New Chiral Structures for Baryon Number Violating Nucleon Decays

We examine the most general nucleon decay interactions that involve three light quarks without being acted upon by a derivative. We identify four generic operator structures that correspond to the irreducible representations in the chiral group <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>SU</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mi mathvariant="monospace">L</a:mi></a:mrow></a:msub><a:mo stretchy="false">⊗</a:mo><a:msub><a:mrow><a:mi>SU</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mi mathvariant="monospace">R</a:mi></a:mrow></a:msub></a:mrow></a:math> of QCD, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mo stretchy="false">{</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">8</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">L</j:mi></j:mrow></j:msub><j:mo stretchy="false">⊗</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">1</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">R</j:mi></j:mrow></j:msub><j:mo>,</j:mo><j:msub><j:mrow><j:mover accent="true"><j:mrow><j:mn mathvariant="bold">3</j:mn></j:mrow><j:mrow><j:mo stretchy="false">¯</j:mo></j:mrow></j:mover></j:mrow><j:mrow><j:mi mathvariant="monospace">L</j:mi></j:mrow></j:msub><j:mo stretchy="false">⊗</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">3</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">R</j:mi></j:mrow></j:msub><j:mo>,</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">6</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">L</j:mi></j:mrow></j:msub><j:mo stretchy="false">⊗</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">3</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">R</j:mi></j:mrow></j:msub><j:mo>,</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">10</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">L</j:mi></j:mrow></j:msub><j:mo stretchy="false">⊗</j:mo><j:msub><j:mrow><j:mn mathvariant="bold">1</j:mn></j:mrow><j:mrow><j:mi mathvariant="monospace">R</j:mi></j:mrow></j:msub><j:mo stretchy="false">}</j:mo></j:mrow></j:math>, plus their chirality partners under the interchange of chiralities <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:mi mathvariant="monospace">L</jb:mi></jb:mrow><jb:mo stretchy="false">↔</jb:mo><jb:mrow><jb:mi mathvariant="monospace">R</jb:mi></jb:mrow></jb:math>. While half of them have been extensively discussed in the literature, the other half, <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mrow><ob:msub><ob:mrow><ob:mn mathvariant="bold">6</ob:mn></ob:mrow><ob:mrow><ob:mi mathvariant="monospace">L</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mi mathvariant="monospace">R</ob:mi><ob:mo stretchy="false">)</ob:mo></ob:mrow></ob:msub><ob:mo stretchy="false">⊗</ob:mo><ob:msub><ob:mrow><ob:mn mathvariant="bold">3</ob:mn></ob:mrow><ob:mrow><ob:mi mathvariant="monospace">R</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mi mathvariant="monospace">L</ob:mi><ob:mo stretchy="false">)</ob:mo></ob:mrow></ob:msub></ob:mrow></ob:math> and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mrow><bc:msub><bc:mrow><bc:mover accent="true"><bc:mrow><bc:mn mathvariant="bold">10</bc:mn></bc:mrow><bc:mrow><bc:mo stretchy="true">¯</bc:mo></bc:mrow></bc:mover></bc:mrow><bc:mrow><bc:mi mathvariant="monospace">L</bc:mi><bc:mo stretchy="false">(</bc:mo><bc:mi mathvariant="monospace">R</bc:mi><bc:mo stretchy="false">)</bc:mo></bc:mrow></bc:msub><bc:mo stretchy="false">⊗</bc:mo><bc:msub><bc:mrow><bc:mn mathvariant="bold">1</bc:mn></bc:mrow><bc:mrow><bc:mi mathvariant="monospace">R</bc:mi><bc:mo stretchy="false">(</bc:mo><bc:mi mathvariant="monospace">L</bc:mi><bc:mo stretchy="false">)</bc:mo></bc:mrow></bc:msub></bc:mrow></bc:math>, are identified for the first time. We perform chiral matching for these interactions at the leading chiral order and find that each has a unique chiral realization in terms of the octet baryons and pseudoscalars. Notably, the chiral interaction in the <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mrow><qc:msub><qc:mrow><qc:mn mathvariant="bold">6</qc:mn></qc:mrow><qc:mrow><qc:mi mathvariant="monospace">L</qc:mi><qc:mo stretchy="false">(</qc:mo><qc:mi mathvariant="monospace">R</qc:mi><qc:mo stretchy="false">)</qc:mo></qc:mrow></qc:msub><qc:mo stretchy="false">⊗</qc:mo><qc:msub><qc:mrow><qc:mn mathvariant="bold">3</qc:mn></qc:mrow><qc:mrow><qc:mi mathvariant="monospace">R</qc:mi><qc:mo stretchy="false">(</qc:mo><qc:mi mathvariant="monospace">L</qc:mi><qc:mo stretchy="false">)</qc:mo></qc:mrow></qc:msub></qc:mrow></qc:math> representation appears at the same chiral order as those of the known ones, while the one in the <dd:math xmlns:dd="http://www.w3.org/1998/Math/MathML" display="inline"><dd:msub><dd:mn mathvariant="bold">10</dd:mn><dd:mrow><dd:mi mathvariant="monospace">L</dd:mi><dd:mo stretchy="false">(</dd:mo><dd:mi mathvariant="monospace">R</dd:mi><dd:mo stretchy="false">)</dd:mo></dd:mrow></dd:msub><dd:mo stretchy="false">⊗</dd:mo><dd:msub><dd:mn mathvariant="bold">1</dd:mn><dd:mrow><dd:mi mathvariant="monospace">R</dd:mi><dd:mo stretchy="false">(</dd:mo><dd:mi mathvariant="monospace">L</dd:mi><dd:mo stretchy="false">)</dd:mo></dd:mrow></dd:msub></dd:math> representation appears at a higher chiral order. These new structures are prevalent in effective field theories and ultraviolet models, and they offer novel experimental avenues to search for baryon number violating nucleon decays.