Nonperturbative effects in the Standard Model with gauged 1-form symmetry

Abstract

A bstract We study the Standard Model with gauged $$ {\mathrm{\mathbb{Z}}}_{N=2,3,6}^{(1)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℤ</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> subgroups of its $$ {\mathrm{\mathbb{Z}}}_6^{(1)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℤ</mml:mi> <mml:mn>6</mml:mn> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> 1-form global symmetry, making the gauge group $$ \frac{\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)}{{\mathrm{\mathbb{Z}}}_N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>SU</mml:mi> <mml:mfenced> <mml:mn>3</mml:mn> </mml:mfenced> <mml:mo>×</mml:mo> <mml:mi>SU</mml:mi> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mo>×</mml:mo> <mml:mi>U</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:mrow> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:mfrac> </mml:math> . We show that, on a finite $$ {\mathbbm{T}}^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> , there are self-dual instantons of fractional topological charge. They mediate baryon- and lepton-number violating processes. We compare their amplitudes to the ones due to the usual BPST-instantons. We find that the small hypercharge coupling suppresses the fractional-instanton contribution, unless the torus size is taken sub-Planckian, or extra matter is added above the weak scale. We also discuss these results in light of the cosmological bounds on the torus size.

Topics & Concepts