First measurement of the absolute branching fractions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> nonleptonic decays and t

Based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">(</a:mo> <a:mn>10087</a:mn> <a:mo>±</a:mo> <a:mn>44</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo>×</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>6</a:mn> </a:msup> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> </a:math> events collected by the BESIII detector at the center-of-mass energy <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msqrt> <e:mrow> <e:mi>s</e:mi> </e:mrow> </e:msqrt> <e:mo>=</e:mo> <e:mn>3.097</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>GeV</e:mi> </e:mrow> </e:math> , the first absolute measurement of the branching fractions for the decays <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi mathvariant="normal">Σ</g:mi> <g:mo>+</g:mo> </g:msup> <g:mo stretchy="false">→</g:mo> <g:mi>p</g:mi> <g:msup> <g:mi>π</g:mi> <g:mn>0</g:mn> </g:msup> </g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi mathvariant="normal">Σ</k:mi> <k:mo>+</k:mo> </k:msup> <k:mo stretchy="false">→</k:mo> <k:mi>n</k:mi> <k:msup> <k:mi>π</k:mi> <k:mo>+</k:mo> </k:msup> </k:math> is performed. The branching fractions are determined to be <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:msub> <o:mrow> <o:mi>B</o:mi> </o:mrow> <o:mrow> <o:msup> <o:mrow> <o:mi mathvariant="normal">Σ</o:mi> </o:mrow> <o:mrow> <o:mo>+</o:mo> </o:mrow> </o:msup> <o:mo stretchy="false">→</o:mo> <o:mi>p</o:mi> <o:msup> <o:mrow> <o:mi>π</o:mi> </o:mrow> <o:mrow> <o:mn>0</o:mn> </o:mrow> </o:msup> </o:mrow> </o:msub> <o:mo>=</o:mo> <o:mo stretchy="false">(</o:mo> <o:mn>49.79</o:mn> <o:mo>±</o:mo> <o:mn>0.06</o:mn> <o:mo>±</o:mo> <o:mn>0.22</o:mn> <o:mo stretchy="false">)</o:mo> <o:mo>%</o:mo> </o:mrow> </o:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>B</u:mi> <u:mrow> <u:msup> <u:mi mathvariant="normal">Σ</u:mi> <u:mo>+</u:mo> </u:msup> <u:mo stretchy="false">→</u:mo> <u:mi>n</u:mi> <u:msup> <u:mi>π</u:mi> <u:mo>+</u:mo> </u:msup> </u:mrow> </u:msub> <u:mo>=</u:mo> <u:mo stretchy="false">(</u:mo> <u:mn>49.87</u:mn> <u:mo>±</u:mo> <u:mn>0.05</u:mn> <u:mo>±</u:mo> <u:mn>0.29</u:mn> <u:mo stretchy="false">)</u:mo> <u:mo>%</u:mo> </u:math> , where the first uncertainties are statistical and the second systematic. Our results show significant deviations from the Particle Data Group values for both decays, with differences of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mrow> <ab:mn>4.4</ab:mn> <ab:mi>σ</ab:mi> </ab:mrow> </ab:math> for <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi mathvariant="normal">Σ</cb:mi> <cb:mo>+</cb:mo> </cb:msup> <cb:mo stretchy="false">→</cb:mo> <cb:mi>p</cb:mi> <cb:msup> <cb:mi>π</cb:mi> <cb:mn>0</cb:mn> </cb:msup> </cb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mrow> <gb:mn>3.4</gb:mn> <gb:mi>σ</gb:mi> </gb:mrow> </gb:math> for <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msup> <ib:mi mathvariant="normal">Σ</ib:mi> <ib:mo>+</ib:mo> </ib:msup> <ib:mo stretchy="false">→</ib:mo> <ib:mi>n</ib:mi> <ib:msup> <ib:mi>π</ib:mi> <ib:mo>+</ib:mo> </ib:msup> </ib:math> . These measurements will play important roles in precise studies of the decay properties of strange, charmed, and beauty baryons with <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msup> <mb:mi mathvariant="normal">Σ</mb:mi> <mb:mo>+</mb:mo> </mb:msup> </mb:math> in the final states. Furthermore, the <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi mathvariant="normal">Δ</pb:mi> <pb:mi>I</pb:mi> <pb:mo>=</pb:mo> <pb:mn>1</pb:mn> <pb:mo>/</pb:mo> <pb:mn>2</pb:mn> </pb:math> rule is tested in nonleptonic <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:msup> <sb:mi mathvariant="normal">Σ</sb:mi> <sb:mo>±</sb:mo> </sb:msup> </sb:math> decays. The observed results deviate from zero by more than <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mn>5</vb:mn> <vb:mi>σ</vb:mi> </vb:math> , indicating the presence of the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:mi mathvariant="normal">Δ</xb:mi> <xb:mi>I</xb:mi> <xb:mo>=</xb:mo> <xb:mn>3</xb:mn> <xb:mo>/</xb:mo> <xb:mn>2</xb:mn> </xb:math> transition amplitude in the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"> <ac:mi mathvariant="normal">Σ</ac:mi> </ac:math> hyperon decays.