p-Adic description of Higgs mechanism IV: elementary particle and hadron masses

TL;DR

This paper analyzes p-adic conformal field theory calculations of elementary particle and hadron masses, incorporating topological mixing, boundary contributions, and CP violation, providing a novel approach to mass spectra and CKM matrix reproduction.

Contribution

It introduces a p-adic framework for calculating particle and hadron masses, including boundary effects and topological mixing, advancing the theoretical understanding of mass generation.

Findings

Exact reproduction of lepton and gauge boson masses.

Reproduction of CKM matrix satisfying empirical constraints.

Explanation of CP violation as a number-theoretic necessity.

Abstract

This paper belongs to a series devoted to the calculation of particle masses in p-adic conformal field theory limit of TGD. In paper III elementary particle masses were calculated. In this paper the results are analyzed. One can reproduce lepton and gauge boson masses exactly by taking into account Coulomb self energy associated with the interior of 3-surface and a small mixing of boundary topologies of charged leptons. Hadronic mass formula in- volves boundary contributions of quarks calculated previously plus interior term consisting isospin-isopin, color magnetic spin-spin and color Coulombic terms. One must take also into account mixing of boundary topologies, the mixing for primary condensate levels (quark spends part of time at lower condensate level) and mixing of I=0,J=0 mesons. Topological mixing implies the nontriviality of CKM matrix. An open question is how uniquely rationality require- ment fixes CKM matrix. It is possible to reproduce CKM matrix sa- tisfying the empirical constraints. CP breaking is a number theo- retical necessity. The large mixing of u and c quarks solves the spin crisis of proton. The parameters associated with other O(p) contributions can be fixed by no Planck mass condition plus some empirical inputs. O(p^2) contributions are also discu- ssed and observed isospin splittings can be reproduced.