This document is a sub-report of the Banya Framework Master Report.

W Boson Cost

Banya Framework Operation Report

Inventor: Han Hyukjin (bokkamsun@gmail.com)

Date: 2026-03-25

Question: Why is the W boson mass 80.4 GeV

The W boson mass $M_W$ is a key parameter of the electroweak interaction. In the Standard Model, $M_W = M_Z \cos\theta_W$, but why this relation holds and why the specific value including 1-loop corrections is 80.4 GeV remains unexplained. Precision measurement of $M_W$ is a critical test of Standard Model self-consistency. The 2022 CDF II measurement ($80.4335 \pm 0.0094$ GeV) once suggested a discrepancy with the Standard Model, shaking the physics community.

Analogy: two gears (W, Z) have a fixed size ratio, but there is no design principle explaining why this ratio.

Status

Hit

D-41 error 0.016%. Derived from $M_Z \cos\theta_W$ (1-loop) as the self-referential serialization cost.

Key Discovery

Round 1. Deriving $M_W$ from Self-Referential Serialization Cost

Step 1. Banya Equation

This round uses the self-referential serialization cost. The cost incurred when the observer serializes its own state manifests as gauge boson masses.

Step 2. Norm Substitution

Derive the W boson mass from the Z boson mass through the electroweak mixing angle $\theta_W$.

Step 3. Constant Insertion

M_Z = 91.1876 GeV (PDG)
sin^2 theta_W = 0.23122 (PDG, MS-bar)
cos theta_W = sqrt(1 - sin^2 theta_W) = 0.87679
1-loop correction: using Banya Framework derived sin^2 theta_W

Step 4. Domain Transform

Combine $M_Z$ and $\cos\theta_W$ to compute $M_W$.

Step 5. Discovery

Confirmed that $M_W$ is the specific value of self-referential serialization cost. Since $\sin^2\theta_W$ is determined by the CAS cost structure, $M_W$ is also an inevitable consequence of CAS cost.

By-products

The relation $M_W/M_Z = \cos\theta_W$ naturally emerges from the Banya Framework's CAS cost structure. Electroweak mixing itself is the cost distribution method of self-referential serialization.

Incomplete Tasks

Summary