Search for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> violations in the production and decay of hyperon-antihyperon pairs

This study introduces a complete joint angular distribution analysis for the process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msup> <a:mrow> <a:mi>e</a:mi> </a:mrow> <a:mrow> <a:mo>+</a:mo> </a:mrow> </a:msup> <a:msup> <a:mrow> <a:mi>e</a:mi> </a:mrow> <a:mrow> <a:mo>−</a:mo> </a:mrow> </a:msup> <a:mo stretchy="false">→</a:mo> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>B</a:mi> <a:mo stretchy="false">(</a:mo> <a:mo stretchy="false">→</a:mo> <a:msub> <a:mrow> <a:mi>B</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mi>π</a:mi> <a:mo stretchy="false">)</a:mo> <a:mover accent="true"> <a:mrow> <a:mi>B</a:mi> </a:mrow> <a:mrow> <a:mo stretchy="false">¯</a:mo> </a:mrow> </a:mover> <a:mo stretchy="false">(</a:mo> <a:mo stretchy="false">→</a:mo> <a:msub> <a:mrow> <a:mover accent="true"> <a:mrow> <a:mi>B</a:mi> </a:mrow> <a:mrow> <a:mo stretchy="false">¯</a:mo> </a:mrow> </a:mover> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mi>π</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> with polarized beams, where <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>B</o:mi> </o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>B</q:mi> <q:mn>1</q:mn> </q:msub> </q:math> are hyperons. We consider both transverse and longitudinal beam polarization and analyze <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>C</s:mi> <s:mi>P</s:mi> </s:math> violation in the production and decay of hyperons. We present the complete Fisher information matrix for the sensitivities of the weak decay parameters <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>α</u:mi> <u:mo>−</u:mo> </u:msub> <u:mo>,</u:mo> <u:msub> <u:mi>α</u:mi> <u:mo>+</u:mo> </u:msub> <u:mo>,</u:mo> <u:msub> <u:mi>ϕ</u:mi> <u:mi mathvariant="normal">Ξ</u:mi> </u:msub> </u:math> , and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mover accent="true"> <x:mi>ϕ</x:mi> <x:mo stretchy="false">¯</x:mo> </x:mover> <x:mi mathvariant="normal">Ξ</x:mi> </x:msub> </x:math> , the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>P</cb:mi> </cb:math> -violating term <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>F</eb:mi> <eb:mi>A</eb:mi> </eb:msub> </eb:math> , and the EDM <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>d</gb:mi> <gb:mi>B</gb:mi> </gb:msub> </gb:math> (derived from the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>C</ib:mi> <ib:mi>P</ib:mi> </ib:math> -violating term <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msub> <kb:mi>H</kb:mi> <kb:mi>T</kb:mi> </kb:msub> </kb:math> ), under the BESIII and STCF statistics. We find that polarization enhances the sensitivity of the parameters. Specifically, longitudinal polarization provides a more significant improvement compared to transverse polarization, with the enhancement being more pronounced for single-step decays than for multistep decays. With the expected statistics from the BESIII experiment, the estimated EDM sensitivities for <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi mathvariant="normal">Λ</mb:mi> </mb:math> and <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:msup> <pb:mi mathvariant="normal">Σ</pb:mi> <pb:mo>+</pb:mo> </pb:msup> </pb:math> are on the order of <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:mrow> <sb:msup> <sb:mn>10</sb:mn> <sb:mrow> <sb:mo>−</sb:mo> <sb:mn>19</sb:mn> </sb:mrow> </sb:msup> <sb:mtext> </sb:mtext> <sb:mtext> </sb:mtext> <sb:mi>e</sb:mi> <sb:mtext> </sb:mtext> <sb:mi mathvariant="normal">c</sb:mi> <sb:mi mathvariant="normal">m</sb:mi> </sb:mrow> </sb:math> , while those for <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msup> <wb:mi mathvariant="normal">Ξ</wb:mi> <wb:mo>−</wb:mo> </wb:msup> </wb:math> and <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:msup> <zb:mi mathvariant="normal">Ξ</zb:mi> <zb:mn>0</zb:mn> </zb:msup> </zb:math> are <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"> <cc:mrow> <cc:msup> <cc:mrow> <cc:mn>10</cc:mn> </cc:mrow> <cc:mrow> <cc:mo>−</cc:mo> <cc:mn>18</cc:mn> </cc:mrow> </cc:msup> <cc:mtext> </cc:mtext> <cc:mtext> </cc:mtext> <cc:mi>e</cc:mi> <cc:mtext> </cc:mtext> <cc:mi mathvariant="normal">c</cc:mi> <cc:mi mathvariant="normal">m</cc:mi> </cc:mrow> </cc:math> . The upcoming STCF experiment is expected to improve these estimates by 1–2 orders of magnitude. Furthermore, <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"> <gc:mi>C</gc:mi> <gc:mi>P</gc:mi> </gc:math> violation in hyperon decays originates from weak-phase differences among partial-wave amplitudes. Based on a refined isospin analysis, we emphasize the non-negligible contr