Coupling Extraction Pipeline: From Data to Effective Parameters

\labelapp:coupling

This appendix specifies a complete and explicit pipeline for extracting effective quantum field theory parameters from observational and experimental data within the informational framework developed in this work.

The purpose of this pipeline is not to postulate coupling constants, but to demonstrate how they arise as stability-selected quantities determined by coarse-graining, renormalization flow, and empirical constraints.

Conceptual Role of Couplings in the Informational Framework

In conventional QFT, coupling constants are free parameters fixed by experiment. Within the present framework, couplings are interpreted as effective stability coefficients describing how informational excitations interact under coarse-graining.

They are not fundamental constants but emergent quantities encoding:

• strength of informational correlations,
• robustness of excitation modes,
• response of the system to perturbations.

Data Inputs

The pipeline begins with empirical data, which may include:

• scattering cross sections,
• decay rates,
• precision electroweak observables,
• cosmological and astrophysical constraints.

These data define empirical correlators and response functions, not couplings directly.

Mapping Observables to Effective Correlators

Experimental observables are mapped to effective correlators:

where $\mathcal{O}_i$ are emergent operator descriptions valid within the QFT phase.

This mapping is theory-independent at the observational level and serves as the bridge between data and structure.

Informational Coarse-Graining Procedure

Correlators are coarse-grained over informational scales using the RG framework introduced in Appendix K.

The coarse-graining step integrates out unstable or rapidly fluctuating informational degrees of freedom, yielding scale-dependent effective parameters:

where $\mu$ denotes the informational resolution scale.

Stability Filtering via the Selection Functional

At each RG scale, candidate parameter sets are evaluated using the pre-physical selection functional $\Xi$.

Only parameter flows that preserve:

• structural stability,
• locality,
• decoherence-induced factorization,

are retained.

Unstable flows are discarded regardless of empirical fit quality.

Fixed Points and Infrared Attractors

Coupling constants correspond to infrared-attractive fixed points of the informational RG flow.

These fixed points are interpreted as structurally inevitable values rather than fine-tuned inputs.

The existence, uniqueness, or multiplicity of such fixed points is a key falsifiable output of the framework.

Parameter Extraction Algorithm

The complete extraction pipeline proceeds as follows:

1. Input empirical correlators.
2. Perform informational coarse-graining.
3. Evolve RG flow toward the infrared.
4. Apply stability selection at each step.
5. Identify surviving fixed-point parameter sets.
6. Compare with observed low-energy values.

This algorithm is explicit, reproducible, and admits numerical implementation.

Error Propagation and Robustness

Uncertainties in experimental data propagate through the pipeline. However, stability selection suppresses sensitivity to small perturbations.

As a result, emergent couplings are expected to exhibit universality and robustness, mirroring observed insensitivity of low-energy physics to ultraviolet details.

Failure Criteria

The pipeline fails if:

• no stable fixed points exist,
• multiple incompatible parameter sets remain equally stable,
• extracted couplings contradict experimental constraints.

Such failure would falsify the claim that observed couplings are stability-selected.

Relation to Fine-Tuning and Naturalness

This pipeline replaces traditional naturalness arguments. Small or large coupling values are not problematic if they correspond to stable attractors.

Fine-tuning is reinterpreted as instability and is excluded by construction.

Scope and Practical Implementation

The pipeline does not require closed-form analytic solutions. It is compatible with numerical RG techniques and existing experimental datasets.

Its completion is a technical task, not a conceptual gap.

Summary

Coupling constants are no longer arbitrary inputs. They are emergent, stability-selected outputs of a well-defined data-to-parameter pipeline.

This appendix completes the operational closure of quantum field theory within the informational framework by demonstrating how empirical numbers arise without postulation.