Gauge and scalar boson mediated proton decay in a predictive SU(5) GUT model

We assess proton decay signatures in the simplest viable <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>5</a:mn><a:mo stretchy="false">)</a:mo></a:math> model with regard to constraints on parameters governing the Standard Model fermion mass spectrum. Experimental signals for all eight two-body proton decay processes result from exchange of two gauge bosons, a single scalar leptoquark, or their combination. Consequently, it enables us to delve into an in-depth anatomy of proton decay modes and anticipate future signatures. Our findings dictate that observing a proton decay into <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>p</e:mi><e:mo stretchy="false">→</e:mo><e:msup><e:mi>π</e:mi><e:mn>0</e:mn></e:msup><e:msup><e:mi>e</e:mi><e:mo>+</e:mo></e:msup></e:math> indicates gauge boson mediation, with the potential for observation of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>p</h:mi><h:mo stretchy="false">→</h:mo><h:msup><h:mi>η</h:mi><h:mn>0</h:mn></h:msup><h:msup><h:mi>e</h:mi><h:mo>+</h:mo></h:msup></h:math> mode. Alternatively, if decay is through the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>p</k:mi><k:mo stretchy="false">→</k:mo><k:msup><k:mi>K</k:mi><k:mo>+</k:mo></k:msup><k:mover accent="true"><k:mi>ν</k:mi><k:mo stretchy="false">¯</k:mo></k:mover></k:math> process, it is mediated by a scalar leptoquark, possibly allowing the observation of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>p</p:mi><p:mo stretchy="false">→</p:mo><p:msup><p:mi>π</p:mi><p:mn>0</p:mn></p:msup><p:msup><p:mi>μ</p:mi><p:mo>+</p:mo></p:msup></p:math>. Detection of both <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>p</s:mi><s:mo stretchy="false">→</s:mo><s:msup><s:mi>π</s:mi><s:mn>0</s:mn></s:msup><s:msup><s:mi>e</s:mi><s:mo>+</s:mo></s:msup></s:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>p</v:mi><v:mo stretchy="false">→</v:mo><v:msup><v:mi>K</v:mi><v:mo>+</v:mo></v:msup><v:mover accent="true"><v:mi>ν</v:mi><v:mo stretchy="false">¯</v:mo></v:mover></v:math> could enhance <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>p</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:msup><ab:mi>π</ab:mi><ab:mn>0</ab:mn></ab:msup><ab:msup><ab:mi>μ</ab:mi><ab:mo>+</ab:mo></ab:msup></ab:math> through constructive interference. The model predicts inaccessibility of <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>p</db:mi><db:mo stretchy="false">→</db:mo><db:msup><db:mi>π</db:mi><db:mo>+</db:mo></db:msup><db:mover accent="true"><db:mi>ν</db:mi><db:mo stretchy="false">¯</db:mo></db:mover></db:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>p</ib:mi><ib:mo stretchy="false">→</ib:mo><ib:msup><ib:mi>η</ib:mi><ib:mn>0</ib:mn></ib:msup><ib:msup><ib:mi>μ</ib:mi><ib:mo>+</ib:mo></ib:msup></ib:math>, <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi>p</lb:mi><lb:mo stretchy="false">→</lb:mo><lb:msup><lb:mi>K</lb:mi><lb:mn>0</lb:mn></lb:msup><lb:msup><lb:mi>e</lb:mi><lb:mo>+</lb:mo></lb:msup></lb:math>, and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>p</ob:mi><ob:mo stretchy="false">→</ob:mo><ob:msup><ob:mi>K</ob:mi><ob:mn>0</ob:mn></ob:msup><ob:msup><ob:mi>μ</ob:mi><ob:mo>+</ob:mo></ob:msup></ob:math>, regardless of the dominant mediation type, in the coming decades. In summary, through a comprehensive analysis of proton decay signals, gauge coupling unification, and fermion masses and mixing, we both accurately and precisely constrain the parameter space of the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>S</rb:mi><rb:mi>U</rb:mi><rb:mo stretchy="false">(</rb:mo><rb:mn>5</rb:mn><rb:mo stretchy="false">)</rb:mo></rb:math> model in question. Published by the American Physical Society 2024