On the Inversion of High Energy Proton

Inversion of the K-fold stochastic autoconvolution integral equation is an elementary nonlinear problem, yet there are no de facto methods to solve it with finite statistics. To fix this problem, we introduce a novel inverse algorithm based on a combination of minimization of relative entropy, the Fast Fourier Transform and a recursive version of Efron's bootstrap. This gives us power to obtain new perspectives on non-perturbative high energy QCD, such as probing the ab initio principles underlying the approximately negative binomial distributions of observed charged particle final state multiplicities, related to multiparton interactions, the fluctuating structure and profile of proton and diffraction. As a proof-of-concept, we apply the algorithm to ALICE proton-proton charged particle multiplicity measurements done at different center-of-mass energies and fiducial pseudorapidity intervals at the LHC, available on HEPData. A strong double peak structure emerges from the inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios, 2D

HyperTrack: Neural Combinatorics for High Energy Physics

Combinatorial inverse problems in high energy physics span enormous algorithmic challenges. This work presents a new deep learning driven clustering algorithm that utilizes a space-time non-local trainable graph constructor, a graph neural network, and a set transformer. The model is trained with loss functions at the graph node, edge and object level, including contrastive learning and meta-supervision. The algorithm can be applied to problems such as charged particle tracking, calorimetry, pile-up discrimination, jet physics, and beyond. We showcase the effectiveness of this cutting-edge AI approach through particle tracking simulations. The code is available online.Comment: CHEP 2023 proceedings. 8 pages (max

Spinful Algorithmization of High Energy Diffraction

High energy diffraction probes fundamental interactions, the vacuum, and quantum mechanically coherent matter waves at asymptotic energies. In this work, we algorithmize our abstract ideas and develop a set of rigid rules for diffraction. To get spin under control, we construct a new Monte Carlo simulation engine, GRANIITTI. It is the first event generator with custom spin-dependent scattering amplitudes for the glueball domain semi-exclusive diffraction, driven by fully multithreaded importance sampling and written in C++. Our simulations provide new computational evidence that the enigmatic glueball filter observable is a spin polarization filter for tensor resonances. For algorithmic spin studies, we automate the classic Laplace spherical harmonics inverse expansion, carefully define the geometric acceptance related phase space issues and study the harmonic mixing properties systematically in different Lorentz frames. To improve the big picture, we generalize the standard soft diffraction observables and definitions by developing a high dimensional probabilistic framework based on incidence algebras, Combinatorial Superstatistics, and solve also a new superposition inverse problem using the Möbius inversion theorem. For inverting stochastic autoconvolution integral equations or `inverting the proton', we develop a novel recursive inverse algorithm based on the Fast Fourier Transform and relative entropy minimization. The first algorithmic inverse results of the proton double multiplicity structure and multiparton interaction rates are obtained using the published LHC data, in agreement with standard phenomenology. For optimal inversion of the detector efficiency response, we build the first Deep Learning based solution working in higher phase space dimensions, DeepEfficiency, which inverts the detector response on an event-by-event basis and minimizes the event generator dependence. Using the ALICE experiment proton-proton data at the LHC at 13 TeV, we obtain the first unfolded fiducial measurement of the multidimensional combinatorial partial cross sections, the first multidimensional maximum likelihood fit of the effective soft pomeron intercept and the first multidimensional maximum likelihood fit of the single, double and non-diffractive component cross sections. Great care is taken with the fiducial and non-fiducial definitions. The second topic of measurements centers on semi-exclusive central diffractive production of hadron pairs, which we study with the ALICE data. We measure and fit the resonance spectra of identified pion and kaon pairs, which is crucial on the road towards solving the mysteries of glueballs, the proton structure fluctuations, and the pomeron.Suurenergiadiffraktio heijastelee luonnon perusvuorovaikutuksia, tyhjiötä ja kvanttimekaanisesti koherentteja aaltoja asymptoottisen suurilla energioilla. Tässä työssä teen abstrakteista ideoista algoritmeja ja kehitän joukon täsmällisiä sääntöjä suurenergiadiffraktiolle. Jotta spin ja kulmaliikemäärä saadaan haltuun, rakennan uuden avoimen lähdekoodin Monte Carlo -simulaatiokoneiston nimeltään GRANIITTI. Se on ensimmäinen törmäysgeneraattori, joka kykenee mallintamaan kattavasti spin-riippuvia relativistisia sironta-amplitudeja keskeisdiffraktion prosesseissa. Näitä hiukkassimulaatioita tarvitaan esimerkiksi CERN:in LHC-kiihdyttimellä tehtävissä kokeissa, joissa keskitytään niin kutsuttujen ”liimapallojen” (eng. glueballs) löytämiseen. Liimapallot ovat vahvan vuorovaikutuksen gluonihiukkasten muodostamia resonoivia kvanttitiloja, joilla on teoreettinen yhteys suurenergiadiffraktioon, mutta joita ei ole saatu kokeellisesti vielä yksikäsitteisesti havaittua. Tämä johtuu niiden monikomponenttiliiman kaltaisesta kvanttitilasta, jossa mukana voi olla myös kvarkkeja. Simulaatioiden avulla löydän uutta laskennallista todistetta sille, että liimapallosuotimena tunnettua arvoituksellista observaabelia ajaa resonanssien spin-polarisaatiotiheys. Suurena tavoitteena on kehittää suurenergiadiffraktion kokonaiskuvaa. Tätä varten esittelen uuden matemaattisen koneiston perustuen todennäköisyyslaskentaan ja kombinatorisiin insidenssialgebroihin. Kutsun tätä kombinatoriseksi superstatistiikaksi. Näin saadaan määriteltyä ja ratkaistua heti uusi inversio-ongelma jo tunnetun Möbius-inversiolauseen avulla. Jatkan inversio-ongelmien saralla ja näytän ensimmäisenä kuinka protoni-protoni -törmäyksissä syntyneiden varattujen hiukkasten todennäköisyysjakauma voidaan algoritmillisesti uudelleenorganisoida. Näin saadaan uusia näkökulmia suurenergiaprotonien monimutkaiseen rakenteeseen ja dynamiikkaan, jossa useat partonit protonin sisältä törmäävät samanaikaisesti. LHC-datan avulla saadut algoritmilliset tulokset ovat samansuuntaisia aiempien mallipohjaisten tulkintojen kanssa. Kehitän myös ensimmäisenä algoritmin, joka syväkorjaa lähes optimaalisesti mittauslaitteiston tehokkuusvasteen moniulotteisessa liikemääräavaruudessa törmäys törmäykseltä. Tämä algoritmi perustuu syviin neuroverkkoihin. Työn kokeellisessa osuudessa hyödynnetään työssä kehitettyjä menetelmiä ja algoritmeja LHC:n ALICE-kokeessa, käyttäen LHC-kiihdyttimen tuottamaa protoni-protoni -törmäysdataa 13 TeV:n massakeskipiste-energialla. Näin tehdään ensimmäinen kokonaisvaltainen pehmeiden törmäysten moniulotteinen fidusiaalimittaus ja ensimmäinen moniulotteinen diffraktiivisten vaikutusalojen suurimman uskottavuuden fidusiaalianalyysi. Lisäksi analysoidaan diffraktiofenomenologian oleellisia parametreja. Toinen mittausten aihe on keskeisdiffraktio. Työssä mitataan hadroniset resonanssispektrit, joiden tutkiminen vie meidät kohti liimapallojen, protonin fluktuoivan sisärakenteen ja pomeronin salaisuuksien ratkaisuja

ALGORITHMICS OF DIFFRACTION

We discuss novel ways to probe high-energy diffraction, first, inclusive diffraction and then, central exclusive processes at the LHC. Our new Monte Carlo synthesis and analysis framework, GRANIITTI, includes differential screening, an expendable set of scattering amplitudes with adaptive Monte Carlo sampling, spin systematics and modern computational technology.Peer reviewe

Observables of QCD Diffraction

A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of diffraction, Regge phenomenology together with AGK cutting rules and random fluctuations.Peer reviewe

Bayesian Classification of Hadronic Diffraction in the Collider Detector at Fermilab

Diffraction is fundamentally a wide scale phenomena, and well understood from macroscopic mechanical waves up to quantum mechanical electron diffraction. However, hadronic diffraction is still missing a rigorous quantum field theoretical formulation, but it can be experimentally probed in high energy accelerators. Because diffraction is inherently a coherent process, it allows a unique perspective to probe partonic inner structure of protons (hadrons) and relativistic space-time evolution of high energy hadron-hadron collisions. In this thesis a Bayesian, probabilistic multivariate approach is developed for experimentally classifying diffractive hadronic scattering events from non-diffractive. For each measured collision event, the algorithm assigns a finite probability to an event to belong to a diffractive or non-diffractive process class. By integrating these probabilities over the full data sample, the interaction probabilities, known as cross sections, are estimated for different processes. The approach is Bayesian because it partly relies on the theoretical prior knowledge of cross sections. This probabilistic way is shown to be a sound approach, because hard event-by-event decisions are both theoretically and experimentally not uniquely definable. The reasons for this are thoroughly explained in this thesis. The underlying algorithm is based on ℓ1-norm regularized multinomial logistic regression. This regularization is shown to provide a mathematical view to the de-facto experimental physical signature of hadronic diffraction, known as the large rapidity gap. The experimental part of the thesis is done with proton-antiproton data collected in the CDF run II experiment at the center of mass collision energy √s = 1.96 TeV at Fermilab. For the first time major components of the proton-antiproton scattering total cross section are estimated using a multivariate algorithm. The obtained cross sections for single diffractive σ(SDL) = (4.87 ± 1.06) mb, σ(SDR) = (4.83 ± 1.04) mb, double diffractive σ(DD) = (6.16±1.93) mb and non-diffractive σ(ND) = (45.20±1.59) mb match the phenomenological theory predictions within errors. Results of the thesis indicate that the probabilistic approach is viable, and emphasize also the importance of experimental forward (small-angle) instrumentation that is limited at the CDF detector