searches.

A breakthrough in fundamental physics experiments measuring particle spin precession may happen if spin-transparent storage rings become adopted tools for such experiments. We present a new design of highly specialized table-sized storage rings, which use low-energy polarized electron beams and Mott polarimetry. Based on the spin transparency ansatz, the spin precession stemming from the magnetic dipole moment is canceled at any beam energy after an electron's turn along the periodic orbit in the ring. Meanwhile, a spin precession induced by the fundamental physics of interest, e.g., the electron's permanent electric dipole moment (EDM) and/or ultralight-dark-matter-mediated forces such as axions, will accumulate. However, capitalizing on such types of rings is not only desirable for measurements of EDMs and axion searches relevant to $CP$ violation and matter-antimatter asymmetry in the Universe, but may also find very promising applications in quantum computing.

In this work, we studied the spectroscopic masses, decay constants, oscillation frequencies, and Isgur-Wise function parameters of $B$, $B_s$, and $B_c$ mesons within the framework of a non-relativistic potential model. The interaction is modelled using the Killingbeck potential, with calculations performed using two complementary approaches: the matrix Numerov method for solving the Schrödinger equation and the quantum mechanical variational method employing the Gaussian wave function. We determined the unknown parameters of the Killingbeck potential by fitting it to the Cornell potential using the ordinary least squares (OLS) method. These calibrated parameters are then used to compute the aforementioned physical observables.We obtained the masses of the heavy mesons with deviations of less than 0.5% from the highly precise experimental data. We also discussed the drawbacks and limitations of the non-relativistic model and highlighted its domain of applicability. At the end, we compare our results obtained from both methods with those from other theoretical frameworks, including QCD sum rules, lattice QCD, and alternative potential model studies.

The first column of the lepton mixing matrix carries two independent magnitude conditions: the trimaximal norm $|U_{e1}|^2=2/3$ and the $\mu$–$\tau$ balance $|U_{\mu1}|=|U_{\tau1}|$. Parameterizing their violation by $\varepsilon_1\equiv\tfrac32|U_{e1}|^2-1$ and $\varepsilon_2\equiv3(|U_{\tau1}|^2-|U_{\mu1}|^2)$, we show that current data treat the two differently in central value: with the first JUNO measurement included, $\varepsilon_1=+0.014\pm0.010$ is consistent with zero, while $\varepsilon_2=+0.29^{+0.07}_{-0.13}$ is large but disfavors zero at only $1.5\sigma$ on the profile likelihood of the global fit, since the phase that drives it remains poorly measured. This asymmetry selects a specific framework, the $\pi/12$ model. Its neutrino sector is $\mathrm{TM}_1$, supplemented by the electron-row condition $|U_{e2}|/|U_{e3}|=2+\sqrt3$ that fixes $\sin^2\theta_{13}=(2-\sqrt3)/12=0.02233$ and $\sin^2\theta_{12}=0.31811$. A charged-lepton 2–3 rotation $R_{23}(\theta_e,\alpha)$ leaves the electron row exactly invariant and generates $\varepsilon_2=\sin2\theta_e\cos\alpha$. In a concrete $S_4\times C_4\times C_3\times C_2$ realization, a single additional flavon alignment forces $\alpha=0$; a natural angle $\theta_e\simeq2^\circ$ then reproduces the observed departure of $\theta_{23}$ from maximal while pinning $\delta=272^\circ\pm2^\circ$, near-maximal CP violation with $\varepsilon_2=-0.066$. The result is a sharp test: the predicted $\delta$ sits $1.7\sigma$ from the present central value on the same profile likelihood, the predicted $\varepsilon_2$ has the opposite sign to the measured one, and the Hyper-Kamiokande design precision of $20^\circ$ on $\delta$ resolves the question at the $3\sigma$ level. The mass predictions are inherited unchanged, $\Sigma m_\nu=65.6$ meV and $m_{\beta\beta}=5.4$ meV, placing the model at the current DESI bound in $\Lambda$CDM.

Within the framework of QCD sum rules, we systematically investigate the mass spectra and possible decay patterns of the $(c\bar{c})(c\bar{q})$ and $(b\bar{b})(b\bar{q})$ tetraquark states with quantum numbers $J^{P}=0^{\pm}$. Based on two distinct color configurations, $[8_c]_{Q\bar{Q}} \otimes [8_c]_{Q\bar{q}}$ and $[1_c]_{Q\bar{Q}} \otimes [1_c]_{Q\bar{q}}$, we construct 18 interpolating currents for these states, and obtain stable sum rules for a subset of them. By calculating the corresponding two-point correlation functions, we extract their mass spectra. For the $(c\bar{c})(c\bar{q})$ system, we identify four possible tetraquark states: two with $J^{P}=0^+$, namely $T_{3c,0}(4760)$ and $T_{3c,0}(5000)$, and two with $J^{P}=0^-$, denoted as $T_{3c,0}(5040)$ and $T_{3c,0}(5370)$. For the $(b\bar{b})(b\bar{q})$ system, the extracted masses are found to lie in the ranges $13.72$–$14.02$ GeV for the $J^{P}=0^+$ states and $13.90$–$14.22$ GeV for the $J^{P}=0^-$ states. We further analyze their possible decay modes. Our results indicate that $T_{3c,0}(5000)$, $T_{3c,0}(5040)$, and $T_{3c,0}(5370)$ can decay into a charmonium state and a charmed meson, and are therefore expected to have appreciable decay widths. By contrast, $T_{3c,0}(4760)$ and all predicted $(b\bar{b})(b\bar{q})$ tetraquark states are expected to be relatively narrow, since the corresponding two-body strong decays via the fall-apart mechanism are kinematically forbidden. Therefore, $T_{3c,0}(4760)$ and all predicted $(b\bar{b})(b\bar{q})$ tetraquark states are promising candidates for experimental searches in final states containing a $D$ or a $\bar{B}$ meson, accompanied by light hadrons or a photon.

The recent observations of the $\Xi_{cc}^{+}$ and the $\Omega_{cc}^{+}$ by the LHCb Collaboration complete the ground-state triplet of doubly charmed baryons, so that its internal mass pattern can be used to test symmetry breaking in the light-quark sector. We study the doubly heavy baryons within the pion mean-field approach, regarding them as bound states of the $N_c-2$ valence light quarks that generate the pion mean field in the presence of a compact heavy diquark. All dynamical parameters for flavor SU(3) and isospin symmetry breaking were determined in the light and singly heavy baryon sectors, and the hyperfine coupling is fixed by the singly heavy spectrum. With the heavy-quark masses taken from the PDG values, the measured $\Xi_{cc}^{++}$ mass is used only to determine the collective rotational energy of the light subsystem, so that the mass splittings within the triplet are predictions. We obtain $M_{\Xi_{cc}^{+}}=(3620.17\pm13.08)$ MeV and $M_{\Omega_{cc}^{+}}=(3746.62\pm13.22)$ MeV. The predicted isospin splitting, $M_{\Xi_{cc}^{++}}-M_{\Xi_{cc}^{+}}=(1.43\pm0.38)$ MeV, is consistent with the LHCb observation of the $\Xi_{cc}^{+}$. We also present the masses of the spin-3/2 doubly charmed states and the doubly bottom spectrum.

We present an analysis of the perturbative modes of dissipation in the minimal warm inflation model where an axion-inflaton is coupled to a gluon thermal bath through the axion-gauge coupling. The corresponding friction coefficient, which generically is governed by IR physics, for the processes we consider is dominated by Landau damping of soft space-like gluons and the plasmon decay of hard on shell gluons. Since both of these processes are IR dominated, the friction coefficient becomes sensitive to the non-perturbative magnetic mass scale $m_{g}^{-1} \sim (\alpha T)^{-1}$ which in turn leads to the friction coefficient's overall linear proportionality to $\alpha$, which is much less suppressed in $\alpha$ powers compared to the well understood term from Chern-Simons (CS) diffusion $(\propto \alpha^5)$. On the other hand, this contribution to the friction coefficient is suppressed due to slow roll. We show that this can be viewed as a suppression of local spontaneous CPT violation for derivative couplings in general and that time correlations of nonlocal variables which do not fall off at large time separations are what allow an unsuppressed friction coefficient.

The QGP-to-hadronic matter phase transition and QCD critical point in heavy-ion collisions can be identified by studying spatial fluctuations among final-state particles using intermittency analysis. First CMC-based intermittency analysis in the two-dimensional angular ($\eta$, $\varphi$) phase space, using EPOS as the background model is presented. Critical fluctuation signals are extremely weak, constituting only a few percent of the total event sample and are severely diluted by the overwhelming non-critical background, rendering traditional intermittency analyses insufficient for reliable signal extraction. To extract the weak critical signal, we employ a two-stage topological machine learning framework combining Topological Data Analysis (TDA) with deep learning. In the first stage, particle events are represented as two-dimensional point clouds and a Delaunay-based sub-level set filtration is constructed to extract Betti curves as multiscale topological invariants, corrected for multiplicity bias via azimuthal randomisation and classified by two complementary architectures, a TopoPointNet (TPN) and Boosted Decision Trees (BDT). Since event-level classification alone is insufficient to restore the critical scaling, a second stage applies a particle-level density filter, explicitly stripping away the diffuse thermal background and isolating the densely packed critical clusters. The two stage pipeline successfully restores the power-law scaling of the normalized factorial moments, enabling accurate recovery of the intermittency index in ($\eta$, $\varphi$) space and establishing topological machine learning as a robust data driven tool for probing the QCD critical point and the phase structure of strongly interacting matter in heavy-ion collisions at LHC energies.

The combined chiral and large-$N_c$ expansion is increasingly employed in precision studies involving the $\eta$ and $\eta'$ mesons, including recent applications to low-energy axion phenomenology within U(3) chiral perturbation theory. We point out that the operator structure of the large-$N_c$ chiral Lagrangian naturally induces correlated directions among the low-energy constants $(F_0,L_4,C_{16})$ and $(F_0,L_6,C_{20})$, implying that phenomenological analyses determine correlated combinations of couplings rather than independent low-energy constants. Using the determination of the pion decay constant as an illustrative example, we reinterpret existing phenomenological and lattice determinations in terms of these correlated directions, showing that the well-known anticorrelation between $F_0$ and $L_4$ extends naturally to NNLO through $C_{16}$. These correlated directions lead to a practical prescription for interpreting and propagating phenomenological determinations of the low-energy constants consistently within the combined chiral and large-$N_c$ framework.

We present a gauge invariant formulation of open path geometric phases in the context of three flavor neutrino oscillations traversing nonuniform matter. In contrast to the standard Berry phase, which is intrinsically associated with closed adiabatic cycles, neutrino propagation from source to detector typically traces an open trajectory within the parameter space of matter dependent Hamiltonians. We derive this formalism within a layered matter framework, where each discrete layer is characterized by a constant density and a local matter eigenbasis. The total evolution operator is expressed as a path ordered product of dynamical propagation factors and interface matrices that bridge adjacent matter eigenbases. This construction naturally yields geometric phase chains composed of endpoint projections and interface overlaps. We demonstrate that these chains remain invariant under arbitrary local rephasings of the instantaneous matter eigenstates, thereby resolving the gauge dependence ambiguity typically associated with open path transport. The proposed formalism elucidates the noncommutative nature of flavor evolution in layered media, illustrating that profiles with identical column densities but distinct ordering can yield different transition amplitudes. Furthermore, we analyze the influence of the Dirac CP phase, showing that it deforms the geometry of matter eigenbasis transport without being equivalent to the geometric phase itself. In the continuous limit, finite interface overlaps converge to Berry connection factors, while endpoint projections remain indispensable for ensuring open path gauge invariance. We discuss the phenomenological implications of this structure, emphasizing that geometric phases are not independent observables but contribute to transition probabilities via interference among coherent propagation chains.

The memory-burden effect can suppress the late-time evaporation of primordial black holes (PBHs), allowing those that would otherwise have evaporated via Hawking radiation to survive until the present epoch. These lighter PBHs emit high-energy and ultra-high-energy neutrinos, opening the tentalizing possibility of discovery via neutrino telescopes. We study the constraints on memory-burdened PBHs from current IceCube HESE, MESE, and EHE data; and forecast the sensitivity reach of IceCube-Gen2 radio and GRAND200k. In particular, we study how this signal depends on whether the initial PBH population is described by a log-normal mass function or by a monochromatic one. We find that log-normally distributed populations can be more strongly constrained than monochromatic populations with the same median mass primarily because their low-mass tails enhance the high-energy neutrino flux. We show that current IceCube data provide the leading limits for a lower memory burden parameter $k$, whereas the projected radio detectors become substantially more sensitive for higher values of $k$. We also study a scenario where future experiments would see a positive signal coming from PBHs. We consider a representative 30-event signal in IceCube-Gen2 radio and GRAND200k and study how well one could distinguish the two mass-function hypotheses. We find that it is easier to disfavor the monochromatic distribution when the log-normal distribution is assumed to be true. Finally, we study how well the parameters of the memory-burdened PBHs can be estimated in these future experiments.

The $A_{4} \times Z_{4}$ symmetry models are constructed to study neutrino masses and mixings, as well as the gravitational-wave spectrum from domain-wall annihilation. The first neutrino mass model is constructed with the flavon's vacuum expectation value and alignment obtained from the self-interacting potential terms, while the second model uses a new vacuum expectation value arising from a potential containing both self-interaction and mixed terms. The resulting neutrino mixing patterns for both models are in good agreement with current neutrino oscillation data with different mixing values. Further, the flavon mixing terms lift the vacua degeneracy that often shows in the spontaneous symmetry breaking of the discrete symmetry. These mixing terms and the modified neutrino mass matrix of the second model are considered to produce the necessary bias for analysing the gravitational waves spectrum. The spectrum predicted by the model could be detected by current and near-future experiments when the flavons have the vacuum expectation value of $10^4$ TeV.

Within the framework of light-cone sum rules, we calculate the hadronic photon corrections to the $\gamma^*\gamma \to f_2(1270)$ transition form factors induced by the leading-twist photon distribution amplitude of the real photon. We establish the factorization formula for the vacuum-to-photon correlation function at next-to-leading order in $\alpha_s$, and extract the perturbative hard matching coefficients by applying the method of regions. The parametrically large logarithms appearing in the hard functions are resummed to next-to-leading logarithmic accuracy by solving the two-loop evolution equation for the corresponding light-ray tensor operator. Combining the resulting light-cone sum rules with the known leading-power contributions from QCD collinear factorization, we provide updated theoretical predictions for the three helicity form factors $T_0(Q^2)$, $T_1(Q^2)$ and $T_2(Q^2)$, including an estimate of the theoretical uncertainties.