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In this work, we propose a novel end-to-end Sinkhorn Autoencoder with a noise generator for efficient data collection simulation. Simulating processes that aim at collecting experimental data is crucial for multiple real-life applications, including nuclear medicine, astronomy, and high energy physics. Contemporary methods, such as Monte Carlo algorithms, provide high-fidelity results at a price of high computational cost. Multiple attempts are taken to reduce this burden, e.g. using generative approaches based on Generative Adversarial Networks or Variational Autoencoders. Although such methods are much faster, they are often unstable in training and do not allow sampling from an entire data distribution. To address these shortcomings, we introduce a novel method dubbed end-to-end Sinkhorn Autoencoder, that leverages the Sinkhorn algorithm to explicitly align distribution of encoded real data examples and generated noise. More precisely, we extend autoencoder architecture by adding a deterministic neural network trained to map noise from a known distribution onto autoencoder latent space representing data distribution. We optimise the entire model jointly. Our method outperforms co mpeting approaches on a challenging dataset of simulation data from Zero Degree Calorimeters of ALICE experiment in LHC. as well as standard benchmarks, such as MNIST and CelebA. In this work, we propose a novel end-to-end sinkhorn autoencoder with noise generator for efficient data collection simulation. Simulating processes that aim at collecting experimental data is crucial for multiple real-life applications, including nuclear medicine, astronomy and high energy physics. Contemporary methods, such as Monte Carlo algorithms, provide high-fidelity results at a price of high computational cost. Multiple attempts are taken to reduce this burden, e.g. using generative approaches based on Generative Adversarial Networks or Variational Autoencoders. Although such methods are much faster, they are often unstable in training and do not allow sampling from an entire data distribution. To address these shortcomings, we introduce a novel method dubbed end-to-end Sinkhorn Autoencoder, that leverages sinkhorn algorithm to explicitly align distribution of encoded real data examples and generated noise. More precisely, we extend autoencoder architecture by adding a deterministic neural network trained to map noise from a known distribution onto autoencoder latent space representing data distribution. We optimise the entire model jointly. Our method outperforms competing approaches on a challenging dataset of simulation data from Zero Degree Calorimeters of ALICE experiment in LHC. as well as standard benchmarks, such as MNIST and CelebA.

In High Energy Physics experiments Particle Flow (PFlow) algorithms are designed to provide an optimal reconstruction of the nature and kinematic properties of the particles produced within the detector acceptance during collisions. At the heart of PFlow algorithms is the ability to distinguish the calorimeter energy deposits of neutral particles from those of charged particles, using the complementary measurements of charged particle tracking devices, to provide a superior measurement of the particle content and kinematics. In this paper, a computer vision approach to this fundamental aspect of PFlow algorithms, based on calorimeter images, is proposed. A comparative study of the state of the art deep learning techniques is performed. A significantly improved reconstruction of the neutral particle calorimeter energy deposits is obtained in a context of large overlaps with the deposits from charged particles. Calorimeter images with augmented finer granularity are also obtained using super-resolution techniques., Comment: 15 pages, 10 figures. Note to admin : updating to journal version

Two remarkable facts about JT two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensemble is described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations -- as derived from the GD construction of the resolvent -- are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed -- in the string-equation context -- and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included -- alongside a brief discussion of quasinormal modes., 107 pages, 50 plots in 25 figures, 2 tables, jheppub-nosort.sty

We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N=1 supersymmetric string theories in four dimensions, or as generating functions for relative Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory., 67 pages, 4 figures; v2: Appendix E added, references added, typos corrected, matches published version

In the design phase and simulation of a circular accelerator, it is fundamental to have a proper understanding of the single-particle non-linear betatronic motion, and of how such dynamics interfere with beam quality. In this work we study stochastically-perturbed Hamiltonian systems using a diffusive framework, based on the Fokker-Plank equation. This study is then applied to the analysis of the non-linear betatronic motion and to the Dynamic Aperture problem. In particular, we lay down the basis for formulating an interpolation procedure for Nekhoroshev-like diffusive processes and we pro-pose an experimental procedure for measuring the local diffusive behaviour inside an accelerator. Dynamic Aperture is a key quantity for the long-term behaviour of an accelerator. However, the measure of this quantity via simulation presents serious computational difficulties. Because of that it is in our interest to develop a functional law which models the DA time-dependence.

Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in $dP_3$, for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill--Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space., 42 pages + appendix

Multi-objective optimization is important for particle accelerators where various competing objectives must be satisfied routinely such as, for example, transverse emittance vs bunch length. We develop and demonstrate an online multi-time scale multi-objective optimization algorithm that performs real time feedback on particle accelerators. We demonstrate the ability to simultaneously minimize the emittance and maintain a reference trajectory of a beam in the electron beamline in CERN’s Advanced Proton Driven Plasma Wakefield Acceleration Experiment. Multi-objective optimization is important for particle accelerators where various competing objectives must be satisfied routinely such as, for example, transverse emittance vs bunch length. We develop and demonstrate an online multi-time scale multi-objective optimization algorithm that performs real time feedback on particle accelerators. We demonstrate the ability to simultaneously minimize the emittance and maintain a reference trajectory of a beam in the electron beamline in CERN's Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE).

Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, an optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics. Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter technique allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, the optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics.

Das Verst��ndnis der elektromagnetischen Interaktion eines Teilchenstrahls mit den Elementen eines Teilchenbeschleunigers in seiner nahen Umgebung - sogenannte indirect space charge driven (ISCD) Effekte - ist entscheidend f��r einen stabile Betrieb eines Teilchenbeschleunigers bei hoher Intensit��t. Diese Thematik wird in dieser Doktorarbeit behandelt, wobei die gewonnen Erkenntnisse am CERN Beschleunigerkomplex f��r eine ��berpr��fung der Theorie Anwendung fanden. Eine akkurate quantitative Beschreibung f��r den ISCD Tune-shift, welcher w��hrend des Betriebs des Large Hadron Colliders (LHC) korrigiert werden muss, fehlte. Der in dieser Arbeit entwickelte Ansatz basiert auf komplexen Greenschen Funktionen. Diese Methode zeigt eine ausgezeichnete ��bereinstimmung mit Messungen mit beispielloser Genauigkeit. Als Hauptursache f��r den ISCD Tune-shift wurde die elektrische Interaktion mit dem sogenannten Beam-screen identifiziert. Ein Model, welches mit Hilfe von geschlossenen Formen ausgedr��ckt werden kann, wurde formuliert. Dieses ist auch auf zuk��nftige Beschleunigerprojekte wie das High Luminosity (HL)-LHC Projekt, bei welchem die Intensit��t des Teilchenstrahls und folglich die dadurch getriebenen Effekte um mehr als einen Faktor zwei h��her sein werden, anwendbar. Bei der Multi-Turn Extraktion im Proton Synchrotron (PS) wird der Teilchenstrahl in einen Hauptstrahl und vier Satellitenstrahlen, - die sogenannten Beamlets - aufgeteilt. In Messungen hat man eine Intensit��tsabh��ngigkeit des Tunes und der Position beobachtet. Diese Effekte konnten in analytische Berechnungen und numerischen Simulationen durch ISCD Effekte erkl��rt werden, welche auf in dieser Arbeit hergeleiteten geschlossenen Formen basieren. Um einfache mathematische Ausdr��cke zu erhalten wurde ein neuer Lorentzoperator der zugrundeliegenden Greenschen Funktionen welche wiederum Operatoren konformer Abbildungen auf der Riemannsph��re sind, und daraus folgend die sogenannte Image-operators f��r beliebige transverse Teilchenstrahlverteilungen, eingef��hrt. Diese Operatoren erlauben es den ISCD Tune-shift von komplexen Beschleunigermodellen abzusch��tzen. Eine neue Methode zur Absch��tzung der (elektrostatischen) Greenschen Funktion f��r beliebige einfach-zusammenh��ngende Gebiete mit einer Fehlerabsch��tzung wird bewiesen. Diese Methode wird verwendet um eine Approximation des LHC Beam-screens anzugeben. Eine neue Integraldarstellung der (magnetostatischen) Neumannfunktion auf der Riemannsph��re f��r glatte einfach-zusammenh��ngende Gebiete wird bewiesen. Dadurch ist es m��glich eine Klassifizierung der Neumannfunktion in beschr��nkte, regulated und ��ussere Gebiete vorzunehmen. Eine neue Methode wird pr��sentiert, welche es erlaubt geschlossene Formen der Neumannfunktion f��r unbeschr��nkte sternf��rmige Gebiete zu finden. Dies erm��glicht es neue geschlossene L��sungen f��r elementare Geometrien wie zum Beispiel =-Pole oder combined-function Magnete des PS zu erhalten (bis jetzt waren nur parallele Platten Modelle bekannt). Zus��tzlich werden neue off-axis Image Tensoren f��r Standardgeometrien, welche sorgf��ltig mit in der Literatur vorhandenen on-axis L��sungen verglichen wurden, in geschlossenen Formen bereitgestellt., The understanding of the electromagnetic interaction of the particle beam with the surrounding elements - so-called indirect space charge driven (ISCD) effects - in particle accelerators, is crucial for stable high-intensity performance. It is addressed and applied at the CERN accelerator complex. An appropriate quantitative explanation for the ISCD tune-shift which must be corrected during the operation of the Large Hadron Collider (LHC) was missing. This work developed an approach based on complex Green functions which provides excellent agreement with the measurement with unprecedented accuracy. As the primary origin of the ISCD tune-shift, the electric interaction with the beam-screen is identified. A closed-form model is obtained, that is also applicable to future accelerator projects as the High Luminosity (HL)-LHC, where these effects will be at least a factor two higher. During the Multi-Turn Extraction in the Proton Synchrotron (PS), the beam is split into the main beam and four islands so-called beamlets. In measurements, an intensity dependence in the beamlet position and tune was observed. It is resolved due to ISCD effects in analytical calculations and numerical simulations based on closed-form expression acquired in this thesis. In order to obtain simple mathematical expressions, a novel Lorentz operator of the Green functions, on the Riemann-sphere (RS), and from it, the so-called image operators for arbitrary beam distributions are derived. These operators allow to estimate the ISCD tune-shift of complex accelerator models. A novel method to approximate the fundamental electrostatic field (the Green function) of arbitrary simply-connected domains, including an error bound, is proven. This method is used to approximate the rect-elliptical LHC beam-screen. Additionally, a new integral representation of the Neumann function on the RS for smooth bounded simply- connected domains is derived. It allows for classifying domains concerning the solution of the Neumann function into bounded, regulated and exterior solutions. A method is presented, to obtain novel closed-form solutions in the case of star- like regulated domains. Consequently, several novel closed-form solutions for the magnetic interaction of essential shapes as the =-poles or the combined-function magnets of the PS are obtained (so far only parallel plates were used). Finally, several new off-axis image tensors for standard geometries are provided.

The well-known modular property of the torus characters and torus partition functions of (rational) vertex operator algebras (VOAs) and 2d conformal field theories (CFTs) has been an invaluable tool for studying this class of theories. In this work we prove that sphere four-point chiral blocks of rational VOAs are vector-valued modular forms for the groups $\Gamma(2)$, $\Gamma_0(2)$, or $\text{SL}_2(\mathbb{Z})$. Moreover, we prove that the four-point correlators, combining the holomorphic and anti-holomorphic chiral blocks, are modular invariant. In particular, in this language the crossing symmetries are simply modular symmetries. This gives the possibility of exploiting the available techniques and knowledge about modular forms to determine or constrain the physically interesting quantities such as chiral blocks and fusion coefficients, which we illustrate with a few examples. We also highlight the existence of a sphere-torus correspondence equating the sphere quantities of certain theories $\mathcal{T}_s$ with the torus quantities of another family of theories $\mathcal{T}_t$. A companion paper will delve into more examples and explore more systematically this sphere-torus duality., Comment: 72 pages, 4 figures

It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection numbers and twisted homology theory to define a coaction on certain hypergeometric functions. The functions we consider admit an integral representation where both the integrand and the contour of integration are associated with positive geometries. As in dimensionally- regularized Feynman integrals, endpoint singularities are regularized by means of exponents controlled by a small parameter ϵ. We show that the coaction defined on this class of integral is consistent, upon expansion in ϵ, with the well-known coaction on multiple polylogarithms. We illustrate the validity of our construction by explicitly determining the coaction on various types of hypergeometric $_{p+1}$F$_{p}$ and Appell functions. It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection numbers and twisted homology theory to define a coaction on certain hypergeometric functions. The functions we consider admit an integral representation where both the integrand and the contour of integration are associated with positive geometries. As in dimensionally-regularized Feynman integrals, endpoint singularities are regularized by means of exponents controlled by a small parameter $\epsilon$. We show that the coaction defined on this class of integral is consistent, upon expansion in $\epsilon$, with the well-known coaction on multiple polylogarithms. We illustrate the validity of our construction by explicitly determining the coaction on various types of hypergeometric ${}_{p+1}F_p$ and Appell functions.

Assuming a certain continuity property, we prove, using the old results of Itzykson and Martin, that, except for an obvious ambiguity, there are only at most two amplitudes reproducing an elastic differential cross section at a given energy., 10 pages, 1 figure

Obtaining insights in the tremendous amount of data in which the Big Data era has brought us, requires to develop specific tools, that are not only summaries of data through classical charts and tables, but that allow full navigation and browsing of a dataset. The proper modeling of databases can enable such navigation and we propose in this Thesis a methodology to achieve the browsing of an information space, through its different facets. To achieve the modeling of such an information space, co-occurrences of data instances are built referring to a common reference type. Historically, the co-occurrences were seen as pairwise relationships and developed as such. The move to hypergraphs enables the possibility to take into account the multi-adicity of the relationships, and to have a representation through the incident graph that simplifies deeply its 2-section. Nonetheless, representing large hypergraphs calls for a coarsening of the information by having insights on important vertices and hyperedges. One classical way to achieve it is to use a diffusion process over the network. Achieving it using an incident matrix is feasible but brings us to a pitfall, as it brings us back to a pairwise relationship. Making proper diffusion requires a tensor approach. This is well known for uniform hypergraphs, where all the hyperedges have same cardinality, but still very challenging for general hypergraphs. After redefining the concept of adjacency in general hypergraphs, we propose a first e-adjacency tensor, that involves a Hypergraph Uniformisation Process and a Polynomial Homogenization Process. This is achieved by uniformisation of the original hypergraph by decomposing it into layers—each of them containing a uniform hypergraph—and filling each layer with additional special vertices and merging them together. This process requires to have as many additional vertices as the number of layers. In order to reduce the number of special vertices, we need to have the possibility of re- peating a vertex when filling, which is not possible with hyperedges as they are sets. We need multisets. It, therefore, requires a new mathematical structure, that we have intro- duced and called hyper-bag-graph—hb-graph for short—, which is a family of multisets of a given universe. Co-occurrences can also have repetitions or individual weighting of their vertices inside a given co-occurrence and hb-graphs fit to handle it. Hence, we introduce a hb-graph framework for co-occurrence networks. We then work on diffusion on such structures, using, in a first step, a matrix approach. Aggregating the ranking of vertices and hb- edges of this diffusion on each of the facet of the information space is achieved by using a multi-diffusion scheme. Since different facets might have different focus of interest, we introduce a biased diffusion that enables a tuning on the point of emphasis on the feature we are interested in. Finally, coming back to e-adjacency tensor, we propose three e-adjacency tensors of hb- graphs, that are based on different ways of filling the hb-edges. The m-uniformisation that is achieved is evaluated and compared to the ones achieved by hb-edge splitting, concluding that any m-uniformisation process has an influence on the exchange-based diffusion that we propose. Hence, we conclude that diffusion using the tensor approach must be done in an informed manner to account for this diffusion change. We finally discuss different possible of achieving it and present a new Laplacian that can help to achieve it.

Jet flavour classification is of paramount importance for a broad range of applications in modern-day high-energy-physics experiments, particularly at the LHC. In this paper we propose a novel architecture for this task that exploits modern deep learning techniques. This new model, called DeepJet, overcomes the limitations in input size that affected previous approaches. As a result, the heavy flavour classification performance improves, and the model is extended to also perform quark-gluon tagging., Comment: 14 pages, 9 figures, accepted for publication in JINST

We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples., 63 pages, 17 figures. V2: minor modifications

In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit. Such a multi-physics, multi-rate and multi-scale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both circuit and magnet level during normal operation and in case of faults. We derive an equivalent magnet model at the circuit side for the linear and the non-linear settings and discuss the convergence of the overall scheme in the framework of optimized Schwarz methods. The efficiency of the developed approach is illustrated by a numerical example of an accelerator dipole magnet with accompanying protection system., Comment: 8 pages, 7 figures

We present the TBA equations and the Y-system for the exact spectrum of general multi-magnon local operators in the $D$-dimensional anisotropic version of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in terms of fishnet planar graphs of multi-wheel and multi-spiral type. These graphs probe the two main building blocks of the TBA approach that are the magnon dispersion relation and the magnon scattering matrix and which we both obtain by diagonalising suitable graph-building operators. We also obtain the dual version of the TBA equations, which relates, in the continuum limit, $D$-dimensional graphs to two dimensional sigma models in $AdS_{D+1}$. It allows us to verify a general formula obtained by A.~Zamolodchikov for the critical coupling., 7 pages, 2 figures

We study the notion of strong integrability for classically integrable $\lambda$-deformed CFTs and coset CFTs. To achieve this goal we employ the Poisson brackets of the spatial Lax matrix which we prove that it assumes the Maillet $r/s$-matrix algebra. As a consequence the system in question are integrable in the strong sense. Furthermore, we show that the derived Maillet $r/s$-matrix algebras can be realized in terms of twist functions, at the poles of which we recover the underlying symmetry algebras., Comment: v1:1+22 pages, Latex, v2: NPB version

We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography., 30 pages, 2 figures; v2 minor changes and references added

Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov--Arnold--Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical simulations, however, a number of shortcomings had been identified and new models are proposed in this paper, which solve the observed issues. The new models have been benchmarked against numerical simulations for a simple system, the 4D H\'enon map, as well as a realistic, non-linear representation of the beam dynamics in the LHC at 6.5 TeV providing in both cases excellent results. Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov–Arnold–Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical simulations, however a number of shortcomings had been identified and new models are proposed in this paper, which solve the observed issues. The new models have been benchmarked against numerical simulations for a simple system, the 4D Hénon map, as well as a realistic, non-linear representation of the beam dynamics in the LHC at 6.5 TeV providing in both cases excellent results.

Recently, we constructed the first-principle derivation of the holographic dual of N=4 SYM in the double-scaled $\gamma$-deformed limit directly from the CFT side. The dual fishchain model is a novel integrable chain of particles in AdS5. It can be viewed as a discretized string and revives earlier string-bit approaches. The original derivation was restricted to the operators built out of one of two types of scalar fields. In this paper, we extend our results to the general operators having any number of scalars of both types, except for a very special case when their numbers are equal. Interestingly, the extended model reveals a new discrete reparametrization symmetry of the "world-sheet", preserving all integrals of motion. We use integrability to formulate a closed system of equations, which allows us to solve for the spectrum of the model in full generality, and present non-perturbative numerical results. We show that our results are in agreement with the Asymptotic Bethe Ansatz of the fishnet model up to the wrapping order at weak coupling., Comment: 30 pages, 11 figures. v2: references added

We introduce a nonperturbative approach to correlation functions of two determinant operators and one non-protected single-trace operator in planar N=4 supersymmetric Yang-Mills theory. Based on the gauge/string duality, we propose that they correspond to overlaps on the string worldsheet between an integrable boundary state and a state dual to the single-trace operator. We determine the boundary state using symmetry and integrability of the dual superstring sigma model, and write down expressions for the correlators at finite coupling, which we conjecture to be valid for operators of arbitrary size. The proposal is put to test at weak coupling., 6 pages. A letter version of arXiv:1906.07733 with new results; v2 typos corrected, references added

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in $AdS_5$. We prove the duality at the full quantum level in the ${\mathfrak u}(1)$ sector and reproduce exactly the spectrum for the cases when it is known analytically., Comment: 38 pages, 3 figures, v2 - typos corrected, references updated, v3 - acknowledgment added

Numerical modeling of complex physical systems involving several coupled physical domains, so called multi-domain and multi-physics systems, poses considerable challenges w.r.t. consistency of the formulation and selection of a suitable representation. The landscape is further complicated in case these phenomena occur at a wide range of temporal (multi-rate) and spatial (multi-scale) scales. Resolving all in one scale may result in unacceptable computational time. Recent development in port-based modeling techniques, in particular the port-Hamiltonian framework originating from control theory, made it possible to model complex multi-domain and multi-physics phenomena represented by means of both ordinary and partial differential equations in a generic and consistent way. The port-Hamiltonian models capture in an elegant way the internal energy flow, storage, dissipation as well as interaction through lumped, distributed, and boundary ports. In the thesis, we employ the port-Hamiltonian formalism to characterize the coupling between the electromagnetic and thermodynamic systems in a superconducting magnet along with an accompanying electrical circuit. In addition, we employ bond graph modeling to graphically represent the energy flow in the considered systems. These methods allow to study the model consistency as well as the computational causality. Similarly, the advances in cooperative simulation, in particular the application of the waveform relaxation algorithm to field/circuit coupling along with the use of preconditioners for field models allowed to achieve satisfactory convergence rates and accurate results. This method is particularly suited to approach multi-rate and multi-scale problems such as the simulation of a superconducting magnet and circuit. In this thesis, an architecture, data structures, and algorithms for automatic handling of hierarchical co-simulation are presented. The resulting framework supports four main co-simulation algorithms (one-way coupling, weak coupling, strong coupling, and waveform relaxation). Furthermore, the evolution of a transient in a co-simulation scenario may call for the adjustment of the model fidelity in order to accurately reproduce a given phenomenon. This is achieved by switching models and coupling algorithms during the co-simulation execution. The performance of the presented co-simulation framework is illustrated with several relevant examples of transient effects in accelerator magnets. The studied co-simulation scenarios involve superconducting accelerator magnets, circuits, and controllers of power converters in nominal and failure conditions. The developed energy-based models support the analysis of the performance of the co-simulation scenarios.

We present the first-principle derivation of a weak-strong duality between the fishnet theory in four dimensions and a discretized string-like model living in five dimensions. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the $4$-point correlator computed before non-perturbatively from the conformal partial wave expansion. Due to the extreme simplicity of our model, it could provide an ideal playground for holography with no super-symmetry. Furthermore, since the fishnet model and ${\cal N}=4$ SYM theory are continuously linked our consideration could shed light on the derivation of AdS/CFT for the latter., 5 pages. v2: references added, v3 - acknowledgment added

We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the geometry of backgrounds of key supergravity theories, which have applications in the context of black holes, string theory, M-theory and the AdS/CFT correspondence unveiling a plethora of existence and uniqueness theorems. Some other aspects of supersymmetric solutions like the Killing superalgebras and the homogeneity theorem are also presented, and the non-existence theorem for certain smooth supergravity flux compactifications is outlined. Amongst the applications described is the proof of the emergence of conformal symmetry near black hole horizons and the classification of warped AdS backgrounds that preserve more than 16 supersymmetries., Comment: Review, 174 pages. v2: Minor changes, references added

Monopole bubbling contributions to supersymmetric 't Hooft loops in 4d $\mathcal{N}=2$ theories are computed by SQM indices. As recently argued, those indices are hard to compute due to the presence of Coulomb vacua that are not captured by standard localization techniques. We propose an algorithmic method to compute the full bubbling contributions that circumvent this issue, by considering SQM with more matter fields and isolating the bubbling terms as residues in flavor fugacities. The enlarged SQMs are read from brane configurations realizing the bubbling sector of a given 't Hooft loop. We apply our technique to loop operators in $\mathcal{N}=2$ conformal SQCD theories. In addition we embed this discussion in the larger setup of a 5d-4d system interacting along a line, associated to the brane systems previously discussed. The bubbling terms arise from residues of specific instanton sectors of 5d line operators in this context., 50 pages, 18 figures

We develop an efficient method to compute the torus partition function of the six-vertex model exactly for finite lattice size. The method is based on the algebro-geometric approach to the resolution of Bethe ansatz equations initiated in a previous work, and on further ingredients introduced in the present paper. The latter include rational Q-system, primary decomposition, algebraic extension and Galois theory. Using this approach, we probe new structures in the solution space of the Bethe ansatz equations which enable us to boost the efficiency of the computation. As an application, we study the zeros of the partition function in a partial thermodynamic limit of M × N tori with N ≫ M. We observe that for N → ∞ the zeros accumulate on some curves and give a numerical method to generate the curves of accumulation points., Journal of High Energy Physics, 2019 (3), ISSN:1126-6708, ISSN:1029-8479

Classical 10d string backgrounds with a 4d de Sitter space-time, D-brane and orientifold sources, are commonly believed to satisfy the following: 1. There is no classical de Sitter solution with parallel sources. 2. Classical de Sitter solutions with intersecting sources are unstable. 3. Classical de Sitter solutions cannot have at the same time a large internal volume, a small string coupling, a bounded number of orientifolds and quantized fluxes. These three conjectures are of particular relevance to the swampland program, and if true, they challenge the connection of string theory to cosmology. We restrict here to a standard solution ansatz for which the problem is well-defined, and we still fail to prove analytically any of these conjectures. While developing new tools and obtaining new constraints, we identify remaining corners of parameter space where counter-examples to these conjectures could be found., Comment: v2: more results on conjecture 2, clarifications on conjecture 3; v3: minor changes, published version

We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The assumptions are minimal, namely those of local quantum field theory (in the case when dispersion relations hold). In Appendix A, lower bounds for the forward particle-particle and particle-antiparticle amplitudes are obtained. This is of independent interest., 18 pages, 5 figures; minor corrections

Several proposals aimed at measuring the Electric Dipole Moment (EDM) for charged particles require very precise simulations and understanding of the systematic errors that can contribute to a spin buildup mimicking the EDM signal to be detected. In what follows, one used the Bogoliubov-Krylov-Mitropolski method of averages to solve the T-BMT equation and calculate the Berry phases arising for a proton EDM storage ring. The formalism employed proved to be particularly useful to determine the evolution of the spin at the observation point, i.e. at the location of the polarimeter. Several selected cases of lattice imperfections were simulated and benchmarked with the analytical estimates. This allowed the proof of the convergence of the numerical simulations and helped gain better understanding of the systematic errors.

We present a novel way to classify Calabi-Yau threefolds by systematically studying their infinite volume limits. Each such limit is at infinite distance in Kahler moduli space and can be classified by an associated limiting mixed Hodge structure. We then argue that the such structures are labeled by a finite number of degeneration types that combine into a characteristic degeneration pattern associated to the underlying Calabi-Yau threefold. These patterns provide a new invariant way to present crucial information encoded in the intersection numbers of Calabi-Yau threefolds. For each pattern, we also introduce a Hasse diagram with vertices representing each, possibly multi-parameter, decompactification limit and explain how to read off properties of the Calabi-Yau manifold from this graphical representation. In particular, we show how it can be used to count elliptic, K3, and nested fibrations and determine relations of elliptic fibrations under birational equivalence. We exemplify this for hypersurfaces in toric ambient spaces as well as for complete intersections in products of projective spaces., Comment: 41 pages, 17 figures

Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice $A_2$, which arose in the study of rank 3 vector bundles on $\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined., 32 pages, 2 figures; v2: discussed $\Delta_{12}=0$ case at end of section 3, added subsection 4.4 on $C_1=C_2$ case (relevant for signature (2,1)), and added several references; v3: published version in Selecta Mathematica (with apologies for not uploading it earlier)

Machine learning has been applied to several problems in particle physics research, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising future research and development areas for machine learning in particle physics. We detail a roadmap for their implementation, software and hardware resource requirements, collaborative initiatives with the data science community, academia and industry, and training the particle physics community in data science. The main objective of the document is to connect and motivate these areas of research and development with the physics drivers of the High-Luminosity Large Hadron Collider and future neutrino experiments and identify the resource needs for their implementation. Additionally we identify areas where collaboration with external communities will be of great benefit., Comment: Editors: Sergei Gleyzer, Paul Seyfert and Steven Schramm

Let $P$ be a Laplace type operator acting on a smooth hermitean vector bundle $V$ of fiber $\mathbb{C}^N$ over a compact Riemannian manifold given locally by $P= - [g^{\mu\nu} u(x)\partial_\mu\partial_\nu + v^\nu(x)\partial_\nu + w(x)]$ where $u,\,v^\nu,\,w$ are $M_N(\mathbb{C})$-valued functions with $u(x)$ positive and invertible. For any $a \in \Gamma(\text{End}(V))$, we consider the asymptotics $\text{Tr} (a e^{-tP}) \underset{t \downarrow 0^+}{\sim} \,\sum_{r=0}^\infty a_r(a, P)\,t^{(r-d)/2}$ where the coefficients $a_r(a, P)$ can be written locally as $a_r(a, P)(x) = \text{tr}[a(x) \mathcal{R}_r(x)]$. The computation of $\mathcal{R}_2$ is performed opening the opportunity to calculate the modular scalar curvature for noncommutative tori., Comment: 32 pages. v2: small modifications in the text, added the missing ancillary Mathematica notebook file which proves, by direct computations, some results established in the paper

By employing CFT techniques, we show how to compute in the context of \lambda-deformations of current algebras and coset CFTs the exact in the deformation parameters C-function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left-right asymmetric current algebras and coset CFTs. In all cases, the derived exact C-functions obey all the properties asserted by Zamolodchikov's c-theorem in two-dimensions., Comment: v1: 1+15 pages, Latex, v2: PLB version, v3: Correcting a typo in footnote 6

F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to string model building, quantum gravity, (non-perturbative) quantum field theories in various dimensions and mathematics. Its computational power derives from the geometrisation of physical reasoning, establishing a deep correspondence between fundamental concepts in gauge theory and beautiful structures of elliptic fibrations. These lecture notes, which are an extended version of my lectures given at TASI 2017, introduce some of the main concepts underlying the recent technical advances in F-theory compactifications and their various applications. The main focus is put on explaining the F-theory dictionary between the local and global data of an elliptic fibration and the physics of 7-branes in Type IIB compactifications to various dimensions via duality with M-theory. The geometric concepts underlying this dictionary include the behaviour of elliptic fibrations in codimension one, two, three and four, the Mordell-Weil group of rational sections, and the Deligne cohomology group specifying gauge backgrounds. F-theory is probably the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to string model building, quantum gravity, (non-perturbative) quantum field theories in various dimensions and mathematics. Its computational power derives from the geometrisation of physical reasoning, establishing a deep correspondence between fundamental concepts in gauge theory and beautiful structures of elliptic fibrations.These lecture notes, which are an extended version of my lectures given at TASI 2017, introduce some of the main concepts underlying the recent technical advances in F-theory compactifications and their various applications. The main focus is put on explaining the F-theory dictionary between the local and global data of an elliptic fibration and the physics of 7-branes in Type IIB compactifications to various dimensions via duality with M-theory. The geometric concepts underlying this dictionary include the behaviour of elliptic fibrations in codimension one, two, three and four, the Mordell-Weil group of rational sections, and the Deligne cohomology group specifying gauge backgrounds.

We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture are given by a discrete multi-variate gaussian over the hidden state space. This allows us to sample the visible sector density function in a straight-forward manner. Furthermore, we show that the visible sector probability density function possesses an affine transform property, similar to the multi-variate gaussian density., Comment: 9 pages, 6 figures

Recent results at the Large Hadron Collider (LHC) have pointed to enhanced physics capabilities through the improvement of the real-time event processing techniques. Machine learning methods are ubiquitous and have proven to be very powerful in LHC physics, and particle physics as a whole. However, exploration of the use of such techniques in low-latency, low-power FPGA hardware has only just begun. FPGA-based trigger and data acquisition (DAQ) systems have extremely low, sub-microsecond latency requirements that are unique to particle physics. We present a case study for neural network inference in FPGAs focusing on a classifier for jet substructure which would enable, among many other physics scenarios, searches for new dark sector particles and novel measurements of the Higgs boson. While we focus on a specific example, the lessons are far-reaching. We develop a package based on High-Level Synthesis (HLS) called hls4ml to build machine learning models in FPGAs. The use of HLS increases accessibility across a broad user community and allows for a drastic decrease in firmware development time. We map out FPGA resource usage and latency versus neural network hyperparameters to identify the problems in particle physics that would benefit from performing neural network inference with FPGAs. For our example jet substructure model, we fit well within the available resources of modern FPGAs with a latency on the scale of 100 ns., Comment: 22 pages, 17 figures, 2 tables, JINST revision

We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of SL(2,Z) on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2,n-2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest., Comment: 24+24 pages

We study the renormalization group equations of the fully anisotropic $\lambda$-deformed CFTs involving the direct product of two current algebras at different levels $k_{1,2}$ for general semi-simple groups. The exact, in the deformation parameters, $\beta$-function is found via the effective action of the quantum fluctuations around a classical background as well as from gravitational techniques. Furthermore, agreement with known results for symmetric couplings and/or for equal levels, is demonstrated. We study in detail the two coupling case arising by splitting the group into a subgroup and the corresponding coset manifold which consistency requires to be either a symmetric-space one or a non-symmetric Einstein-space., Comment: v1: 1+19 pages, Latex; v2: NPB version; v3: Mild simplifications of the conventions in section 2.1.2

From the Publisher: In the 1990s, a new type of learning algorithm was developed, based on results from statistical learning theory: the Support Vector Machine (SVM). This gave rise to a new class of theoretically elegant learning machines that use a central concept of SVMs—-kernels--for a number of learning tasks. Kernel machines provide a modular framework that can be adapted to different tasks and domains by the choice of the kernel function and the base algorithm. They are replacing neural networks in a variety of fields, including engineering, information retrieval, and bioinformatics. Learning with Kernels provides an introduction to SVMs and related kernel methods. Although the book begins with the basics, it also includes the latest research. It provides all of the concepts necessary to enable a reader equipped with some basic mathematical knowledge to enter the world of machine learning using theoretically well-founded yet easy-to-use kernel algorithms and to understand and apply the powerful algorithms that have been developed over the last few years.

We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincar\'e duality. We relate the topological Euler characteristic of elliptic Calabi-Yau threefolds with $\mathbb Q$-factorial terminal singularities to dimensions of Lie algebras and certain representations, Milnor and Tyurina numbers and other birational invariants of an elliptic fibration. We give an interpretation in terms of complex deformations. We state a conjecture on the extension of Kodaira's classification of singular fibers on relatively minimal elliptic surfaces to the class of birationally equivalent relatively minimal genus one fibered varieties and we give results in this direction., Comment: 35 pages

A numerical study on the distributions of primes in short intervals of length $h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$ but $h \ll N$, providing support to the Montgomery and Soundararajan conjecture on the variance of the prime distribution at this scale., Comment: 8 pages, 6 figures

We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic polylogarithms and iterated integrals of modular forms. We illustrate how to use our formalism to derive relations among elliptic polylogarithms, in complete analogy with the non-elliptic case. We then analyze the symbol alphabet of elliptic polylogarithms evaluated at rational points, and we observe that it is given by Eisenstein series for a certain congruence subgroup. We apply our formalism to hypergeometric functions that can be expressed in terms of elliptic polylogarithms and show that they can equally be written in terms of iterated integrals of Eisenstein series. Finally, we present the symbol of the equal-mass sunrise integral in two space-time dimensions. The symbol alphabet involves Eisenstein series of level six and weight three, and we can easily integrate the symbol in terms of iterated integrals of Eisenstein series., Comment: 65 pages

In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the optimization of the magnetic field quality under nominal conditions. The magneto-thermal models allow for the analysis of transient phenomena occurring during quench initiation, propagation, and protection. Mechanical analysis of quenching magnets is of high importance considering the design of new protection systems and the study of new superconductor types. We use field/circuit coupling to determine temperature and electromagnetic force evolution during the magnet discharge. These quantities are provided as a load to existing mechanical models. The models are discretized with different meshes and, therefore, we employ a mesh-based interpolation method to exchange coupled quantities. The coupling algorithm is illustrated with a simulation of a mechanical response of a standalone high-field dipole magnet protected with CLIQ (Coupling-Loss Induced Quench) technology., 5 pages, 6 figures

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques., Comment: 29 pages, 11 figures, final version published in Neurocomputing

We explicitly construct families of integrable $\sigma$-model actions smoothly interpolating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels $k_1$ and $k_2-k_1$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries., Comment: 1+27 pages, text improvements, version published in JHEP

The Standard Model (SM) of Particle Physics has been incredibly successful and accurate in describing the fundamental particles that make up the world around us and the way they behave. However, we know it is not the ultimate theory of nature as some phenomena remain unexplained. Outstanding questions include what is dark matter, this mysterious material which can be inferred from observations of the universe but has not been directly detected; and where does gravity fit into the picture? These questions motivate our search for physics Beyond the Standard Model (BSM) at the Large Hadron Collider at the CERN research facility. Here we accelerate protons around a 27 km ring and collide them at four experiments located underground. When we collide protons we effectively collide the more fundamental particles within the protons, quarks and gluons. This thesis focuses on research undertaken at the CMS experiment studying the heaviest quarks, top quarks, which are not found in nature but instead are produced in high-energy experiments. Top quarks are most often produced in pairs, however, this thesis focuses on the search for the simultaneous production of four top quarks, which is an incredibly rare process in comparison. A precision measurement of this rare process would be a stringent test on the SM and may give hints of physics beyond the standard model. Untangling the signal of four-top-quark production from the overwhelming background of top-quark-pair production in the output of the detector is incredibly difficult. Algorithms, which are often used in developing artificial intelligence, are therefore employed to exploit subtle differences in signatures, greatly increasing the sensitivity. Results are presented which place tight limits on the rate of four-top-quark production and projections of the future sensitivity are made. This includes an estimate of when CMS will have sufficient data to definitively observe this process at SM rates. The results also allow us to place constraints on properties of hypothesised BSM particles. Here we interpret the results to place constraints on the mass and top quark-coupling of one such particle, the sgluon.

The most important performance parameters for a particle collider are the beam energy and the luminosity. An event is the rate of useful interactions, and it’s a very important term in particle collider world. The quantity that defines the ability of a collider to produce events is called the luminosity (L). Precise luminosity measurements are of crucial importance, as it determines the precision of any physics cross section measurement. After the first Long Shutdown (LS1) the original performance goal for the luminosity of 1 × 10 34 cm −2 s −1 was reached with 10 11 protons per bunch and bunch spacing of 25 ns. In such conditions radiation hard detectors with extremely fast response are required, especially for instrumentation near the beam. BCM1F measures separately both luminosity and machine induced background particles with an excellent time resolution. Particles originating from collisions and machine induced back- ground arrive with 12 ns time difference. The performance of the BCM1F detector is investigated channel by channel using average hit rate per bunch crossing plots for fill 6061 in August 2017. cross section determination using Van der Meer scan method was done for fill 6016 in July 2017.