Parton distribution functions (PDFs) play a central role in describing experimental data at colliders and provide insight into the structure of nucleons. As the LHC enters an era of high-precision measurements, a robust PDF determination with a reliable uncertainty quantification has become mandatory in order to match the experimental precision. The NNPDF collaboration has pioneered the use of machine learning (ML) techniques for PDF determinations, using neural networks (NNs) to parametrise the unknown PDFs in a flexible and unbiased way. The NNs are then trained on experimental data by means of stochastic gradient descent algorithms. The statistical robustness of the results is validated by extensive closure tests using synthetic data. In this work, we develop a theoretical framework based on the neural tangent kernel (NTK) to analyse the training dynamics of neural networks. This approach allows us to derive, under precise assumptions, an analytical description of the neural network evolution during training, enabling a quantitative understanding of the training process. Having an analytical handle on the training dynamics allows us to clarify the role of the NN architecture and the impact of the experimental data in a transparent way. Similarly, we are able to describe the evolution of the covariance of the NN output during training, providing a quantitative description of how uncertainties are propagated from the data to the fitted function. Interestingly, the methodology developed in this work can be used to understand the minimization of a loss function for any kind of parametrization, thereby providing a unified framework to compare different PDF determinations, like, e.g., fits based on a particular functional form. While our results are not a substitute for PDF fitting, they do provide a powerful diagnostic tool to assess the robustness of current fitting methodologies. Beyond its relevance for particle physics phenomenology, our analysis of PDF determinations provides a testbed to apply theoretical ideas about the learning process developed in the ML community. As seen in applications from other domains, we find that our results deviate from the simple picture of the lazy training regime discussed in the ML literature.
There is lattice evidence that the QCD matter above the chiral restoration temperature T ch and below the deconfinement temperature T d , called stringy fluid, is characterized by approximate chiral spin symmetry, which is a symmetry of confinement in QCD with light quarks. The energy density, pressure and entropy density in the stringy fluid scale as N c 1 , which is in contrast to the N c 0 scaling in the hadron gas and to the N c 2 scaling in the quark-gluon plasma. Here we clarify the origin of the N c 1 scaling. We employ a solvable field-theoretical large N c chirally symmetric and confining model. In vacuum the confining potential induces a spontaneous breaking of chiral symmetry. The mesons are spatially localized states of quarks and antiquarks. Still in the confining regime the system undergoes the chiral restoration phase transition at T ch because of Paili blocking of the quark levels required for the existence of the quark condensate, by the thermal excitation of quarks and antiquarks. The same Paili blocking leads to a delocalization of the color singlet low-spin meson-like states that become infinitely large in the chiral limit. Consequently the stringy fluid represents a very dense medium of the overlapping huge color-singlet low-spin quark-antiquark systems. The Bethe-Salpeter equation that determines the rest-frame excitation energies of the color-singlet quark-antiquark system is N c -independent both in vacuum and in the medium in the confining regime. The excitation energy of the quark-antiquark color-singlet systems scales as N c 0 , i.e. as meson mass in vacuum. The N c 1 scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.
This study investigates the performance of bent silicon crystals intended to channel hadrons in a fixed-target experiment at the Large Hadron Collider (LHC). The phenomenon of planar channelling in bent crystals enables extremely high effective bending fields for positively charged hadrons within compact volumes. Particles trapped in the potential well of high-purity, ordered atomic lattices follow the mechanical curvature of the crystal, resulting in macroscopic deflections. Although the bend angle remains constant across different momenta (i.e., the phenomenon is non-dispersive), the channelling acceptance and efficiency still depend on the particle momentum. Crystals with lengths in the range of 5 to 10 cm, bent to angles between 5 and 15 mrad, are under consideration for measurements of the electric and magnetic dipole moments of short-lived charmed baryons, such as the Λ c + . Such large deflection angles over short distances cannot be achieved using conventional magnets. The principle of inducing spin precession through bent crystals for magnetic dipole moment measurements was first demonstrated experimentally in the 1990s. Building on this concept, experimental layouts are now being explored for implementation at the LHC. The feasibility of such measurements depends, among other factors, on the availability of crystals that exhibit the required mechanical properties to reach the necessary channelling performance. To address this, a dedicated machine experiment - TWOCRYST - has been installed in the LHC to carry out beam tests in the TeV energy range. The bent crystals for TWOCRYST were fabricated and tested using both X-ray diffraction and high-momentum hadron beams at 180 GeV/c at the CERN Super Proton Synchrotron (SPS) extraction lines. Two crystals based on established technologies were included in this test. In addition, a crystal bent via anodic bonding was tested for the first time with high-energy hadrons to assess its potential for future accelerator applications. This paper presents an analysis of the performance of the three tested crystals and, where possible, outlines key differences in their properties attributed to the respective bending techniques.
We present a study of the impact of data from the upcoming Electron Ion Collider (EIC) on the determination of the strong coupling within the context of the global MSHT fitting framework. To achieve this, we generate EIC electron-proton scattering pseudodata according to both conservative and optimistic experimental uncertainty projections and perform a simultaneous fit to obtain the proton PDFs and the value of the strong coupling. In the conservative case the impact is found to be moderate, but non-negligible, while in the optimistic case it is observed to be rather significant. These results therefore underline the promising potential for the EIC in the determination of the strong coupling. We in addition explore the impact of any potential tensions between the EIC data and the rest of the data in the global fit by injecting explicit inconsistencies into the pseudodata generation. This can lead to a noticeable bias in the extracted value of the strong coupling, highlighting the importance of accounting for all sources of theoretical uncertainty in the fit as well as the relevance of an enlarged, conservative, error definition in the determination of the strong coupling.
The Crab (Calibrated nuclear Recoils for Accurate Bolometry) project aims to precisely characterize the response of cryogenic detectors to sub-keV nuclear recoils of direct interest for coherent neutrino-nucleus scattering and dark matter search experiments. The Crab method relies on the radiative capture of thermal neutrons in the target detector, resulting in a nuclear recoil with a well-defined energy. We present a new experimental setup installed at the TRIGA Mark-II reactor at Atominstitut (Vienna), providing a low intensity beam of thermal neutrons sent to the target cryogenic detector mounted inside a wet dilution refrigerator Kelvinox 100. After the presentation of all components of the setup we report the analysis of first commissioning data with CaWO 4 detectors of the Nucleus experiment. They show stable operation of the cryostat and detectors on a week-scale. Due to an energy resolution currently limited to 20 eV we use neutron beam induced events at high energy, in the 10 to 100 keV range, to demonstrate the excellent agreement between the data and simulation and the accurate understanding of external background. Thanks to these data we also propose an updated decay scheme of the low-lying excited states of 187 W. Finally, we present the first evidence of neutron-capture induced coincidences between BaF 2 γ -detectors installed around the dewar and the inner cryogenic detector. These promising results pave the way for an extensive physics program with various detector materials, like CaWO 4 , Al 2 O 3 , Ge and Si.
The NEXT collaboration is dedicated to the study of double beta decays of 136 Xe using a high-pressure gas electroluminescent time projection chamber. This advanced technology combines exceptional energy resolution ( ≤ 1 % FWHM at the Q β β value of the neutrinoless double beta decay) and powerful topological event discrimination. Building on the achievements of the NEXT-White detector, the NEXT-100 detector started taking data at the Laboratorio Subterráneo de Canfranc (LSC) in May of 2024. Designed to operate with xenon gas at 13.5 bar, NEXT-100 consists of a time projection chamber where the energy and the spatial pattern of the ionising particles in the detector are precisely retrieved using two sensor planes (one with photo-multiplier tubes and the other with silicon photo-multipliers). The detector has been operating at stable conditions using argon and xenon gases at ∼ 4 bar and drift fields of 74 V cm - 1 and 118 V cm - 1 , respectively. Alpha decays from the 222 Rn chain have been used to test and monitor the stability of the detector, showing a constant electron lifetime in the drift volume. In this paper, in addition to reporting the results of the commissioning run, we provide a detailed description of the NEXT-100 detector, describe its assembly, and present the current estimation of the radiopurity budget.
This work explores exotic signatures from confining dark sectors that may arise in the e + e - collision mode at the Future Circular Collider. Assuming the Higgs boson mediates the interaction between the Standard Model and the dark sector, dark quarks can be produced in e + e - collisions. The ensuing strong dynamics may lead to semi-visible jet final states, containing both visible and invisible particles. We investigate semi-visible jets with different fractions of invisible states, and enriched in leptons and photons. When the invisible component is large, selections based on kinematic features, such as the missing energy in the event, already provide good signal-to-background discrimination. For smaller invisible fractions, the reduced missing energy makes these signals more similar to Standard Model events, and we therefore employ a graph neural network jet tagger exploiting differences in jet substructure. This machine learning strategy improves sensitivity and enhances the discovery prospects of Higgs boson-induced semi-visible jets at the Future Circular Collider. Our results show that the proposed strategy can effectively probe a wide parameter space for the models considered, and a variety of signatures, constraining the Higgs boson exotic branching ratios into dark quarks at the permille-level.
We present updates within the MSHT global PDF fit that focus on the high x region, and on improving our understanding of the interplay of various theoretical contributions and experimental constraints here. We revisit the question of target mass and higher twist corrections, considering their impact for the first time at approximate N 3 LO order in a global PDF analysis. Their inclusion is found to be moderate but not negligible on both the PDFs and preferred value of the strong coupling. Increased stability in these at aN 3 LO is observed in comparison to lower orders. We also study the impact of an updated treatment of various fixed-target DIS data, the inclusion of SeaQuest fixed-target Drell Yan data, and new ZEUS data that extends coverage into the high x region. The SeaQuest data have the largest effect of these, in particular on the light quark separation at high x, while the impact of the other updates is rather mild.
Providing accurate theoretical predictions in the Standard Model for processes with polarised electroweak bosons is crucial to understand more in-depth the electroweak-symmetry breaking mechanism and to enhance the sensitivity to potential new-physics effects. Motivated by the rapidly increasing number of polarisation analyses of di-boson processes with LHC data, we carry out a comprehensive study of the inclusive production of two polarised Z bosons in the decay channel with four charged leptons. We perform a detailed comparison of fixed-order predictions obtained with various Monte Carlo programs which rely on different signal-definition strategies, assessing non-resonant and interference effects by contrasting polarised results with unpolarised and full off-shell ones. For the first time, we accomplish the combination of NNLO QCD and NLO EW corrections, setting the new state-of-the-art perturbative accuracy for polarised Z-boson pairs at the LHC. The impact of parton-shower matching and multi-jet merging is investigated by scrutinising calculations obtained with event generators that are typically used in experimental analyses. Integrated and differential results are discussed in a realistic fiducial setup and compared to publicly available ATLAS results.
In this paper, we studied the impact of the off-diagonal SNSI parameters in the future long-baseline neutrino oscillation experiments DUNE and P2SO. In our analysis, we found that the sensitivities of these experiments altered in a very non-trivial way due to the presence of these parameters. Depending on the values of these parameters, they can either completely mimic the standard scenario or can wash out their CP sensitivity. For large values of parameters η e μ and η e τ , we obtained larger mass ordering and octant sensitivities as compared to the standard three flavour scenario. For the parameter η μ τ , the mass ordering sensitivity and the precision of Δ m 31 2 deteriorated compared to the standard scenario. Our results also showed that the sensitivities were significantly influenced by the phases of the off-diagonal parameters.
NUCLEUS is a cryogenic detection experiment which aims to measure Coherent Elastic Neutrino-Nucleus Scattering (CE ν NS) and to search for new physics at the Chooz nuclear power plant in France. This article reports on the prediction of particle-induced backgrounds, especially focusing on the sub-keV energy range, which is a poorly known region where most of the CE ν NS signal from reactor antineutrinos is expected. Together with measurements of the environmental background radiations at the experimental site, extensive Monte Carlo simulations based on the Geant4 package were run both to optimize the experimental setup for background reduction and to estimate the residual rates arising from different contributions such as cosmic ray-induced radiations, environmental gammas and material radioactivity. The NUCLEUS experimental setup is predicted to achieve a total rejection power of more than two orders of magnitude, leaving a residual background component which is strongly dominated by cosmic ray-induced neutrons. In the CE ν NS signal region of interest between 10 and 100 eV, a total particle background rate of ∼  250 d-1 kg-1 keV-1 is expected in the CaWO4 target detectors. This corresponds to a signal-to-background ratio ≳ 1, and therefore meets the required specifications in terms of particle background rejection for the detection of reactor antineutrinos through CE ν NS.
It is well-known that the momentum spectra of particles confined to finite spatial volumes deviate from the continuous spectra used for unconfined particles. In this article, we consider real scalar particles confined to finite volumes with periodic boundary conditions, such that the particles' spectra are discrete. We directly compute the density matrices describing the decay processes ϕ → φ 2 and ϕ → φ χ ν , and subsequently derive expressions for the decay probabilities both for confined and unconfined particles. The latter decay process is used as a rough toy model for a neutron decaying into a proton, an electron, and an anti-electron neutrino. We propose that finite volume effects can have an impact on the outcomes of experiments measuring the neutron lifetime. In addition, our findings at the toy model level suggest that taking into account possible initial correlations between neutrons and their daughter particles might be relevant as well.
A primary objective in contemporary low background physics is the search for rare and novel phenomena beyond the Standard Model of particle physics, e.g. the scattering off of a potential Dark Matter particle or the neutrinoless double beta decay. The success of such searches depends on a reliable background prediction via Monte Carlo simulations. A widely used toolkit to construct these simulations is Geant4, which offers the user a wide choice of how to implement the physics of particle interactions. For example, for electromagnetic interactions, Geant4 provides pre-defined sets of implementations: physics constructors. As decay products of radioactive contaminants contribute to the background mainly via electromagnetic interactions, the physics constructor used in a Geant4 simulation may have an impact on the total energy deposition inside the detector target. To facilitate the selection of physics constructors for simulations of experiments that are using CaWO 4 and Ge targets, we quantify their impact on the total energy deposition for several test cases. These cases consist of radioactive contaminants commonly encountered, covering energy depositions via α , β , and γ particles, as well as two examples for the target thickness: thin and bulky. We also consider the computing performance of the studied physics constructors.
We study the cosmology of multi-field Dark Energy, using a well-motivated axio-dilaton model that contains the minimal number of fields to have the 2-derivative sigma-model interactions that power-counting arguments show naturally compete with General Relativity at low energies. Our analysis differs from earlier, related, studies by treating the case where the dilaton's couplings to matter are large enough to require screening to avoid unacceptable dilaton-mediated forces in the solar system. We use a recently proposed screening mechanism that exploits the interplay between stronger-than-gravitational axion-matter couplings with the 2-derivative axion-dilaton interactions to suppress the couplings of the dilaton to bulk matter. The required axion-matter couplings also modify cosmology, with the axion's background energy density turning out to resemble early dark energy. We compute the properties of the axion fluid describing the rapid oscillations of the axion field around the time-dependent minimum of its matter-dependent effective potential, extending the usual formalism to include nontrivial kinetic sigma-model interactions. We explore the implications of these models for the Cosmic Microwave Background and the growth of structure and find that for dilaton potentials of the Albrecht-Skordis form (itself well-motivated by UV physics), successful screening can be consistent with the early dark energy temporarily comprising as much as 10% of the total density in the past. We find that increasing the dilaton-matter coupling decreases the growth of structure due to enhanced Hubble friction, an effect that dominates the usual fifth-force effects that amplify structure growth.
This paper presents a search for new physics through the process where a massive particle, X, decays into a Higgs boson and a second particle, Y. The Higgs boson subsequently decays into a bottom quark-antiquark pair, which is reconstructed as a single large-radius jet. The decay products of Yare also assumed to produce a single large-radius jet. The identification of the Yparticle is enhanced by computing the anomaly score of its candidate jet using an autoencoder, which measures deviations from typical quark- or gluon-induced jets. This allows a simultaneous search for multiple Ydecay scenarios within a single analysis. In the main benchmark process, Yis a scalar particle that decays into a Wboson pair. Two other scalar Ydecay processes are also considered as benchmarks: decays to a light quark-antiquark pair, and decays to a top quark-antiquark pair. A fourth benchmark process considers Yas a hadronically decaying top quark, arising from the decay of a vector-like quark into a top quark and a Higgs boson. Data recorded by the CMS experiment at a center-of-mass energy of 13 Te V in 2016-2018, corresponding to an integrated luminosity of 138 fb - 1 , are analyzed. The search covers Xmasses between 1.4 and 3.0 Te V and Ymasses between 90 and 400 Ge V , with all simulated signals produced in the narrow-width approximation. No significant excess above the standard model background expectation is observed. The most stringent upper limits to date are placed on benchmark signal cross sections for various masses of X and Y particles.
A unique feature of gas xenon electroluminescent time projection chambers (GXeEL TPCs) in β β 0 ν searches is their ability to reconstruct event topology, in particular to distinguish "single-electron" from "double-electron" tracks, the latter being the signature of a β β 0 ν decay near the decay endpoint Q β β . Together with excellent energy resolution and the t 0 provided by primary scintillation, this topological information is key to suppressing backgrounds. Preserving EL, however, requires operation in pure xenon (with helium as the only benign additive), where electron diffusion is large. Consequently, reconstructed track fidelity is limited by diffusion and intrinsic EL blurring. We propose augmenting the detector with the ability to image not only the electron track but also the corresponding mirror ion track. Introducing trace amounts of NH 3 ( ∼ 100 ppb) converts primary xenon ions into ammonium ions, NH 4 + , via a fast two-step ion-molecule process involving charge transfer followed by proton transfer, while leaving EL unaffected. Electrons drift rapidly to the anode, producing the standard EL image, whereas NH 4 + ions drift slowly toward the cathode, allowing time to determine the event energy and barycenter. For events in the region of interest, an ion sensor near the cathode at the projected barycenter captures the ions. Laser interrogation of the sensor's molecular layer then reveals an ion-track image with sub-millimeter diffusion and no EL-induced smearing. Combined electron-ion imaging strengthens topological discrimination, improving background rejection by about an order of magnitude and significantly extending the discovery potential of GXeEL TPCs for very long β β 0 ν lifetimes.
Triboson production processes play a crucial role in probing the electroweak sector of the Standard Model, as they involve quartic gauge-boson couplings already at the tree level. With these measurements entering the precision era at the Large Hadron Collider (LHC), accurate theoretical predictions become indispensable. We present the computation of the next-to-next-to-leading-order (NNLO) QCD radiative corrections to the production of a W boson in association with two photons ( W γ γ ) at the LHC. The calculation is exact, except for the finite part of the two-loop contribution, which is included in the leading-colour approximation. Predictions for the fiducial cross section and selected kinematic distributions are provided at a centre-of-mass energy of s = 13  TeV, under standard experimental selection cuts. In line with observations for other multiboson processes involving direct photons, we find sizable NNLO corrections that enhance the next-to-leading-order predictions by about 23 % , with residual perturbative uncertainties that can be roughly estimated to be at the 5 % level.
High-Energy Physics experiments are facing a multi-fold data increase with every new iteration. This is certainly the case for the upcoming High-Luminosity LHC upgrade. Such increased data processing requirements forces revisions to almost every step of the data processing pipeline. One such step in need of an overhaul is the task of particle track reconstruction, a.k.a., tracking. A Machine Learning-assisted solution is expected to provide significant improvements, since the most time-consuming step in tracking is the assignment of hits to particles or track candidates. This is the topic of this paper. We take inspiration from large language models. As such, we consider two approaches: the prediction of the next word in a sentence (next hit point in a track), as well as the one-shot prediction of all hits within an event. In an extensive design effort, we have experimented with three models based on the Transformer architecture and one model based on the U-Net architecture, performing track association predictions for collision event hit points. In our evaluation, we consider a spectrum of simple to complex representations of the problem, eliminating designs with lower metrics early on. We report extensive results, covering both prediction accuracy (score) and computational performance. We have made use of the REDVID simulation framework, as well as reductions applied to the TrackML data set, to compose five data sets from simple to complex, for our experiments. The results highlight distinct advantages among different designs in terms of prediction accuracy and computational performance, demonstrating the efficiency of our methodology. Most importantly, the results show the viability of a one-shot encoder-classifier based Transformer solution as a practical approach for the task of tracking.
We present a detailed investigation of the performance of transition-edge sensor (TES) microcalorimeters with 163 Ho atoms embedded by ion implantation, as part of the HOLMES experiment aimed at neutrino mass determination. The inclusion of 163 Ho atoms introduces an excess heat capacity due to a pronounced Schottky anomaly, which can affect the detector's energy resolution, signal height, and response time. We fabricated TES arrays with varying levels of 163 Ho activity and characterized their performance in terms of energy resolution, decay time constants, and heat capacity. The intrinsic energy resolution was found to degrade with increasing 163 Ho activity, consistent with the expected scaling of heat capacity. From the analysis, we determined the specific heat capacity of 163 Ho to be ( 2.9 ± 0.4 ( stat ) ± 0.7 ( sys ) ) J/K/mol at ( 94 ± 1 )  mK, close to the literature values for metallic holmium. No additional long decay time constants correlated with 163 Ho activity were observed, indicating that the excess heat capacity does not introduce weakly coupled thermodynamic systems. These results suggest that our present TES microcalorimeters can tolerate 163 Ho activities up to approximately 5 Bq, with only about a factor of three degradation in performance compared to detectors without 163 Ho. For higher activities, reducing the TES transition temperature is necessary to maintain or improve the energy resolution. These findings provide critical insights for optimizing TES microcalorimeters for future neutrino mass experiments and other applications requiring embedded radioactive sources. The study also highlights the robustness of TES technology in handling limited amounts of implanted radionuclides while maintaining high-resolution performance.
We present a deep learning pipeline to perform a model-independent, likelihood-free search for anomalous (i.e., non-background) events in the proposed next-generation multi-ton scale liquid xenon-based direct detection experiment, DARWIN. We train an anomaly detector comprising a variational autoencoder (VAE) and a classifier on high-dimensional simulated detector response data and construct a 1D anomaly score to reject the background-only hypothesis in the presence of an excess of non-background-like events. We use simulated validation data to determine the power of the method to reject the background-only hypothesis in the presence of a WIMP dark matter signal, without any model-dependent assumption about the nature of the signal. We show that our neural networks learn relevant features of the events from low-level, high-dimensional detector outputs, avoiding lossy and computationally expensive compression into lower-dimensional observables. Our approach is complementary to the usual likelihood-based analysis, in that it reduces the reliance on many of the corrections and cuts that are traditionally part of the analysis chain, with the potential of achieving higher accuracy and significant reduction of analysis time. We envisage the methodology presented in this work augmenting or complementing likelihood-based and other data-driven methods currently utilized in the DARWIN (and in the future, XLZD) analysis pipeline.