Light new physics in <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:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><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>?

Abstract

The study of the rare decays <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:msup><a:mi>K</a:mi><a:mrow><a:mo stretchy="false">(</a:mo><a:mo>*</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:msup><a:mi>ν</a:mi><a:mover accent="true"><a:mi>ν</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> offers a window into the dynamics operating at the electroweak scale, allowing studies of the Standard Model and searches for heavy new physics. However, the analysis of these decays is also potentially sensitive to the on shell production of new light bosons <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>X</h:mi></h:math> through the process <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>B</j:mi><j:mo stretchy="false">→</j:mo><j:msup><j:mi>K</j:mi><j:mrow><j:mo stretchy="false">(</j:mo><j:mo>*</j:mo><j:mo stretchy="false">)</j:mo></j:mrow></j:msup><j:mi>X</j:mi></j:math>. In particular, Belle II has recently measured <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>B</o:mi><o:mo>+</o:mo></o:msup><o:mo stretchy="false">→</o:mo><o:msup><o:mi>K</o:mi><o:mo>+</o:mo></o:msup><o:mi>ν</o:mi><o:mover accent="true"><o:mi>ν</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math>, finding a <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mn>2.8</t:mn><t:mi>σ</t:mi></t:math> excess under the assumption of heavy new physics. Since this excess is rather localized in the kaon energy, a fit that includes the decay mode <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>B</v:mi><v:mo>+</v:mo></v:msup><v:mo stretchy="false">→</v:mo><v:msup><v:mi>K</v:mi><v:mo>+</v:mo></v:msup><v:mi>X</v:mi></v:math> to the kinematic distributions prefers <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>m</y:mi><y:mi>X</y:mi></y:msub><y:mo>≈</y:mo><y:mn>2</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:mi>GeV</y:mi></y:math> with branching fraction <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>Br</ab:mi><ab:mo stretchy="false">[</ab:mo><ab:mi>B</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:mi>K</ab:mi><ab:mi>X</ab:mi><ab:mo stretchy="false">]</ab:mo><ab:mo>=</ab:mo><ab:mo stretchy="false">(</ab:mo><ab:mn>8.8</ab:mn><ab:mo>±</ab:mo><ab:mn>2.5</ab:mn><ab:mo stretchy="false">)</ab:mo><ab:mo>×</ab:mo><ab:msup><ab:mn>10</ab:mn><ab:mrow><ab:mo>−</ab:mo><ab:mn>6</ab:mn></ab:mrow></ab:msup></ab:math> and a significance of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mo>≈</hb:mo><hb:mn>3.6</hb:mn><hb:mi>σ</hb:mi></hb:math>. However, no excess was found in the measurements of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi>B</jb:mi><jb:mo stretchy="false">→</jb:mo><jb:msup><jb:mi>K</jb:mi><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mo>*</jb:mo><jb:mo stretchy="false">)</jb:mo></jb:mrow></jb:msup><jb:mi>ν</jb:mi><jb:mover accent="true"><jb:mi>ν</jb:mi><jb:mo stretchy="false">¯</jb:mo></jb:mover></jb:math>, and a global analysis of the Belle II and data leads to <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>Br</qb:mi><qb:mo stretchy="false">[</qb:mo><qb:mi>B</qb:mi><qb:mo stretchy="false">→</qb:mo><qb:mi>K</qb:mi><qb:mi>X</qb:mi><qb:mo stretchy="false">]</qb:mo><qb:mo>=</qb:mo><qb:mo stretchy="false">(</qb:mo><qb:mn>5.1</qb:mn><qb:mo>±</qb:mo><qb:mn>2.1</qb:mn><qb:mo stretchy="false">)</qb:mo><qb:mo>×</qb:mo><qb:msup><qb:mn>10</qb:mn><qb:mrow><qb:mo>−</qb:mo><qb:mn>6</qb:mn></qb:mrow></qb:msup></qb:math> with a reduced significance of <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mo>≈</xb:mo><xb:mn>2.4</xb:mn><xb:mi>σ</xb:mi></xb:math>. We then study various simplified dark-flavored models and present a possible UV completion based on a gauged <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msub><zb:mi>B</zb:mi><zb:mn>3</zb:mn></zb:msub><zb:mo>−</zb:mo><zb:msub><zb:mi>L</zb:mi><zb:mn>3</zb:mn></zb:msub></zb:math> symmetry, highlighting the discovery potential of dedicated searches for <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi>B</bc:mi><bc:mo stretchy="false">→</bc:mo><bc:msup><bc:mi>K</bc:mi><bc:mrow><bc:mo stretchy="false">(</bc:mo><bc:mo>*</bc:mo><bc:mo stretchy="false">)</bc:mo></bc:mrow></bc:msup><bc:mi>X</bc:mi></bc:math> at Belle II. Published by the American Physical Society 2024

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