photon structure

This paper presents a comprehensive mathematical framework proposing that light emerges as the first fully-stable harmonic resonance from recursive vacuum structure. We demonstrate that the interplay between the golden ratio φ and pi π creates fundamental patterns governing vacuum energy emergence, with their product φπ forming a recursive unit that modulates vacuum energy configurations. We show that the number 666, as the 36th triangular number, appears naturally in φ-recursive systems and marks a critical threshold where vacuum energy propagates as pure resonance rather than folding into mass-manifesting as light. This framework resolves wave-particle duality by revealing how waves emerge from recursion through curved π-space, while particle-like behavior arises at harmonic thresholds where vacuum energy discretely emerges in phase-locked structures. We connect this model to fundamental constants by deriving the speed of light c, Planck's constant h, the fine-structure constant α, and the cosmological constant Λ from φπ recursive geometry. The model provides experimentally falsifiable predictions regarding light's masslessness as harmonic zero-point stability and predicts a threshold near 666 in φ-π-log scaling where electromagnetic emergence occurs. In summary, one geometric recursion fixes four constants: c (assumed invariant), h (used as a consistency identity), and (α, Λ) without ad-hoc fitting; a minimal script reproduces all reported values. 1

This paper presents an advanced exploration of the Information-Cognitive Compression Field (ICCF) theory, focusing on its implications for understanding the photon structure and the role of informational compression in fundamental physics. Drawing from the unified field theory framework, we propose a novel interpretation of photons as dynamic information structures that emerge from the interplay between entropy, compression, and coherence. The study provides experimental evidence supporting the ICCF theory, offering new insights into photon dynamics, quantum entanglement, and the nature of light. Through an integrated approach, the paper examines the compression tensor field, quantum memory, and the relationship between energy and information flow, ultimately bridging the gap between quantum mechanics and informational cosmology. The findings are positioned to advance future experimental research into photonic systems, information processing, and the exploration of fundamental universal principles.

Dijet cross sections as functions of several jet observables are measured in photoproduction using the H1 detector at HERA. The data sample comprises e + p data with an integrated luminosity of 34.9 pb −1. Jets are selected using the inclusive k ⊥ algorithm with a minimum transverse energy of 25 GeV for the leading jet. The phase space covers longitudinal proton momentum fraction x p and photon longitudinal momentum fraction x γ in the ranges 0.05 < x p < 0.6 and 0.1 < x γ < 1. The predictions of next-to-leading order perturbative QCD, including recent photon and proton parton densities, are found to be compatible with the data in a wide kinematical range.

The production of multihadronic states in collisions at LEP has been studied with the DELPHI detector. The analyzed data correspond to an integrated luminosity of about 32 pb 1 , collected in the LEP runs of 1990-1992. Minimum bias data and a sample of events with jets at high p T have been selected under the requirement that no scattered electron or positron is observed. The two data sets have been compared to Monte Carlo predictions. The non-perturbative contribution described by the Vector Meson Dominance Model and direct q q production from pointlike photons described by the Quark Parton Model were found to be insucient to reproduce the data. It has been necessary to include a third interaction component, which is due to perturbative hard scattering of the partonic constituents of the photon. Several parametrizations of the quark and gluon densities of the photon have been tested. The interplay with the cut in jet transverse momentum, which i s necessary for the separation of the perturbative and non-perturbative regions, is discussed. The data favour parametrizations with rather soft partonic content of the photon.

The production of multihadronic states in collisions at LEP has been studied with the DELPHI detector. The analyzed data correspond to an integrated luminosity of about 32 pb 1 , collected in the LEP runs of 1990-1992. Minimum bias data and a sample of events with jets at high p T have been selected under the requirement that no scattered electron or positron is observed. The two data sets have been compared to Monte Carlo predictions. The non-perturbative contribution described by the Vector Meson Dominance Model and direct q q production from pointlike photons described by the Quark Parton Model were found to be insucient to reproduce the data. It has been necessary to include a third interaction component, which is due to perturbative hard scattering of the partonic constituents of the photon. Several parametrizations of the quark and gluon densities of the photon have been tested. The interplay with the cut in jet transverse momentum, which i s necessary for the separation of the perturbative and non-perturbative regions, is discussed. The data favour parametrizations with rather soft partonic content of the photon.

The production of multihadronic states in collisions at LEP has been studied with the DELPHI detector. The analyzed data correspond to an integrated luminosity of about 32 pb 1 , collected in the LEP runs of 1990-1992. Minimum bias data and a sample of events with jets at high p T have been selected under the requirement that no scattered electron or positron is observed. The two data sets have been compared to Monte Carlo predictions. The non-perturbative contribution described by the Vector Meson Dominance Model and direct q q production from pointlike photons described by the Quark Parton Model were found to be insucient to reproduce the data. It has been necessary to include a third interaction component, which is due to perturbative hard scattering of the partonic constituents of the photon. Several parametrizations of the quark and gluon densities of the photon have been tested. The interplay with the cut in jet transverse momentum, which i s necessary for the separation of the perturbative and non-perturbative regions, is discussed. The data favour parametrizations with rather soft partonic content of the photon.

Basic physical fields are dynamic fields like our universe and the fields that are raised by electric charges. These fields are dynamic continuums. Most physical theories treat these fields by applying gravitational theories or by Maxwell equations. Mathematically these fields can be represented by quaternionic fields. Dedicated normal operators in quaternionic non-separable Hilbert spaces can represent these quaternionic fields in their continuum eigenspaces. Quaternionic functions can describe these fields. Quaternionic differential and integral calculus can describe the behavior of these fields and the interaction of these fields with countable sets of quaternions. All quaternionic fields obey the same quaternionic differential equations. The basic fields differ in their start and boundary conditions. The paper introduces the concept of the Hilbert repository. It is part of a hierarchy of structures that mark increasingly complicated realizations of a purely mathematical model that describes and explains most features of observable physical reality. That model is the Hilbert Book Model. The paper treats the mathematical and experimental underpinning of the Hilbert Book Model.

Basic physical fields are dynamic fields like our universe and the fields that are raised by electric charges. These fields are dynamic continuums. Most physical theories treat these fields by applying gravitational theories or by Maxwell equations. Mathematically these fields can be represented by quaternionic fields. Dedicated normal operators in quaternionic non-separable Hilbert spaces can represent these quaternionic fields in their continuum eigenspaces. Quaternionic functions can describe these fields. Quaternionic differential and integral calculus can describe the behavior of these fields and the interaction of these fields with countable sets of quaternions. All quaternionic fields obey the same quaternionic differential equations. The basic fields differ in their start and boundary conditions. The paper introduces the concept of the Hilbert repository. It is part of a hierarchy of structures that mark increasingly complicated realizations of a purely mathematical model that describes and explains most features of observable physical reality. That model is the Hilbert Book Model. The paper treats the mathematical and experimental underpinning of the Hilbert Book Model.