Implications of an enhanced <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mi>ν</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> branching ratio
Rigo Bause, Hector Gisbert, Gudrun Hiller
Abstract
Rare decays mediated by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi><a:mo stretchy="false">→</a:mo><a:mi>s</a:mi><a:mi>ν</a:mi><a:mover accent="true"><a:mi>ν</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> transitions have been reported by the Belle II experiment. The branching ratio of the decay <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>B</f:mi><f:mo>+</f:mo></f:msup><f:mo stretchy="false">→</f:mo><f:msup><f:mi>K</f:mi><f:mo>+</f:mo></f:msup><f:mi>ν</f:mi><f:mover accent="true"><f:mi>ν</f:mi><f:mo stretchy="false">¯</f:mo></f:mover></f:math> is found to be enhanced with respect to the standard model value. If taken at face value, the implications are profound; either lepton flavor universality is violated at the (multi)-TeV-scale, or light new physics is involved. This holds in general if <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">B</k:mi><k:mo stretchy="false">(</k:mo><k:msup><k:mi>B</k:mi><k:mo>+</k:mo></k:msup><k:mo stretchy="false">→</k:mo><k:msup><k:mi>K</k:mi><k:mo>+</k:mo></k:msup><k:mi>ν</k:mi><k:mover accent="true"><k:mi>ν</k:mi><k:mo stretchy="false">¯</k:mo></k:mover><k:mo stretchy="false">)</k:mo></k:math> exceeds <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>1.2</s:mn><s:mo>×</s:mo><s:msup><s:mn>10</s:mn><s:mrow><s:mo>−</s:mo><s:mn>5</s:mn></s:mrow></s:msup><s:mo stretchy="false">(</s:mo><s:mn>1.3</s:mn><s:mo>×</s:mo><s:msup><s:mn>10</s:mn><s:mrow><s:mo>−</s:mo><s:mn>5</s:mn></s:mrow></s:msup><s:mo stretchy="false">)</s:mo></s:math> at <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mi>σ</w:mi></w:math> (<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mn>2</y:mn><y:mi>σ</y:mi></y:math>), which tightens with a decreasing upper limit on <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="script">B</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mi>B</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:msup><ab:mi>K</ab:mi><ab:mo>*</ab:mo></ab:msup><ab:mi>ν</ab:mi><ab:mover accent="true"><ab:mi>ν</ab:mi><ab:mo stretchy="false">¯</ab:mo></ab:mover><ab:mo stretchy="false">)</ab:mo></ab:math>, that is in reach of the Belle II experiment. In view of the strong constraints on electron-muon universality violation in <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mo stretchy="false">|</ib:mo><ib:mi mathvariant="normal">Δ</ib:mi><ib:mi>b</ib:mi><ib:mo stretchy="false">|</ib:mo><ib:mo>=</ib:mo><ib:mo stretchy="false">|</ib:mo><ib:mi mathvariant="normal">Δ</ib:mi><ib:mi>s</ib:mi><ib:mo stretchy="false">|</ib:mo><ib:mo>=</ib:mo><ib:mn>1</ib:mn></ib:math> processes, viable explanations are heavy, (5–10)-TeV tree-level new physics mediators that couple only to tau-flavors, or lepton flavor violating ones. In addition, couplings of similar size to both left- and right-handed quarks are generically required, implying nonminimal beyond the standard model sectors which are carefully balanced against flavor constraints. The decay <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msubsup><qb:mi>B</qb:mi><qb:mi>s</qb:mi><qb:mn>0</qb:mn></qb:msubsup><qb:mo stretchy="false">→</qb:mo><qb:mtext>invisibles</qb:mtext></qb:math> can shed light on whether new physics is light or heavy. In the former case, branching ratios can be as large as <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msup><tb:mn>10</tb:mn><tb:mrow><tb:mo>−</tb:mo><tb:mn>5</tb:mn></tb:mrow></tb:msup></tb:math>. Published by the American Physical Society 2024