BKT-85-ART v4.0 Relational closure in bottomonium formation.

Abstract

Relational closure in bottomonium formation. A restricted Υ(1S) realization, measurement map and transfer test Author: Robert KupskiVersion: BKT-85-ART v4.0 Introduction Bottomonium formation provides a sectoral setting for investigating the Law of One Mechanism hypothesis (LOM; PJM in Polish). The starting point is the relationship between configuration compatibility and the dynamics of reaching and maintaining a structural class. Within the programme, the Global Theory of Shared Fundamental Couplings (GTSFC; GTWSSF in Polish) describes couplings, while the Universal Structural Code (USC) specifies admissibility, tolerances and closure. The central question is whether a restricted mechanism can predict relations between observables after calibration in a separate kinematic region, without retuning. Quantum chromodynamics (QCD) and its nonrelativistic formulation (NRQCD) remain the reference frameworks; a sectoral result, a possible beyond-Standard-Model interpretation and the metafield hypothesis retain distinct status. Abstract A restricted LOM–GTSFC–USC realization is presented for inclusive Υ(1S) in jets in proton–proton collisions at 13 TeV. Inclusive production comprises direct production and feed-down from heavier states. A dimensionless configuration-compatibility cost defines a tilt of the real jump chain at fixed exit rates. The same generator determines the probability of reaching the target class, the accumulated transport-activity distribution and the joint momentum transform. Explicitly assumed proportionality of local transport coefficients yields a conditional relation between longitudinal logarithmic loss and the second moment of the transverse impulse. The primary test quantity is the dimensionless contrast C⋆(Ω)=Cov⁡1S,Ω ⁣[zC,exp⁡ ⁣(−jT2J⋆2)],J⋆=2 GeV.C_\star(\Omega)= \operatorname{Cov}_{1S,\Omega} \!\left[z_C,\exp\!\left(-\frac{j_T^2}{J_\star^2}\right)\right], \qquad J_\star=2\ \mathrm{GeV}. Here zCz_C denotes the projected longitudinal momentum fraction, jTj_T the momentum magnitude perpendicular to the jet axis, and Ω\Omega a fixed signal-selection domain. The map from model variables to observables incorporates kinematically admissible support, four-momentum conservation for the modelled fragmenting system, production, feed-down and dimuon decays, jet reconstruction, measurement response and normalization after selection. Latent variables are not identified with measured quantities. In a synthetic experiment, one parameter is calibrated on 17,894 events in the reconstructed jet-momentum interval 60≤pTJ<75 GeV60\le p_T^J<75\ \mathrm{GeV}. The contrast is then predicted, without refitting the mechanism parameters, for a disjoint sample of 19,064 events at 75≤pTJ<100 GeV75\le p_T^J<100\ \mathrm{GeV}. The common-activity model predicts C⋆=−0.00446065±0.00010294C_\star=-0.00446065\pm0.00010294, whereas the validation sample gives −0.00446213±0.00013438-0.00446213\pm0.00013438; uncertainties denote standard errors. An independent-clock alternative also remains compatible under the specified local, two-sided 95% criterion. The result does not distinguish these mechanisms at the chosen sample size using this single statistic. The integral mathematical and physical formalism includes closure and non-closure diagnostics, logarithmic estimators, identifiability limits, quantum-reduction conditions and associated error bounds. The implemented demonstrator uses a surrogate parent and explicitly assumed response; it is not a calibration of QCD production or the CMS detector. No empirical test on CMS events is performed. The contribution is a unified model linking a specified formation rule, a measurement map and a transfer test while retaining the inconclusive result. The formal and synthetic findings constitute neither confirmation of the metafield hypothesis nor evidence of a departure from the Standard Model. Keywords: LOM; PJM; GTSFC; USC; bottomonium; Υ(1S); relational closure; Markov processes; common activity; longitudinal–transverse correlations; measurement map; calibration; transfer test; identifiability; QCD; NRQCD.