## Spinful Algorithmization of High Energy Diffraction

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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 MÃ¶bius 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 $\sqrt{s}$ = 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.

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