Seeking a Game in which the standard model Group shall Win

TL;DR

The paper proposes a group-dependent quantity based on quadratic Casimirs, designed to uniquely favor the Standard Model group as the 'winner,' potentially explaining why Nature selected this particular gauge group.

Contribution

It introduces a novel group-dependent measure involving quadratic Casimirs and U(1) corrections to explain the Standard Model group's special status.

Findings

The measure favors the Standard Model group over others.

A correction involving U(1) helps the Standard Model group win.

The scheme suggests a possible reason for the Standard Model's selection.

Abstract

It is attempted to construct a group-dependent quantity that could be used to single out the Standard Model group S(U(2) x U(3)) as being the "winner" by this quantity being the biggest possible for just the Standard Model group. The suggested quantity is first of all based on the inverse quadratic Cassimir for the fundamental or better smallest faithful representation in a notation in which the adjoint representation quadratic Cassimir is normalized to unity. Then a further correction is added to help the wanted Standard Model group to win and the rule comes even to involve the Abelian group U(1) to be multiplied into the group to get this correction be allowed. The scheme is suggestively explained to have some physical interpretation(s). By some appropriate proceedure for extending the group dependent quantity to groups that are not simple we find a way to make the Standard Model Group the absolute "winner". Thus we provide an indication for what could be the reason for the Standard Model Group having been chosen to be the realized one by Nature.