We study the semiclassical limit of SL_2-opers on the four-punctured sphere in Nekrasov-Rosly-Shatashvili Darboux coordinates. Using exact Wentzel-Kramers-Brillouin (WKB) connection formulae, we express the trace coordinates of the corresponding SL_2(C) character variety as finite Laurent sums of Voros exponentials. Tropicalizing these formulae and the NRS relations gives a chamberwise integer affine linear system for the leading logarithms of the NRS coordinates. In chambers where this system is unimodular and the selected cycles form a primitive symplectic pair, the leading asymptotics agree, up to flavor-period shifts, with Seiberg-Witten periods of the N=2 SU(2) theory with N_f=4 fundamental hypermultiplets. We verify this mechanism in a sample chamber and in the weak-coupling degeneration. No global coordinate-independent recovery theorem is claimed; non-unimodular or degenerate chambers are treated as limitations of the chosen NRS chart. In the weak-coupling degeneration, we show that the NRS chart can be chosen compatibly with the plumbing limit so that the resulting chamber is unimodular and non-degenerate away from tropical walls.

We study two-point functions of half-BPS operators in maximally supersymmetric Yang-Mills theory continued to $d=4-2\,\varepsilon$ dimensions. Using supersymmetric localization on $S^d$, we derive perturbative matrix-model expressions for the $\varepsilon$-expansion of these correlators and obtain all-loop results at leading order in $\varepsilon$ in the planar limit, with extensions to finite-$N$ corrections and higher-charge operators. We compare the localization results with direct perturbative computations in flat space. At order $\varepsilon$ the two descriptions agree perfectly, while at higher orders our construction fails to reproduce the perturbative data due to the breaking of conformal symmetry away from four dimensions. Nevertheless, in the case of the dimension-two operator we conjecture an all-loop formula at order $\varepsilon^2$ by exploiting the precise form of the mismatch.

Type II string theory in the absence of orientifolds requires the target spacetime $X$ to admit a spin structure. We show that this familiar requirement arises directly from the consistency of the worldsheet GSO projection. The obstruction is a mixed global anomaly between $(-1)^{\text{F}_L}$ and the target space background data, detected by the spin bordism group $Ω_3^{\mathrm{spin}}(B\mathbb{Z}_2\times X)$. We compute the relevant mixed bordism group and identify the bordism class of the GSO-projected worldsheet theory. For smooth target spaces, vanishing of the anomaly reduces to the condition that $X$ is spin, while for general orbifolds $[\hat{X}/G]$, $\hat{X}$ has to carry a $G$-equivariant spin structure. We also classify all possible theta angles in the worldsheet theory and show that they correspond to all possible continuous and discrete background fields of the target space theory visible in string perturbation theory.

We study two-point functions of protected scalar operators in N=4 SYM, focusing on their transcendentality properties in dimensional reduction, where quantum corrections are subleading in the regulator. We compute the correlators explicitly through two loops and operators up to classical dimension 10, for all trace structures. The one-loop correction is universal. At two loops, we find a controlled partial breaking of uniform transcendentality for higher-dimensional operators, which can be cancelled by suitable combinations of correlators in a fully predictable way. A main result is a complete planar extrapolation for two-loop correlators at arbitrary dimension and trace structure, whose dependence is entirely controlled by the number of stress-tensor multiplet factors in the operator. The perturbative results agree with localization predictions in all cases where comparisons are possible.

A long-standing conjecture claims that Virasoro conformal blocks exponentiate in the semiclassical limit $c \to \infty$ with $h/c$ finite. However, this has been proven only for four-point blocks on the sphere and one-point blocks on the torus. Here we extend the proof to general conformal blocks for higher-point functions and higher-genus backgrounds in arbitrary channels. The statement is to be understood at the level of a formal power series. Our proof builds upon a novel extension of the oscillator method for the computation of conformal blocks to cases where three internal lines meet at a vertex. This extension also gives a new constructive method to compute global conformal blocks in 2d CFTs at general genus.

We study the dynamics of first-order inverse phase transitions (driven by superheating) at strong coupling, focusing on the top-down Witten-Sakai-Sugimoto model for holographic QCD. Two cases are considered: the deconfinement transition in the unflavored version of the model and a chiral symmetry-restoring transition occurring in the deconfined phase of the full theory. In both cases, we imagine driving the system into a metastable phase at high temperature, inducing the nucleation of bubbles of the stable phase. For both classes of transitions, we find the corresponding Euclidean bounce solutions and compute the bubble nucleation rates and the relevant transition parameters. For the deconfinement transition, the large jump in the number of degrees of freedom between the two phases suggests that the bubble wall velocity is parametrically small; we provide a rough estimate of it near the critical temperature. In the case of the chiral transition, instead, we compute the bubble wall velocity and the friction force exerted on the bubbles employing motivated ansatze and approximations for the steady-state configurations.

Superconducting qubits offer a versatile platform for quantum simulation. In this architecture, quantum information can be encoded in the bosonic modes of a microwave cavity, offering an alternative to conventional qubit-based encoding schemes. These cavity bosonic modes can be manipulated using a single ancillary qubit. In this work, we investigate the quantum simulation of two- and three-flavor neutrino oscillations using Fock-basis encoding of a cavity mode. We design pulse sequences for implementing the required unitary operations through selective number-dependent arbitrary phase (SNAP) and displacement gates. Pulse-level control is employed to realize high-fidelity gate operations on the encoded cavity mode. The resulting neutrino oscillation probabilities obtained from quantum simulation exhibit close agreement with the corresponding theoretical predictions, demonstrating the feasibility of cavity-based bosonic encoding schemes for quantum simulation.

We establish a new connection between supersymmetric theories and scattering amplitudes. We show that the Coon amplitude coincides with the 3d $\mathcal{N}=2$ half-index of the XYZ model with nontrivial boundary conditions. Our 3d theory, intrinsically defined in the UV, flows to a sigma model in the IR whose partition function is the Veneziano amplitude. Crossing symmetry is realized as a consequence of 3d $\mathcal{N}=2$ mirror symmetry between XYZ and SQED. We use this correspondence to construct a meromorphic modification of the Coon amplitude by promoting the long-standing dressing factor $\mathfrak{q}^{ST}$ responsible for a branch cut to an elliptic completion thereof. This illustrates that one does not have to give up single-valuedness to achieve positivity at the physical poles.

We compute the one-loop mixing of bosonic and two-fermion interactions into two-fermion operators in the dimension-eight Standard Model Effective Field Theory (SMEFT). Together with the results in arXiv:2106.05291, arXiv:2205.03301, arXiv:2409.15408, and arXiv:2512.21724, this leaves only the mixing of four-fermion operators into two-fermion ones as the remaining piece to complete the SMEFT renormalization program at this order.

We present a comprehensive study of the radiative decays of fully heavy tetraquarks ($T_{4c}$, $T_{4b}$) and mixed heavy-flavor tetraquarks ($T_{bc\bar{b}\bar{c}}$) into charmonium/bottomonium states, within the nonrelativistic QCD factorization framework. Numerical result indicates that the decay widths of fully charm tetraquark $T_{4c}$ into $γJ/ψ(η_c)$ are around 1 MeV. Crucially, the $γJ/ψ$ signal channel receives less experimental background near the $J/ψJ/ψ$ threshold, providing a compelling way to search for the possible tetraquark states X(6200). For $T_{4b}$, the decay width is highly suppressed by the bottom quark mass, just lying in tens eV level. We further find that the decay widths of $T_{bc\bar{b} \bar{c}} \to γΥ$ exceed those to $γJ/ψ$ by 3-4 orders of magnitude, indicating preferential $c\bar{c}$-pair annihilation over $b\bar{b}$. These radiative decay modes can be measured in the future experiments, and are helpful to understand the inner structure of the full heavy tetraquark.

We study diffractive photo- and electroproduction of the $S$-wave heavy quarkonia $J/ψ$, $ψ(2S)$, and $Υ(nS)$ at energies relevant for the Electron-Ion Collider (EIC). The production amplitude is evaluated while retaining the full transverse-momentum ($\ell_t$) dependence of the hard two-gluon kernel, that is, without expanding the impact-parameter Bessel kernel as is done in the small-size color-dipole limit. The quarkonia light-cone wave functions are built from Cornell-potential solutions of the Schrödinger equation, normalized to the measured leptonic widths, and combined with a modern collinear gluon distribution. After benchmarking the framework against the full set of HERA charmonium cross-section ratio data, we provide a consistent set of bottomonium cross-section ratio predictions in EIC kinematics. We find that the full $\ell_t$-resolved treatment systematically improves the description of the radially excited states relative to the leading dipole limit, and we identify the kinematic windows where this difference is largest.

We systematically investigate the semi-invisible decays of hyperons (hyperon $\to π(/γ)\ +$ invisible($ψ$)) in the Mesogenesis mechanism by the effective Lagrangian approach. The one-loop hadronic contribution of triangle diagrams with final-state interactions is fully examined in the present work. Our analysis indicates that the triangle diagram yield sizable corrections to the branching ratio that are as significant as those from tree diagrams. Especially for the $Σ^-\to π^-ψ$ and $Ξ^0 \to π^0 ψ$, their loop contributions cannot be ignored. Consequently, the branching ratios of hyperon hadronic semi-invisible decays are found to be of order $10^{-5}$, particularly for $Σ^+\toπ^+ψ$, $Ξ^0\toπ^0ψ$, and $Ξ^-\toπ^-ψ$, whereas those of radiative semi-invisible decays are less than $10^{-7}$.

The two gluon exchange model serves as a key framework for describing the photoproduction of heavy vector mesons, and the photoproduction cross sections derived from it provide essential input for studies of Ultra-Peripheral Collisions (UPCs). Building on the model successful description of $J/ψ$ and $ψ(2S)$ photoproduction in previous work, we use the STARlight program to systematically investigate charmonium UPCs in PbPb and $p$Pb collisions at LHC energies. To reduce discrepancies between theoretical predictions and experimental data for rapidity and transverse momentum distributions in PbPb collisions, a phenomenological suppression factor is introduced to correct the theoretical results. We find that, in the TeV energy range, the corrected predictions agree well with experimental data within uncertainties and successfully reproduce the characteristic double-peak structure in rapidity distributions. In contrast, no significant suppression is observed in $p$Pb UPCs, which reflects the asymmetric photon fluxes and the dominant contribution from the photoproduction interaction branch. The transverse momentum distributions from STARlight simulations also match the diffractive pattern of coherent production seen experimentally, although the overall yield remains slightly overpredicted. This work further validates the applicability of photoproduction cross sections from the two gluon exchange model for charmonium UPC studies, and offers valuable phenomenological guidance for future experimental design and data analysis in UPC measurements of charmonium production.

We analyze the mixing between the $π^0$ meson and the photon in the presence of a strong uniform magnetic field, in the context of a two-flavor Nambu-Jona-Lasinio model. It is shown that only one specific photon polarization state can get mixed with the $π^0$ state, a fact that can be understood on general grounds. For magnetic fields with values up to 1 GeV$^2$/e, it is found that the effect of the mixing on the pion mass and pion-quark couplings is relatively small (below a level of 15%), which is at variance with previous results reported in the literature.

The fast reconstruction and detector-simulation pipelines are widely used in different scientific domains, such as, in High Energy Physics (HEP) and medical imaging, where the full experimental or the device-level simulation is computationally challenging. Instead of the use of the global data context, these pipelines use simplified response models which assume reconstruction uncertainty relies on local input parameters. To probe the robustness of the local assumption, a domain-agnostic context-aware stress testing pipeline is introduced, and a reconstruction response depending on the global parameters is also allowed. For an instance in HEP at High-Luminosity LHC (HL-LHC) simulation, this work shows that the decay channel $Z \rightarrow \ell\ell$, as a benchmark, violates the local assumption resulting in a significant reconstruction bias and resolution degradation. Using the unsupervised regime-mapping framework, this work also restores this peak stability and recovers the truth-level resolution, where a robust diagnostic tool for next-generation fast simulation pipelines is accommodated.

The success of DUNE's MeV physics program depends upon high-precision knowledge of the charged-current (CC) $ν_e+\mathrm{^{40}Ar}$ cross section. While there are indirect constraints at the 10% level for the nuclear transitions that constitute this cross section, the only direct measurement in the MeV range has an uncertainty of $\sim$50%. We show, surprisingly, that the cross section can be precisely measured using the solar-neutrino data themselves. This is possible because of independent knowledge of the $^8$B flux and survival probability, plus the distinctive angular distributions of the Fermi and Gamow-Teller transitions that comprise the cross section. We propose new methods to extract the transition strengths, considering both intuitive groupings and a Principal Component Analysis. Under pessimistic assumptions about detection, but taking detector uncertainties to be controlled, we demonstrate that a precision of $\lesssim$2% on the cross section can be achieved in the 9-15 MeV energy range. These results will be an important foundation for studying the cross section up to several tens of MeV, where the complexity increases significantly due to nuclear breakup channels but where reducing uncertainties is critical for supernova and atmospheric neutrino studies.

The sign problem is a notorious obstacle for classically simulating quantum theories with fermions. We propose an effective field theory method for analyzing the sign problem. At high temperatures, a $d$+1 dimensional field theory reduces to a bosonic $d$-dimensional theory; the phase of the Pfaffian in the higher dimensional theory is encoded in an operator in the lower dimensional theory. We apply this framework to the D0-brane/BFSS matrix quantum mechanics, where the phase becomes an operator in a bosonic multi-matrix integral. Our results show that the continuum theory has a sign problem that persists in the large-$N$ 't Hooft regime. However, detecting the sign problem involves going to 10-loop order in the high-temperature expansion. This delayed onset follows from the fact that the Pfaffian phase transforms as an $O(9)$ pseudoscalar. Furthermore, the relevant diagrams give a numerically small prefactor. Consequently, ignoring the sign problem leads to a relatively small fractional error in thermodynamic quantities for temperatures $T \gtrsim λ^{1/3}$. However, at stronger coupling in the 't Hooft regime, the sign problem may become more severe. Finally, we initiate the application of this framework to higher-dimensional maximally supersymmetric Yang-Mills theories.

The Collins-Soper kernel is calculated from a vacuum soft function using space-like Wilson lines with complex-directional vectors on the Euclidean lattice. Our pure gauge calculations with this method achieve high statistical precision in computing the soft function, whose rapidity dependence is well described by Collins-Soper evolution across a wide range of rapidity differences. The extracted kernel contains errors comparable to those achieved in state-of-the-art lattice calculations based on hadronic observables, but exhibits saturated behavior at large transverse Wilson-line separations.

At the 2025 International Conference on the Structure of Baryons (Baryons 2025), I presented our recent progress in lattice calculations of baryon light-cone distribution amplitudes (LCDAs). In Ref.[1], we implemented a novel hybrid renormalization scheme for octet baryons, leading to reliable determinations of quasi-distribution amplitudes (quasi-DAs). The calculations were performed on $N_f=2+1$ ensembles with stout-smeared clover fermions and a Symanzik-improved gauge action at three lattice spacings, $a = 0.052,0.077,0.105$ fm. The hybrid renormalization removes linear divergences in lattice matrix elements and yields smooth, self-consistent quasi-DAs, providing a solid foundation for LaMET-based extractions of baryon LCDAs. Results at the continuum limit and physical pion mass will be reported in the near future.

We discuss how the $Z'$-boson of the $B-L$ Supersymmetric (SUSY) Standard Model (BLSSM) could evade the current lower bound of around 5 TeV on the mass of such a resonance (of sequential nature) from the Large Hadron Collider (LHC) by a significant margin. This happens when the experimental sensitivities are critically impaired as the $Z'$-boson becomes `fat' or develops some leptophobia or possesses an optimally large decay Branching Ratio (BR) to BLSSM-specific states (including the SUSY ones) or when some or all of these are at play simultaneously. We describe how such a $Z'$-boson could acquire there features while still respecting the non-negotiable precision constraints from the LEP and the SLC experiments running at the $Z$-pole as well as those from the multi-purpose experiments at the LHC that search for such a resonance. We explore the interplay of the aforementioned phenomena and identify the regions of the BLSSM parameter space that give rise to the described situation by carrying out a thorough scan of it. We find that $M_{Z'}$ masses as low as 2.24 TeV may still be allowed in the BLSSM under favorable circumstances.

We study the $I^G(J^{PC})=0^+(1^{++})$ $K\bar Kπ$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $πa_0$-$K\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_Sπ^0$ invariant-mass distribution in the $J/ψ\toγ(K^0_SK^0_Sπ^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \begin{align} \sqrt{s_{f_1(1285)}}&= \left(1277\pm2\pm1\right) -i\left(12\pm1\pm0\right)\text{MeV}\,,\notag\\ \sqrt{s_{f_1(1420)}}&= \left(1435\pm2\pm7\right) -i\left(40\pm2\pm1\right)\text{MeV}\,.\notag \end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $πa_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.

This work presents a comprehensive analysis of polarization transfer in the decays \(χ_{cJ}\) (\(J=0,1,2\)) to octet baryon-antibaryon pairs within a polarized electron-positron collision environment. Using the spin density matrix formalism, we trace the polarization from the initial beams through the production chain \(e^+e^- \to ψ(2S) \to γχ_{cJ}\) to the final-state baryon-antibaryon system. The helicity amplitude analysis for \(χ_{c1} \to B\bar{B}\) confirms the universal angular distribution parameter \(α= -1/3\), as dictated by the charge-conjugation helicity selection rule. For \(χ_{c2}\) decays, \(α\) and the transverse polarization depend on two independent amplitudes, and our quark-model calculations agree with existing data. We demonstrate that the longitudinal beam polarization \(P_z\) modifies the spin observables for \(χ_{c1}\) and \(χ_{c2}\), offering new experimental handles at future polarized facilities like the Super \(τ\)-Charm Facility(STCF) to test decay mechanisms and explore baryonic spin entanglement as a quantum information resource.

We present a systematic analysis of the semi-leptonic decays $B_{(s)}\to D_{(s)}(1S,2S)\ellν_\ell$ and $B_{(s)}\to D^*_{(s)}(1S,2S)\ellν_\ell$ with $\ell=e,μ,τ$ within the covariant light-front quark model (CLFQM). Using the form factors of the transitions $B_{(s)}\to D_{(s)}(1S,2S)$ and $B_{(s)}\to D^*_{(s)}(1S,2S)$, we calculate the branching ratios of the relevant semi-leptonic decays and find that $Br(B_{(s)}\to D_{(s)}\ell^\primeν_{\ell^\prime})$ and $Br(B_{(s)}\to D^*_{(s)}\ell^\primeν_{\ell^\prime})$ with $\ell^\prime=e,μ$ are agree well with the data, while $Br(B_{(s)}\to D_{(s)}τν_τ)$ and $Br(B_{(s)}\to D^*_{(s)}τν_τ)$ are systematically smaller than the experimental measurements. This naturally gives rise to the so-called $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ anomalies. Our predictions $\mathcal{R}(D)=0.261\pm0.013$ and $\mathcal{R}(D^*)=0.228\pm0.026$ show $3.1σ$ and $2.1σ$ deviations from the current experimental world averages compiled by the Heavy Flavor Averaging Group (HFLAV), respectively, yet only deviate by $0.16σ$ and $1.5σ$ from the latest LHCb measurements. For the decays $B_{(s)}\to D_{(s)}(2S)\ellν_\ell$ and $B_{(s)}\to D^*_{(s)}(2S)\ellν_\ell$, their branching ratios lie in the range $10^{-4}\sim10^{-3}$, which are much larger than the results from the Bethe Salpeter (BS) equation , but agree with the relativistic quark model (RQM) calculations. Furthermore, we also calculate the forward-backward asymmetries $\mathcal{A}_{FB}$ and longitudinal polarization fractions $f_L$ for the corresponding decays. Our predictions are consistent with most other theoretical results and experimental data

While the Standard Model (SM) of particle physics contains the most precise set of predictions ever devised by humanity, that precision comes at a cost. The strange nature of the Higgs particle requires its parameters to be tuned so precisely that if the SM is indeed the true description of reality, one is forced to wonder how such a miracle as galactic structure and life could occur. Instead, we search in this work for a natural explanation. The concept of naturalness is comprehensively explored, and a new tuning measure proposed, with an aim to place it on well-defined Bayesian footing. We then turn this measure on to the analysis of a class of intriguing new physics - Composite Higgs models. These effective models are the result of a plethora of underlying theories, and they allow the production of a naturally light Higgs particle, appearing as the SM Higgs at low energy. We establish the background required to appreciate the N-site 4D Composite Higgs model, and subsequently focus on the simplest incarnations of this class. A global fit is performed on the Minimal 4D Composite Higgs model (M4DCHM), with strong exclusion bounds placed on collider search channels. We analyse any improvement in tuning that could be gained from several extensions to this model. The Leptonic M4DCHM is explored, with a composite tau lepton embedded in various representations. The possibility of a dark matter candidate existing in the Next-to-Minimal 4DCHM is considered. Ultimately, we are able to define what, if any, benefit to naturalness can come to the Composite Higgs sector by introducing these extensions.

The Deep Underground Neutrino Experiment (DUNE) far detector is sensitive to $\mathcal{O}(10)$ MeV electron neutrinos through $ν_e$ charged-current reaction with argon. This capability is a unique window into the $ν_e$ component of a Galactic core-collapse supernova flux. Extracting the properties of the supernova spectrum is, however, limited by the poorly-known $ν_e$-Ar cross section. We propose a data-driven strategy that leverages $^8$B solar neutrinos and muon-decay-at-rest neutrinos as standard candles for this process. These calibration samples constrain both the low-energy and high-energy components of the cross section relevant for supernova detection. Our method reduces the reliance on nuclear models, which can bias the extraction of the spectral parameters by as much as 300$\%$.

The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) is a prolific muon producer, making it an ideal location for studying dark sector particles produced in muon decays at rest. In this paper, we explore sub-GeV dark particle detection possibilities in a tons-scale, highly capable hydrocarbon scintillator ($HC^2$) detector at the SNS. We consider a search for $e^+e^-$ final states produced by decays of long-lived, $O(10-100)$ MeV axion-like particles and heavy neutral leptons. The $HC^2$ technology space, exemplified by the PROSPECT and Mobile Antineutrino Demonstrator detectors, offers strong rejection capabilities for the cosmic ray backgrounds that would normally dominate this search. By benchmarking on-surface cosmic ray signatures with data from PROSPECT at ORNL, we generate robust predictions for a multi-year SNS deployment of a range of $HC^2$ detector implementations. Results indicate the potential for order-of-magnitude improvements in sensitivity to axion-like particles and heavy neutral leptons in the 10-100 MeV mass regime compared to current global limits. We also comment on the neutrino detection possibilities of a $HC^2$ deployment at the SNS.

Jet production is the dominant high-$p_{\rm T}$ process at hadron colliders and provides a central testing ground for perturbative QCD, parton distribution functions and determinations of the strong coupling. This contribution summarises recent measurements of inclusive-jet, dijet and jet-multiplicity observables presented at DIS2026, with emphasis on the interplay between experimental precision, next-to-next-to-leading-order predictions, non-perturbative and electroweak corrections, and the treatment of correlated systematic uncertainties. Inclusive jet measurements from CMS and ATLAS constrain the gluon distribution at large Bjorken $x$ and enable extractions of $α_s(m_Z)$ compatible with the world average. Dijet measurements provide complementary sensitivity through the dijet invariant mass, rapidity separation and longitudinal boost, while ratios of inclusive jet multiplicities reduce several experimental and PDF uncertainties and directly probe additional QCD radiation. Recent progress in jet-energy calibration, together with new results from RHIC, ALICE and CMS on jet substructure and heavy-quark radiation, illustrates the breadth of current high-$p_{\rm T}$ jet physics and its relevance for Run~3 and future global PDF analyses.

The Large Hadron electron Collider (LHeC) would add a high-current Energy Recovery Linac to the HL-LHC, delivering electron-proton collisions at centre-of-mass energies around the TeV scale. This contribution summarises the QCD and parton-distribution-function (PDF) aspects of the recent LHeC bridge-project study. The combination of high luminosity, a very large lever arm in Bjorken $x$ and $Q^2$, and clean neutral- and charged-current deep-inelastic scattering measurements would enable a coherent determination of all proton PDFs in a single experiment. The resulting constraints would substantially reduce uncertainties in the gluon, valence, strange and heavy-flavour distributions, provide stringent tests of perturbative and small-$x$ QCD, and improve the parton luminosities that enter precision and discovery measurements at the HL-LHC and at future hadron colliders. The same programme gives competitive and complementary determinations of the strong coupling and weak mixing angle, including measurements of its running over a wide range of scales.

The gluon dominance model describes multiparticle production of secondary particles at high energies in lepton and hadron interactions, including annihilation processes and heavy quarkonium decays. According to this model, the multiparticle process is divided into two stages. The first stage describes the development of a quark-gluon cascade as a Markov branching process in the region of perturbation QCD. For the second stage, the transformation of quarks and gluons into observable hadrons (hadronization), a phenomenological scheme is proposed. It is universal and based on an experiment. The gluon dominance model demonstrates good agreement with data over a wide energy region. It testifies that in hadron interactions valence quarks remain in the leading particles, and gluons are the sources of secondary hadrons. Quantitative estimates of the model parameters confirm the fragmentation mechanism of hadronization in leptonic interactions and the recombination mechanism in hadronic ones. The model description of the experimental distributions on the number of neutral pions in proton interactions at 50 GeV beams in the high multiplicity region are presented for the first time. It is shown that the main contribution to this region is made by gluon fission. These results can be useful in planning of future experiments.

We present methods for electromagnetic shower reconstruction and identification in the FASERnu emulsion detector using 100 GeV and 200 GeV electron test-beam data from the CERN SPS H4 beamline. The reconstruction employs a clustering-based algorithm without energy-dependent tuning to determine shower axes. A multi-level identification chain comprising track pre-selection, a cut-based selection, and a BDT classifier achieves combined background rejection rates of 99.99% (100 GeV) and 99.94% (200 GeV). The method reaches total reconstruction and identification efficiencies of 58.9% (100 GeV) and 70.8% (200 GeV) evaluated from simulated samples. Energy reconstruction using the total number of reconstructed segments as the calorimetric estimator yields relative biases of +0.6% (100 GeV) and -0.8% (200 GeV), with resolutions of 25.4% and 22.6%, respectively. Systematic uncertainties on the energy reconstruction are dominated by variations in emulsion film detection efficiency, contributing (+10.9%/-8.2%) at 100 GeV and (+10.3%/-6.9%) at 200 GeV. The methodology provides a validated framework for electron neutrino identification with the FASERnu detector at the LHC.