Explaining Belle data on <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> decays via dark <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Z</mml:mi> </mml:math> resonances

Abstract

The Belle II Collaboration reported the first measurement on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Br</a:mi> <a:mo stretchy="false">(</a:mo> <a:msup> <a:mi>B</a:mi> <a:mo>+</a:mo> </a:msup> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mi>K</a:mi> <a:mo>+</a:mo> </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:mo stretchy="false">)</a:mo> </a:math> , which lies <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mn>2.7</h:mn> <h:mi>σ</h:mi> </h:mrow> </h:math> away from the Standard Model expectation. This result may be manifestation of new physics beyond the Standard Model. In present work, motivated by the Belle II measurement, we investigate the effect of a dark photon/dark <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>Z</j:mi> </j:math> on the rare <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>B</l:mi> </l:math> meson decay <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msup> <n:mi>B</n:mi> <n:mo>+</n:mo> </n:msup> <n:mo stretchy="false">→</n:mo> <n:msup> <n:mi>K</n:mi> <n:mo>+</n:mo> </n:msup> <n:mi>ν</n:mi> <n:mover accent="true"> <n:mi>ν</n:mi> <n:mo stretchy="false">¯</n:mo> </n:mover> </n:math> and show that the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>Br</s:mi> <s:mo stretchy="false">(</s:mo> <s:msup> <s:mi>B</s:mi> <s:mo>+</s:mo> </s:msup> <s:mo stretchy="false">→</s:mo> <s:msup> <s:mi>K</s:mi> <s:mo>+</s:mo> </s:msup> <s:mi>ν</s:mi> <s:mover accent="true"> <s:mi>ν</s:mi> <s:mo stretchy="false">¯</s:mo> </s:mover> <s:mo stretchy="false">)</s:mo> </s:math> excess from Belle II over the Standard Model expectation explained by the appearance of the dark <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>Z</z:mi> </z:math> especially in resonances. We also derive constraints on various parameters of the two-Higgs-doublet model extended with a dark Abelian gauge group, in light of the measurement of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>Br</bb:mi> <bb:mo stretchy="false">(</bb:mo> <bb:msup> <bb:mi>B</bb:mi> <bb:mo>+</bb:mo> </bb:msup> <bb:mo stretchy="false">→</bb:mo> <bb:msup> <bb:mi>K</bb:mi> <bb:mo>+</bb:mo> </bb:msup> <bb:mi>ν</bb:mi> <bb:mover accent="true"> <bb:mi>ν</bb:mi> <bb:mo stretchy="false">¯</bb:mo> </bb:mover> <bb:mo stretchy="false">)</bb:mo> </bb:math> by the Belle-II Collaboration as well as the upper bound on <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>Br</ib:mi> <ib:mo stretchy="false">(</ib:mo> <ib:msup> <ib:mi>B</ib:mi> <ib:mn>0</ib:mn> </ib:msup> <ib:mo stretchy="false">→</ib:mo> <ib:msup> <ib:mi>K</ib:mi> <ib:mrow> <ib:mo>*</ib:mo> <ib:mn>0</ib:mn> </ib:mrow> </ib:msup> <ib:mi>ν</ib:mi> <ib:mover accent="true"> <ib:mi>ν</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> <ib:mo stretchy="false">)</ib:mo> </ib:math> decay, set by the Belle data. Our results indicate that there exists a common region where both experimental results are satisfied for a dark <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi>Z</pb:mi> </pb:math> mass around 4.5 GeV with suitable values of the other parameters.

Topics & Concepts